Plug In Gait Reference Guide
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Plug-in Gait Reference Guide
Contents
About this guide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Regulatory information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Plug-in Gait models and templates . . . . . . . . . . . . . . . . . . . 5
Lower body modeling with Plug-in Gait . . . . . . . . . . . . . . . . . . 6
Upper body modeling with Plug-in Gait . . . . . . . . . . . . . . . . . 18
Full body modeling with Plug-in Gait . . . . . . . . . . . . . . . . . . . 26
Plug-in Gait labeling skeleton templates (VSTs) in
Vicon Nexus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Plug-in Gait bones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
Complete list of Plug-in Gait bones . . . . . . . . . . . . . . . . . . . . 34
Plug-in Gait virtual markers . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
Plug-in Gait joint centers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
Plug-in Gait lower body forces and moments . . . . . . . . . 40
Plug-in Gait kinematic and kinetic calculations . . . . . . . 43
About Plug-in Gait processes . . . . . . . . . . . . . . . . . . . . . . . . . 44
Segment meshes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
© Copyright 2016–2018 Vicon Motion Systems Limited. All rights reserved.
Vicon Motion Systems Limited reserves the right to make changes to information in this document without notice.
Companies, names, and data used in examples are fictitious unless otherwise noted. No part of this publication may be
reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic or mechanical, by
photocopying or recording, or otherwise without the prior written permission of Vicon Motion Systems Ltd.
Vicon® is a registered trademark of Oxford Metrics plc. Vicon Blade™, Vicon Control™, Vicon Lock™, Vicon Lock+™,
Vicon Nexus™, Vicon MX™, Vicon Pegasus™, Vicon ProCalc™, Vicon Shogun™, Vicon Studio™, T-Series™, Vicon Tracker™,
Vicon Vantage™, Vicon Vero™, Vicon Vertex™, and Vicon Vue™ are trademarks of Oxford Metrics plc.
VESA® is a registered trademark owned by VESA (www.vesa.org/about-vesa/). Other product and company names herein may
be the trademarks of their respective owners.
Vicon Motion Systems is an Oxford Metrics plc company. Email: support@vicon.com
Web: http://www.vicon.com
Plug-in Gait internal models . . . . . . . . . . . . . . . . . . . . . . . . . . 46
Overview of the Plug-in Gait modeling process . . . . . . . . . . 47
Static vs. dynamic models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
The chord function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
Lower body kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
Upper body kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
Angle outputs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
Kinetic modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
Plug-in Gait output angles . . . . . . . . . . . . . . . . . . . . . . . . . 74
Angle definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
Plug-in Gait kinematic variables . . . . . . . . . . . . . . . . . . . . . . . 78
Upper body angles as output from Plug-in Gait . . . . . . . . . 88
Lower body angles as output from Plug-in Gait . . . . . . . . . . 93
Plug-in Gait output specification . . . . . . . . . . . . . . . . . . . 96
Global (laboratory) co-ordinate system . . . . . . . . . . . . . . . . . 97
Pelvis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
Femur . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
Tibia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
Foot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
Joint kinematic definitions . . . . . . . . . . . . . . . . . . . . . . . . . . 102
Joint kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
© Copyright 2016–2018 Vicon Motion Systems Limited. All rights reserved.
Vicon Motion Systems Limited reserves the right to make changes to information in this document without notice.
Companies, names, and data used in examples are fictitious unless otherwise noted. No part of this publication may be
reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic or mechanical, by
photocopying or recording, or otherwise without the prior written permission of Vicon Motion Systems Ltd.
Vicon® is a registered trademark of Oxford Metrics plc. Vicon Blade™, Vicon Control™, Vicon Lock™, Vicon Lock+™,
Vicon Nexus™, Vicon MX™, Vicon Pegasus™, Vicon ProCalc™, Vicon Shogun™, Vicon Studio™, T-Series™, Vicon Tracker™,
Vicon Vantage™, Vicon Vero™, Vicon Vertex™, and Vicon Vue™ are trademarks of Oxford Metrics plc.
VESA® is a registered trademark owned by VESA (www.vesa.org/about-vesa/). Other product and company names herein may
be the trademarks of their respective owners.
Vicon Motion Systems is an Oxford Metrics plc company. Email: support@vicon.com
Web: http://www.vicon.com
Plug-in
Gait
Reference
About this guide
This guide provides in-depth descriptions of Plug-in Gait models and templates, and
details of the calculations performed by Plug-in Gait. For information on how to use
Plug-in Gait with Vicon Nexus, see Modeling with Plug-in Gait in the Vicon Nexus User
Guide.
It is assumed that you are familiar with standard motion capture, data processing, and
data management in Nexus; and with data visualization, analysis and reporting in Vicon
Polygon. For more information on these processes, see the documentation for Nexus
and Polygon.
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Regulatory information
For Vicon Nexus regulatory details, see Vicon Nexus regulatory information in the
Nexus documentation area of the Vicon website (docs.vicon.com).
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Plug-in Gait models and templates
The following topics contain information on the differences between the Plug-in Gait
models, including details of the relevant outputs and marker sets. A description of the
labeling skeleton templates that you can use with Plug-in Gait is also available:
Lower body modeling with Plug-in Gait on page 6
Upper body modeling with Plug-in Gait on page 18
Full body modeling with Plug-in Gait on page 26
Plug-in Gait labeling skeleton templates (VSTs) in Vicon Nexus on page 31
If you are using Plug-in Gait for gait analysis, the precision of the marker placement is
critical for obtaining accurate clinical results. Use the information and illustrations in
the above topics to place markers on the patient.
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Lower body modeling with Plug-in Gait
This section describes lower body modeling with Plug-in Gait. It covers the following
information:
Outputs from Plug-in Gait lower body model on page 6
Marker sets for Plug-in Gait lower body model on page 8
Marker placement for Plug-in Gait lower body model on page 9
KAD marker sets for Plug-in Gait lower body model on page 14
KAD marker placement for Plug-in Gait lower body model on page 15
For details about the labeling skeleton templates to be used with Plug-in Gait lower
body models, see Plug-in Gait labeling skeleton templates (VSTs) in Vicon Nexus on
page 31.
Outputs from Plug-in Gait lower body model
Use a Plug-in Gait lower body model if you require the kinematic and kinetic calculation
outputs listed in the following table. The output variables are prefixed by the
appropriate context (L for left or R for right).
Joint angles, force, and moments are expressed in the three anatomical planes: sagittal,
frontal, and coronal. Even if the joint powers are scalar, they can also be expressed in
the anatomical planes in Vicon Polygon. Forces, moments, and powers are all
normalized to the subject's height and body mass.
Output
Description
Kinematics:
Angles
AbsAnkleAngle
The angle between the AJC to KJC vector and the AJC to
TOE vector.
AnkleAngles
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Relative. The angles between the shank and the foot.
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Output
Description
FootProgressAngles
Absolute. The angles between the foot and the global
coordinate system.
HipAngles
Relative. The angles between the pelvis and the thigh.
KneeAngles
Relative. The angles between the thigh and the shank.
PelvisAngles
Absolute. The angles between the pelvis and the laboratory
coordinate system.
Kinetics:
Forces
AnkleForce
The force between the shank and the foot.
GroundReactionForce
The force exchanged between the foot and the ground
while walking.
HipForce
The force between the pelvis and the thigh.
KneeForce
The force between the thigh and the shank.
NormalizedGRF
The ground reaction force expressed as a percentage of
the body weight.
WaistForce
The force between the pelvis and the thorax.a
Moments
AnkleMoment
The moment between the shank and the foot.
HipMoment
The moment between the pelvis and the thigh.
KneeMoment
The moment between the thigh and the shank.
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Output
Description
WaistMoment
The moment between the pelvis and the thorax.a
Powers
a
AnklePower
The power between the shank and the foot.
HipPower
The power between the pelvis and the thigh.
KneePower
The power between the thigh and the shank.
WaistPower
The power between the pelvis and the thorax.a
This output variable is calculated only if you use a Plug-in Gait model that contains
the thorax.
Marker sets for Plug-in Gait lower body model
All Plug-in Gait marker sets are designed for the Newington-Helen Hayes model on
which Plug-in Gait is based. The marker set for Plug-in Gait lower body modeling
includes markers for the pelvis and the lower limbs.
There are two variations of the standard marker set for the lower body model:
A single sacral (SACR) marker for the pelvis
Two posterior superior iliac spine (PSIS) markers for the pelvis
These markers provide the same function; if you use two PSIS markers, Plug-in Gait
calculates the midpoint between them and uses that to perform the calculations. If you
use a single SACR marker, you identify that position to Plug-in Gait rather than having it
calculated.
Using the two PSIS markers has the benefit of providing redundancy, so if one of the
pelvis markers is missing, it is possible to reconstruct a virtual marker based on the
remaining three markers. You can do this using a Rigid Body Fill in Nexus.
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Marker placement for Plug-in Gait lower body model
To demonstrate where to attach the standard lower body model markers to your
patient, the following images show front, back, and side views. Some markers are
shown from two views to help you better determine their position on your patient.
Important
As shown in the following images, some asymmetry is desirable as it helps the
auto labeling routine distinguish right from left. In a lower body marker set,
you can place the THI and/or TIB markers asymmetrically. Similarly, avoid
symmetrical placement of marker clusters or groups of markers and also
ensure markers are asymmetrical within each cluster/group.
The following image shows the front view. The left lower body markers are not labeled;
place markers on the left side in a similar way to those on the right.
Important
The THI and TIB markers anterior-posterior position is critical for identifying
the orientation of the knee and ankle flexion axis.
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The following image shows the back view. The figure includes the SACR marker
variation, which is highlighted in orange. The right lower body markers are not labeled;
attach markers on that side in a similar way to those on the left (with some asymmetry,
as described above).
The following image shows the right side view. The left side view is not shown; attach
markers on that side in a similar way to the right markers (with some asymmetry, as
described above).
The following tables list the markers defined in Plug-in Gait templates for lower body
modeling and describe where to place them on the patient:
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Pelvis marker placement
The following markers are positioned on the patient's pelvis:
Marker
Definition
Position on patient
Sacral
On the skin mid-way between the posterior superior iliac
label
SACR
spines (PSIS) and positioned to lie in the plane formed by the
ASIS and PSIS points.
LASI
Left ASIS
Left anterior superior iliac spine
RASI
Right
Right anterior superior iliac spine
ASIS
LPSI
Left PSIS
Left posterior superior iliac spine (immediately below the
sacro-iliac joints, at the point where the spine joins the pelvis)
This marker is used with the RPSI marker as an alternative to
the single SACR marker.
RPSI
Right
Right posterior superior iliac spine (immediately below the
PSIS
sacro-iliac joints, at the point where the spine joins the pelvis)
This marker is used with the LPSI marker as an alternative to
the single SACR marker.
In some patients, especially obese individuals, the markers either can't be placed
exactly on the ASIS, or are invisible in this position to cameras. In these cases, move
each marker laterally by an equal amount along the ASIS-ASIS axis. The true inter-ASIS
distance must then be manually measured and entered in the Properties pane at the
bottom of the Subjects tab on the Resources pane. These markers, together with either
the SACR marker or the LPSI and RPSI markers, define the pelvic coronal plane.
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Lower limb marker placement
The following markers are positioned on each of the patient's lower limbs. For
additional guidance, see the notes at the bottom of the table.
Marker
Definition
Position on patient
label
Left lower limb markers
LTHI
Left thigh
Over the lower lateral 1/3 surface of the left thigh
LKNE
Left knee
On the flexion-extension axis of the left knee
LTIB
Left tibia
Over the lower 1/3 surface of the left shank
LANK
Left ankle
On the lateral malleolus along an imaginary line that passes
through the transmalleolar axis
LHEE
Left heel
On the calcaneous at the same height above the plantar
surface of the foot as the toe marker
LTOE
Left toe
Over the second metatarsal head, on the mid-foot side of the
equinus break between fore-foot and mid-foot
Right lower limb markers
RTHI
Right
Over the upper lateral 1/3 surface of the right thigh
thigh
RKNE
Right
On the flexion-extension axis of the right knee.
knee
RTIB
Right
Over the upper 1/3 surface of the right shank
tibia
RANK
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Right
On the lateral malleolus along an imaginary line that passes
ankle
through the transmalleolar axis
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Marker
Definition
Position on patient
Right
On the calcaneous at the same height above the plantar
heel
surface of the foot as the toe marker
Right toe
Over the second metatarsal head, on the mid-foot side of the
label
RHEE
RTOE
equinus break between fore-foot and mid-foot
Notes
Knee markers To locate the precise point for placing the knee markers (LKNE, RKNE),
passively flex and extend the knee a little while watching the skin surface on the lateral
aspect of the knee joint. Identify where knee joint axis passes through the lateral side
of the knee by finding the lateral skin surface that comes closest to remaining fixed in
the thigh. This landmark should also be the point about which the lower leg appears to
rotate. Mark this point with a pen. With an adult patient standing, this pen mark should
be about 1.5 cm above the joint line, mid-way between the front and back of the joint.
Attach the marker at this point.
If you are using a knee alignment device (KAD), see also KAD marker placement for Plugin Gait lower body model on page 15.
Thigh markers The thigh markers (LTHI, RTHI) are used to calculate the knee flexion
axis orientation. Place the LTHI marker over the lower lateral 1/3 surface and the RTHI
marker over the upper lateral 1/3 surface of the thigh, just below the swing of the hand,
although the height is not critical. The anterior-posterior placement of the marker is
critical for correct alignment of the knee flexion axis. Try to keep the thigh marker off
the belly of the muscle, but place the thigh marker at least two marker diameters
proximal of the knee marker. Adjust the position of the marker so that it is lies in the
plane that contains the hip and knee joint centers and the knee flexion/extension axis.
If you are using a KAD, the precise placement of the thigh markers is not crucial.
Tibia markers The tibia markers (LTIB, RTIB) are used to determine the alignment of the
ankle flexion axis. Similarly to the thigh markers, place the LTIB marker over the lower 1
/3 surface of the shank and the RTIB marker over the upper 1/3 surface of the shank.
The tibial marker should lie in the plane that contains the knee and ankle joint centers
and the ankle flexion/extension axis. In a normal patient, the ankle joint axis between
the medial and lateral malleoli is externally rotated by around 20 degrees with respect
to the knee flexion axis. The placements of the shank markers should reflect this.
If you are using a KAD, the ankle dorsi-plantar flexion axis is assumed to be parallel to
the knee flexion axis unless:
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The tibial torsion is manually measured and entered in the Properties pane at the
bottom of the SubjectsResources pane.
or
One marker on each medial malleolus is attached (RMED, LMED). During the static
trial, Plug-in Gait automatically calculates the tibial torsion as the angle between the
knee flexion and the ankle dorsi-plantar flexion axes.
Toe and heel markers If the toe markers (LTOE, RTOE) cannot be placed level with the
heel markers (LHEE, RHEE), you must configure Plug-in Gait to compensate for this. For
details of the relevant settings, see Plug-in Gait Static pipeline in the Vicon Nexus User
Guide.
KAD marker sets for Plug-in Gait lower body model
In addition to the standard lower body marker sets, an alternative marker set enables
you to use a knee alignment device (KAD).
The KAD is a light-weight, spring-loaded G-clamp, whose adjustable jaws bridge the
knee and whose stem is aligned with the knee flexion axis.
One standard-sized marker is fixed to the tip of the stem and two markers are mounted
on the ends of two additional rods fixed to the device. The three markers are
equidistant from the point where the stem meets the jaws of the clamp, enabling the
3D position of this point, known as the 'virtual knee marker', to be calculated.
Instead of the THI and TIB markers in the standard model, the KAD markers (left and
right KAX, KD1, and KD2) are used to calculate the orientation of the medio-lateral axes
of knee and ankle respectively.
The KAD is applied to the patient during a static trial to enable Plug-in Gait to
calculate:
The offset angle between the knee flexion axis orientation as calculated by using the
KAD markers and knee flexion axis orientation as calculated by using the THI markers
(Thigh Rotation Offset). When a KAD is present, the ankle dorsi-plantar flexion axis is
assumed to be aligned with the knee flexion axis unless the tibial torsion
measurement is entered.
The angle between the ankle dorsi-plantar flexion axis orientation as calculated by
using the KAD and the tibial torsion measurement and the ankle dorsi-plantar flexion
axis orientation as calculated using the TIB markers (Shank Rotation Offset).
These calculations eliminate the reliance on the anterior posterior position of the THI
and TIB markers.
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A variation of the KAD marker set defines the additional LMED and RMED markers for
the medial malleoli.
When you use a KAD, the tibial torsion measurement is critical for Plug-in Gait to
identify the correct orientation of the ankle dorsi-plantar flexion axis. In fact, if the
tibial torsion is left at 0 (zero), the ankle flex axis is assumed to be aligned with the
knee flex axis. To enable Plug-in Gait to automatically calculate the tibial torsion
measurement, attach the LMED and RMED markers on the medial malleoli of your
patient.
When the static trial has been processed, you can remove the KAD and the MED
markers, and for dynamic trials, place the KNE marker exactly where the KAD pad used
to be on the femural epicondyle.
KAD marker placement for Plug-in Gait lower body model
The following images show front, back, and side views to demonstrate where to attach
the lower body model markers to your patient. You do this before capturing a static trial
as described in the Vicon Nexus User Guide. Some markers are shown from two views
to help you better determine their position on your patient.
The following image shows the front view. It includes the knee alignment device (KAD)
marker variations, which are highlighted in orange.
The left lower body markers are not labeled; attach markers on that side in a similar
way to those on the right (with some asymmetry as described in Marker placement for
Plug-in Gait lower body model on page 9).
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The following image shows the back view. It includes the knee alignment device (KAD)
marker variations, which are highlighted in orange.
The right lower body markers are not labeled in this figure; attach markers on that side
in a similar way to those on the left (with some asymmetry as described in Marker
placement for Plug-in Gait lower body model on page 9).
The following image shows the right side view. It includes the knee alignment device
(KAD) marker variations, which are highlighted in orange.
The left side view is not shown; attach markers on that side in a similar way to the right
markers (with some asymmetry as described in Marker placement for Plug-in Gait lower
body model on page 9).
If a knee alignment device (KAD) is used, it is attached instead of the LKNE and RKNE
markers for the static trial only. Before dynamic capture and modeling, it must be
removed and LKNE and RKNE markers attached instead.
The KAD markers are constructed in such a way as to enable the model to calculate a
position for a virtual knee marker, which corresponds to the external pad. So, the
external pad should be positioned as described for the knee marker.
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The following table shows the KAD marker labels included for static trials.
Marker
Definition
Position
Left knee
Left KAD axis
Label
LKAX
For the left side, labeling goes counter clockwise from this
LKAX marker
LKD1
Device 1
Left KAD marker 1
LKD2
Device 2
Left KAD marker2
RKAX
Right
Right KAD axis
knee
For the right side, labeling goes clockwise from the RKAX
marker
RKD1
Device 1
Right KAD marker 1
RKD2
Device 2
Right KAD marker 2
For dynamic trials, the KAD must be removed, and the left or right KNE marker
positioned at the same point as the external KAD pad.
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Upper body modeling with Plug-in Gait
This section describes Plug-in Gait upper body modeling, so you can determine if an
upper body model will provide the data you require for your clinical analysis.
The following topics are covered:
Outputs from Plug-in Gait upper body model on page 18
Marker sets for Plug-in Gait upper body modeling on page 20
Marker placement for Plug-in Gait upper body model on page 20
For details about the labeling skeleton templates to be used with Plug-in Gait upper
body models, see Plug-in Gait labeling skeleton templates (VSTs) in Vicon Nexus on
page 31.
Outputs from Plug-in Gait upper body model
Use a Plug-in Gait upper body model if you require the kinematic and kinetic
calculation outputs listed in the following table. The output variables are prefixed by
the appropriate context (L for left or R for right).
Output
Description
Kinematics:
Angles
ElbowAngles
Relative. The angles between the upper arm and the forearm.
HeadAngles
Absolute. The angles between the head and the laboratory
coordinate system.
NeckAngles
The angles between head relative to thorax.
ShoulderAngles
Relative. The angles between the upper arm and the thorax.
SpineAngles
The angles between the thorax relative to the pelvis.
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Output
Description
ThoraxAngles
Absolute. The angles between the thorax and the laboratory
coordinate system.
WristAngles
Relative. The angles between the forearm and the hand.
Kinetics:
Forces
ElbowForce
The force between the upper arm and the forearm.
NeckForce
The force between the head relative to thorax.
ShoulderForce
The force between the upper arm and the thorax.
WristForce
The force between the forearm and the hand.
Moments
ElbowMoment
The moment between the upper arm and the forearm.
NeckMoment
The moment between the head relative to thorax.
ShoulderMoment
The moment between the upper arm and the thorax.
WristMoment
The moment between the forearm and the hand.
Powers
ElbowPower
The power between the upper arm and the forearm.
NeckPower
The power between the head relative to thorax.
ShoulderPower
The power between the upper arm and the thorax.
WristPower
The power between the forearm and the hand.
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Marker sets for Plug-in Gait upper body modeling
The marker set for Plug-in Gait upper body modeling includes markers for the head,
torso, and upper limbs.
There are two variations of the standard marker set for the upper body model:
Additional upper arm (UPA) and forearm (FRM) markers
No UPA and FRM markers
The UPA and FRM markers are optional; however, using them improves marker tracking
during dynamic trials.
Marker placement for Plug-in Gait upper body model
The following images show front, back, and side views to demonstrate where to attach
the upper body markers to your patient. You do this before capturing a static trial as
described in the Vicon Nexus User Guide. Some markers are shown from two views to
help you better determine their position on your patient.
Important
As shown in the following images, some asymmetry is desirable as it helps the
auto labeling routine distinguish right from left. For upper body modeling, you
can place the UPA and FRM markers asymmetrically. Similarly, avoid
symmetrical placement of marker clusters or groups of markers and also
ensure markers are asymmetrical within each cluster/group.
The following image shows the front view. The left upper body markers are not labeled;
attach markers on that side in a similar way to those on the right (with some asymmetry
as described above).
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The following image shows the back view. The right upper body markers are not
labeled; attach markers in a similar way to those on the left (with some asymmetry as
described above).
The following image shows the right side view. The left side view is not shown; attach
markers on that side in a similar way to those on the right (with some asymmetry as
described above).
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The following tables list the markers defined in Plug-in Gait templates for upper body
modeling and describe where to place them on the patient:
Head markers
The following table describes the markers positioned on the patient's head. To save
time, many users buy a headband and permanently attach markers to it.
Marker
Definition
Position on patient
Left front
Left temple
label
LFHD
head
RFHD
Right
Right temple
front
head
LBHD
RBHD
Left back
Left back of head (defines the transverse plane of the head,
head
together with the frontal markers)
Right
Right back of head (defines the transverse plane of the head,
back
together with the frontal markers)
head
Important
If the back markers cannot be placed level with the front markers, you must
configure Plug-in Gait to compensate for this during the subject calibration
process. To do this, in the Properties for the Process Static Plugin Gait Model
pipeline operation, under Assume Horizontal, select Head.
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Torso markers
The following table describes the markers positioned on the patient's torso. The torso
markers (C7, T10, CLAV, STRN) define the thorax sagittal plane; therefore, their lateral
positioning is most important.
Marker
Definition
Position on patient
7th
On the spinous process of the 7th cervical vertebra
label
C7
cervical
vertebra
T10
10th
On the spinous process of the 10th thoracic vertebra
thoracic
vertebra
CLAV
Clavicle
On the jugular notch where the clavicles meet the sternum
STRN
Sternum
On the xiphoid process of the sternum
RBAK
Right
Anywhere over the right scapula
back
(This marker has no equivalent marker on the left side. This
asymmetry helps the autolabeling routine determine right
from left on the subject. Placement is not critical as it is not
included in the Plug-in Gait model calculations.)
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Upper limb markers
The following table describes the markers positioned on the patient's upper body.
Marker labels shown with an asterisk * are optional; however, using them improves
marker tracking during dynamic trials.
Marker
Definition
Position on patient
label
Left upper limb markers
LSHO
Left
On the acromio-clavicular joint
shoulder
*LUPA
Left
On the upper lateral 1/3 surface of the left arm (Place
upper
asymmetrically with RUPA)
arm
LELB
Left
On the lateral epicondyle
elbow
*LFRM
LWRA
Left
On the lower lateral 1/3 surface of the left forearm (Place
forearm
asymmetrically with RFRM)
Left wrist
At the thumb side of a bar attached to a wristband on the
marker A
posterior of the left wrist, as close to the wrist joint center as
possible. Loose markers can be used but for better tracking
of the axial rotations, a bar is recommended.
LWRB
Left wrist
At the little finger side of a bar attached to a wristband on
marker B
the posterior of the left wrist, as close to the wrist joint
center as possible. Loose markers can be used but for better
tracking of the axial rotations, a bar is recommended.
LFIN
Left
Just proximal to the middle knuckle on the left hand
finger
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Marker
Definition
Position on patient
label
Right upper limb markers
RSHO
Right
On the acromio-clavicular joint
shoulder
*RUPA
Right
On the lower lateral 1/3 surface of the right arm (Place
upper
asymmetrically with LUPA)
arm
RELB
Right
On the lateral epicondyle approximating the elbow joint axis
elbow
*RFRM
RWRA
RWRB
RFIN
Right
On the lower lateral 1/3 surface of the right forearm (Place
forearm
asymmetrically with LFRM)
Right
At the thumb side of a bar attached symmetrically with a
wrist
wristband on the posterior of the right wrist, as close to the
marker A
wrist joint center as possible
Right
At the little finger side of a bar attached symmetrically with a
wrist
wristband on the posterior of the right wrist, as close to the
marker B
wrist joint center as possible
Right
Just below the middle knuckle on the right hand
finger
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Full body modeling with Plug-in Gait
If you require Plug-in Gait full body modeling, use both a lower and an upper body
model to provide the data you require for your clinical analysis.
This topic explains:
Outputs from Plug-in Gait full body model on page 26
Marker sets for Plug-in Gait full body modeling on page 26
Marker placement for Plug-in Gait full body model on page 27
For a description of the labeling skeleton templates to be used with Plug-in Gait lower
body, upper body, or full body models, see Plug-in Gait labeling skeleton templates
(VSTs) in Vicon Nexus on page 31.
Outputs from Plug-in Gait full body model
Use a Plug-in Gait lower body and upper body model if you require the kinematic and
kinetic calculation outputs listed in Outputs from Plug-in Gait lower body model on
page 6 and Outputs from Plugin Gait upper body model. The output variables are
prefixed by the appropriate context (L for left or R for right).
Marker sets for Plug-in Gait full body modeling
There are two variations of the standard lower body model:
A single sacral (SACR) marker
Two posterior superior iliac spine (PSIS) markers for the pelvis.
These markers provide the same function; if you use two PSIS markers, Plug-in Gait
calculates the midpoint between them and uses that to perform the calculations. If you
use a single SACR marker, you identify that position to Plug-in Gait rather than having it
calculated.
In addition to the standard lower body marker sets, an additional marker set enables
you to use a knee alignment device (KAD). The KAD markers (left and right KAX, KD1,
and KD2) are used instead of the THI and TIB markers in the standard model to
calculate the orientation of the medio-lateral axes of knee and ankle respectively.
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A variation of the KAD marker set defines the additional LMED and RMED markers for
the medial malleoli. The MED markers enable Plug-in Gait to automatically calculate the
tibial torsion measurement. For further information on the KAD and MED markers, see
KAD marker sets for Plug-in Gait lower body model on page 14.
When you use KAD+MED markers, in order to verify the ankle axis, the Plug-in Gait
Static pipeline displays the torsioned tibia instead of the untorsioned tibia. If joint
angles are required, you must also run the Plug-in Gait Dynamic pipeline.
Marker placement for Plug-in Gait full body model
The following images show front, back, and side views to demonstrate where to attach
the full body model markers to your patient. You do this when you are capturing a
static trial as described in the Vicon Nexus User Guide.
Some markers are shown from two views to help you better determine their position on
your patient.
The following image shows the front view. This view includes the knee alignment
device (KAD) marker variations, which are highlighted in orange. If you have chosen to
use a Plug-in Gait marker set that includes KAD markers, attach the KAD pad to the
patient instead of the THI and TIB markers. For details on the KAD, see KAD marker
placement for Plug-in Gait lower body model on page 15.
Important
As shown in the following images, some asymmetry is desirable as it helps the
auto labeling routine distinguish right from left. For a full body set, you can
place the THI, TIB, UPA and FRM markers asymmetrically. Similarly, avoid
symmetrical placement of marker clusters or groups of markers and also
ensure markers are asymmetrical within each cluster/group.
The left body markers are not labeled in this figure; attach markers on that side in a
similar way (with some asymmetry) to those on the right.
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Tip
To assist with labeling, place the UPA, FRM, THI, and TIB markers at slightly
different heights on the left and right sides:
Upper 1/3: LUPA, RFRM, RTHI. RTIB
Lower 1/3: RUPA, LRFM, LTHI, LTIB
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The following image shows the back view. This view includes the sacral (SACR) and
knee alignment device (KAD) marker variations, which are highlighted in orange. For
details on the SACR marker, see Marker sets for Plug-in Gait lower body model on page
8. If you have chosen to use a Plug-in Gait marker set that includes KAD markers,
attach the KAD pad to the patient instead of the THI and TIB markers. For details on
the KAD, see KAD marker sets for Plugin Gait lower body model.
The right body markers are not labeled in this figure; attach markers on that side in a
similar way to those on the left (with some asymmetry as described above). The RBAK
marker has no equivalent marker on the left side; this asymmetry helps the autolabeling
routine determine right from left on the subject.
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The following image shows the right side view. This view includes the knee alignment
device (KAD) marker variations, which are highlighted in orange. If you have chosen to
use a Plug-in Gait marker set that includes KAD markers, attach the KAD pad to the
patient instead of the THI and TIB markers. For details on the KAD, see KAD marker sets
for Plug-in Gait lower body model on page 14.
The left side view is not shown; attach markers on that side in a similar way to the right
markers (with some asymmetry as described above).
For detailed guidance on placing markers on a patient for full body modeling, the
following sections:
Marker placement for Plug-in Gait lower body model on page 9
KAD marker placement for Plugin Gait lower body model on page 15
Marker placement for Plugin Gait upper body model on page 20
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Plug-in Gait labeling skeleton templates (VSTs)
in Vicon Nexus
The Plug-in Gait biomechanical model calculates joint kinematics and kinetics from the
XYZ marker positions and specific subject anthropometric measurements. As with all
motion capture and analysis in Vicon Nexus, the information about the marker set as
well as the generic relationship between the physical markers attached to a subject is
contained in a labeling skeleton template (.vst) file. This template defines a generic
model of the chosen marker set.
You create a subject in Nexus based on a specific template file and then you calibrate
the generic marker set model defined in the template to your particular subject. The
calibration process creates a labeling skeleton (.vsk) file which is strictly specific to
your subject. Nexus then uses this subject-specific .vsk file to automatically label
dynamic motion capture trials for that patient both in real time and in post-processing.
Important
The labeling skeleton templates included in the supplied .vst files are used
only to define the marker set and to enable Nexus to perform automatic
labeling. They are not biomechanical models that will output valid joint angles
or other kinematic/kinetic variables. To derive valid kinematics or kinetics, use
Plug-in Gait or create your own biomechanical model using Vicon BodyBuilder,
Python or MATLAB.
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The following table lists the predefined Plug-in Gait labeling skeleton templates ( .vst
files) supplied with Nexus, identifying the portion of the body it applies to for gait
analysis.
Plug-in Gait
Description
template file
PlugInGait
Full body model defining two markers on
FullBody Ai.
the posterior superior iliac spine (PSIS)
Lower
Upper
body
body
modeling
modeling
y
y
y
n
vst
PlugInGait
Lower body model defining two markers
LowerBody
on the posterior superior iliac spine (PSIS)
Ai.vst
An extended version of Plug-in Gait that defines additional markers for foot modeling is
available. For information about the Oxford Foot Model plug-in, contact Vicon Support.
These Plug-in Gait template files are installed under the Nexus ModelTemplates folder
(by default, C:\Program Files (x86)\Vicon\Nexus2.#\ModelTemplates). If you create a
template of your own, store it in this location, so that it will be immediately available for
selection from the drop-down list when you create a subject node based on a
predefined template file. (If you choose not to store it in this location, you can instead
browse to the relevant location.)
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Plug-in Gait bones
For information on Plug-in Gait bones, see the following topics:
Complete list of Plug-in Gait bones on page 34
Plug-in Gait virtual markers on page 38
Plug-in Gait joint centers on page 39
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Complete list of Plug-in Gait bones
Name
Description
Name
Description
PELO
Pelvis Origin
HEDO
Head Origin
PELP
Pelvis Proximal
HEDP
Head Proximal
PELA
Pelvis Anterior
HEDA
Head Anterior
PELL
Pelvis Lateral
HEDL
Head Lateral
RFEO
Right Femur Origin
TRXO
Thorax Origin
RFEP
Right Femur Proximal
TRXP
Thorax Proximal
RFEA
Right Femur Anterior
TRXA
Thorax Anterior
RFEL
Right Femur Lateral
TRXL
Thorax Lateral
LFEO
Left Femur Origin
CSPO
C Spine Origin
LFEP
Left Femur Proximal
CSPP
C Spine Proximal
LFEA
Left Femur Anterior
CSPA
C Spine Anterior
LFEL
Left Femur Lateral
CSPL
C Spine Lateral
RTIO
Right Tibia Origin
SACO
Sacrum Origin
RTIP
Right Tibia Proximal
SACP
Sacrum Proximal
RTIA
Right Tibia Anterior
SACA
Sacrum Anterior
RTIL
Right Tibia Lateral
SACL
Sacrum Lateral
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Name
Description
Name
Description
LTIO
Left Tibia Origin
RCLO
Right Clavicle Origin
LTIP
Left Tibia Proximal
RCLP
Right Clavicle Proximal
LTIA
Left Tibia Anterior
RCLA
Right Clavicle Anterior
LTIL
Left Tibia Lateral
RCLL
Right Clavicle Lateral
RFOO
Right Foot Origin
LCLO
Left Clavicle Origin
RFOP
Right Foot Proximal
LCLP
Left Clavicle Proximal
RFOA
Right Foot Anterior
LCLA
Left Clavicle Anterior
RFOL
Right Foot Lateral
LCLL
Left Clavicle Lateral
LFOO
Left Foot Origin
RHUO
Right Humerus Origin
LFOP
Left Foot Proximal
RHUP
Right Humerus Proximal
LFOA
Left Foot Anterior
RHUA
Right Humerus Anterior
LFOL
Left Foot Lateral
RHUL
Right Humerus Lateral
RTOO
Right Toe Origin
LHUO
Left Humerus Origin
RTOP
Right Toe Proximal
LHUP
Left Humerus Proximal
RTOA
Right Toe Anterior
LHUA
Left Humerus Anterior
RTOL
Right Toe Lateral
LHUL
Left Humerus Lateral
LTOO
Left Toe Origin
RRAO
Right Radius Origin
LTOP
Left Toe Proximal
RRAP
Right Radius Proximal
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Name
Description
Name
Description
LTOA
Left Toe Anterior
RRAA
Right Radius Anterior
LTOL
Left Toe Lateral
RRAL
Right Radius Lateral
LRAO
Left Radius Origin
LRAP
Left Radius Proximal
LRAA
Left Radius Anterior
LRAL
Left Radius Lateral
RHNO
Right Hand Origin
RHNP
Right Hand Proximal
RHNA
Right Hand Anterior
RHNL
Right Hand Lateral
LHNO
Left Hand Origin
LHNP
Left Hand Proximal
LHNA
Left Hand Anterior
LHNL
Left Hand Lateral
RFIO
Right Finger Origin
RFIP
Right Finger Proximal
RFIA
Right Finger Anterior
RFIL
Right Finger Lateral
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Name
Description
Vicon Motion Systems Ltd.
Name
Description
LFIO
Left Finger Origin
LFIP
Left Finger Proximal
LFIA
Left Finger Anterior
LFIL
Left Finger Lateral
RTBO
Right Thumb Origin
RTBP
Right Thumb Proximal
RTBA
Right Thumb Anterior
RTBL
Right Thumb Lateral
LTBO
Left Thumb Origin
LTBP
Left Thumb Proximal
LTBA
Left Thumb Anterior
LTBL
Left Thumb Lateral
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Plug-in Gait virtual markers
Plug-in Gait creates virtual markers that lie on the axes of a segment's coordinate
systems: at the origin, anterior axis, lateral axis, and proximal (vertical) axis. These
virtual markers are not necessary for the basic use of Plug-in Gait. Advanced users may
use them for exporting the rotational and translational motion of the segments for
analysis.
The following table lists the virtual markers created for each segment.
Virtual marker
Segment coordinate system
sgmentNameO
segment Origin
segmentNameA
Anterior axis
segmentNameP
Proximal axis
segmentNameL
Lateral axis
For example, Plug-in Gait would create the following virtual markers for the pelvis
segment:
PELO: pelvis Origin
PELA: pelvis Anterior axis
PELP: pelvis Proximal axis
PELL: pelvis Lateral axis
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Plug-in Gait joint centers
The following image shows Plug-in Gait joint centers:
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Plug-in Gait lower body forces and moments
The forces calculated by Plug-in Gait and displayed by Vicon Polygon are in the local coordinate frame of the distal segment in the hierarchical kinetic chain.
This means that the Ankle joint forces are recorded in the Foot segment axis system.
Therefore:
Ground Reaction force Z will look similar to Ankle Force X
Ground Reaction Force Y will look similar to Ankle Force Z
Ground Reaction Force X will look similar to Ankle Force Y
For the tibia this changes, as the axis orientation now changes:
Z force is therefore compression or tension at the joint
Y force is mediolateral forces at the joint
X force is anteroposterior forces at the joint
The positive force acts in the positive direction of the axis in the distal segment on
which it acts. A negative force acts in the negative direction along the axis.
In Plug-in Gait, we use an external moment and force description. That means that:
For the Z axis, a negative force is compression and a positive force, tension
For the Y axis, a positive force for the right side is medial and negative lateral
For the X axis, a positive force is anterior and negative posterior
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The following table lists all the lower body forces and moments with their positive and
negative descriptors.
Description
Segment
Force or moment
+ve
-ve
axes
component
descriptor
descriptor
Foot
Compression/Tension
Tension
Compression
Right Foot
Medial/Lateral
Medial
Lateral
Foot
Anterior/Posterior
Anterior
Posterior
Knee Force X
Tibia
Anterior/Posterior
Anterior
Posterior
RKnee Force
Right Tibia
Medial/Lateral
Medial
Lateral
Left Tibia
Medial/Lateral
Lateral
Medial
Knee Force Z
Tibia
Tension/Compression
Tension
Compression
Hip Force X
Thigh
Anterior/Posterior
Anterior
Posterior
RHip Force Y
Right
Medial/Lateral
Medial
Lateral
Ankle Force
X
RAnkle Force
Y
Ankle Force
Z
Y
LKnee Force
Y
Thigh
LHip Force Y
Left Thigh
Medial/Lateral
Lateral
Medial
Hip Force Z
Thigh
Tension/Compression
Tension
Compression
Ankle
Foot
Dorsi/Plantar flexion
Dorsiflexion
Plantar
Moment X
Ankle
flexion
Foot
Abduction/Adduction
Adduction
Abduction
Moment Y
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Description
Ankle
Segment
Force or moment
+ve
-ve
axes
component
descriptor
descriptor
Foot
Rotation
Internal
External
Tibia
Flexion/Extension
Flexion
Extension
Tibia
Varus/Valgus
Varus
Valgus
Tibia
Rotation
Internal
External
Thigh
Flexion/Extension
Flexion
Extension
Thigh
Abduction/Adduction
Adduction
Abduction
Thigh
Rotation
Internal
External
Moment Z
Knee
Moment X
Knee
Moment Y
Knee
Moment Z
Hip Moment
X
Hip Moment
Y
Hip Moment
Z
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Plug-in Gait kinematic and kinetic calculations
The following topics describe the way in which Plug-in Gait performs calculations to
measure the kinematics and kinetics of subjects. They provide an in-depth
understanding of marker placement, and will help you to interpret the results. They
describe the geometrical relationships between markers, and segments, and gives fixed
values applied to the kinetic segments. Given the same inputs, you should be able to
replicate the results.
Lower body kinematics on page 50
Upper body kinematics on page 62
Angle outputs on page 68
Kinetic modeling on page 69
The internal structure and the specific algorithms used are not covered.
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About Plug-in Gait processes
The Plug-in Gait Dynamic pipeline consists of the following components: all individual
pipeline operations:
A quintic spline filter based on code written by Herman Woltring. This filter is
intended to be applied to the real marker trajectory data before the modeling stage.
No further explicit filtering of the data occurs during the modeling stage.
Operations that automatically detect and autocorrelate gait cycle events.
The modeling stage, which takes the real marker trajectories, and generates 'virtual'
marker trajectories that represent kinematic and kinetic quantities (angles, moments
etc.) and representations of the modeled segments.
An export operation, to enable you to save your processed trial data to a C3D file.
This guide covers only the modeling stage of the process. You can perform modeling on
the real marker data independently from the filtering and event detection processes by
selecting the appropriate check box in the pipeline.
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Segment meshes
Plug-in Gait outputs virtual markers that are used for several purposes:
To calculate variables
For visualization purposes, such as to define the positions of meshes (representing
bones), which can be displayed in the Polygon application. These mesh outputs are
rigidly linked to the calculated rigid body segments but are not necessarily the same.
The origins and axes for the meshes are dependent on the meshes contained in the
Polygon mesh file.
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Plug-in Gait internal models
Internally, the modeling stage consists of four interdependent models:
A kinematic lower body
A kinematic upper body
A kinetic lower body
A kinetic upper body
The kinematic models are responsible for the definitions of the rigid body segments,
and the calculations of joint angles between these segments.
The kinetic models then apply masses and moments of inertia to the segments, and
enable the "reactions" that occur on the segments to be calculated.
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Overview of the Plug-in Gait modeling process
To run the models, you must supply the required subject measurements. When you
have done this, the stages of the Plug-in Gait modeling process are:
The initial stage checks that the required components are present. This includes
checks for required markers present in the trial, and subject parameter values.
Modeling only continues if these requirements are met. The pelvis markers are the
minimum required for the lower body model, and the thorax markers are required for
the upper body model.
Various static values that can be calculated as being fixed for the whole trial, and are
needed for the definitions of the segments, are calculated.
The positions of the rigid segments are defined on a frame-by-frame basis. Each
segment is defined by an origin in global (laboratory) coordinates, and three
orthogonal axis directions.
In general, the three axis directions are defined using two directions derived from the
marker data.
One of these directions is taken as a dominant or principal direction, and used to
directly define one of the axes in the segment.
The second direction is subordinate to the first, and is used with the first direction to
define a plane.
The third axis of the segment is taken to be perpendicular to this plane.
Then the second axis can be found that is perpendicular to both the first and third
axes. All segment axis systems are right-handed systems.
The outputs that are required from the modeling are then calculated, based on the
frame-by-frame positions of the segments.
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Static vs. dynamic models
The kinematic models are run slightly differently for the static trials, to calculate certain
static 'calibration' angles that are required for the dynamic modeling. These differences
are noted in the descriptions of the models, otherwise it should be assumed that the
model is calculated in the same way for both trial types.
When the static modeling is being performed, calculated subject measurements are
output to the subject measurements file. This is not done for the dynamic trial, even if
new values are calculated internally to enable the model to be run.
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The chord function
To define joint centers, the chord function is used extensively in the Plug-in Gait
models. Three points are used to define a plane. One of these points is assumed to be a
previously calculated joint center, and a second is assumed to be a real marker, at some
known, perpendicular distance (the joint center offset) from the required joint center.
(It's called a chord because by definition, the three points (two joint centers and the
joint marker) lie on the periphery of a circle.)
A modified version of the function calculates the required joint center position when
the plane definition marker is rotated out of this plane by a known angle round the
proposed joint center axis. For an illustration of this, see Dynamic knee joint center
calculation on page 54.
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Lower body kinematics
Lower body fixed values on page 50
Pelvis on page 52
Knee Alignment Device (KAD) on page 52
Knee joint center on page 53
Femur on page 55
Ankle joint center on page 55
Tibia on page 58
Foot on page 59
Lower body fixed values
The Newington-Gage model is used to define the positions of the hip joint centers in
the pelvis segment.
If the InterAsis distance has not been entered in the subject measurements, this is
calculated as the mean distance between the LASI and RASI markers, for each frame in
the trial for which there is a valid position for each marker.
If the Asis to Trocanter distances have not been entered, they are calculated from the
left and right leg lengths using the formula:
AsisTrocDist = 0.1288 * LegLength – 48.56
This is done independently for each leg.
The value C is then calculated from the mean leg length:
C = MeanLegLength*0.115 – 15.3, aa is half the InterAsis distance, and mm the marker
radius.
These are used to then calculate the offset vectors for the two hip joint centers (LHJC
and RHJC) as follows:
X = C*cos(theta)*sin(beta) – (AsisTrocDist + mm) * cos(beta)
Y = -(C*sin(theta) – aa)
Z = -C*cos(theta)*cos(beta) – (AsisTrocDist + mm) * sin(beta)
where theta is taken as 0.5 radians, and beta as 0.314 radians.
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For the right joint center, the Y offset is negated (since Y is in the lateral direction for
the pelvis embedded coordinate system).
The position of the top of the lumbar vertebra 5 (the reference point for Dempster data
on page 104) is then estimated as
(LHJC + RHJC)/2 + (0.0, 0.0, 0.828) * Length(LHJC – RHJC)
where the value 0.828 is a ratio of the distance from the hip joint center level to the
top of the lumbar 5 compared to distance between the hip joint centers on the pelvis
mesh.
Knee and ankle offsets are then calculated by adding half the measured joint width and
marker diameter to give the distance from the center point of the marker to the joint
center.
The general direction of the subject walking in the global coordinate system is then
found by looking at the first and last valid position of the LASI marker. The X
displacement is compared to the Y displacement. If the X displacement is bigger, the
subject is deemed to have been walking along the X axis either positively or negatively,
depending on the sign of the X offset. Otherwise, the Y axis is chosen. These directions
are used to define a coordinate system matrix (similar to a segment definition) denoted
the ProgressionFrame. Note that it's assumed that the Z axis is always vertical, and that
the subject is walking along one of these axes, and not diagonally, for example.
If the distance between the first and last frame of the LASI marker is less than a
threshold of 800mm however, the progression frame is calculated using the direction
the pelvis is facing during the middle of the trial. This direction is calculated as a mean
over 10% of the frames of the complete trial. Within these frames, only those which
have data for all the pelvis markers are used. For each such frame, the rear pelvis
position is calculated from either the SACR marker directly, or the center point of the
LPSI and RPSI markers. The front of the pelvis is calculated as the center point
between the LASI and RASI markers. The pelvis direction is calculated as the direction
vector from the rear position to the front. This direction is then used in place of the
LASI displacement, as described above, and compared to the laboratory X and Y axes to
choose the Progression Frame.
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Pelvis
First the pelvis segment coordinate system is defined from the waist markers. The
origin is taken as the midpoint of the two asis markers. The dominant axis, taken as the
Y axis, is the direction from the right asis marker to the left asis marker. The secondary
direction is taken as the direction from the sacrum marker to the right asis marker. If
there is no sacrum marker trajectory, the posterior markers are used. If both are visible,
the mean is used. If just one is visible, then that one is used. The Z direction is generally
upwards, perpendicular to this plane, and the X axis generally forwards.
The position and scale of the pelvis is thus determined by the two asis markers, since
they determine the origin of the coronal orientation of the pelvis. The posterior sacral
markers (or psis markers) determine only the anterior tilt of the pelvis. Their actual
distance behind the asis markers and lateral position is immaterial, allowing a sacral
wand marker to be used, for example.
If the asis markers are also used to calculate the inter asis distance, they are therefore
also used to determine the lateral positions of the hip joint centers within the pelvis
segment. It is important for these to be as accurate as possible, since they affect the
determination of the femur segments, and thus influence both the hip angles, and also
the knee joint angles.
Knee Alignment Device (KAD)
For the model to determine the knee and ankle joint centers, the markers must be very
carefully positioned, and it is the responsibility of clinical staff to use their anatomical
knowledge to position markers such that the model is able to make as good an
approximation to the joint centers as possible.
The dynamic model uses the Thigh and Shank wand markers to define the plane of
containing the joint centers, and one method of marker placement is to carefully
position these markers to align with your judgment of where the joint centers are.
Alternatively, the Knee Alignment Device (KAD) may be used. This must be placed on
the patient during the static trial to indicate the plane of the knee joint center. Then
the model calculates the relative angle of the Thigh wand marker, and this angle is
used in the dynamic trial to determine the joint center without the KAD. This technique
relies on the accurate placement of the KAD, rather than the accurate placement of
the wand marker.
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Knee joint center
Static knee joint center calculation on page 53
Dynamic knee joint center calculation on page 54
Static knee joint center calculation
If a KAD is being used in the static model, firstly a virtual KNE marker is determined by
finding the point that is equidistant from the three KAD markers, such that the
directions from the point to the three markers are mutually perpendicular.
For the right knee, the markers RKAX, RKD1, RKD2 must be labeled in a clockwise
direction, and for the left knee, the markers LKAX, LKD1, LKD2 must be labeled anticlockwise. That is, if the two KD markers are positioned anteriorly, the upper marker
should be KD1.
The joint center KJC is then determined using the chord function with the HJC, KNE
and KAX. The HJC-KJC and KJC-KNE lines will be perpendicular, and the KJC-KNE line
has a length equal to the knee offset (KO).
The thigh marker rotation offset (
) is then calculated by projecting its position on to
a plane perpendicular to the HJC-KJC line.
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If a KAD is not being used in a static trial, then processing proceeds exactly as for a
dynamic trial.
Note that for static trials without a KAD, the anterior-posterior position of the KJC is
determined by the position of the THI wand marker, and the value of wand offset value
that is entered (if you do not enter a value, a value of zero is assumed). Correct
determination of the KJC (and the AJC) is very important, especially for the kinetic
calculations. In the clinic, you have to assess which method of marker positioning gives
the best estimate of the KJC: using a KAD or using the THI marker.
Dynamic knee joint center calculation
In the dynamic model, the KJC is determined using the modified chord function, from
the global position of the HJC, the thigh wand marker (THI), and the knee marker (KNE),
together with the knee offset (KO), and thigh wand angle offset (
) from the subject
measurements.
KJC is found such that the KNE marker is at a distance of KO from the KJC, in a
direction perpendicular to the line from the HJC to KJC. It is also found such that the
angle between the KJC-KNE line and the KJC-THI line, projected onto a plane
perpendicular to the HJC-KJC line, is the same as the thigh wand offset angle.
There is only one position for the KJC that satisfies these two conditions.
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Femur
The femur origin is taken as the knee joint center. The primary Z axis is taken from the
knee joint center (KJC) to the hip joint center (HJC). The secondary axis is taken
parallel to the line from the knee joint center to the knee marker (or virtual knee
marker, for static KAD trials). This in fact directly gives the direction of the Y axis. For
both the left and the right femur, the Y axis is directed towards the left of the subject.
The X axis for both femura is hence directed forwards from the knee.
Note that in a static trial although a KAD determines the plane in which the knee joint
center lies, it does not directly determine the lateral orientation of the "knee axis"
which is implicitly defined as the Y axis of the femur segment. The lateral orientation is
defined by the vertical orientation of the Z axis (the line joining the hip and knee joint
centers). The Y axis may pass either above or below the KNE marker.
Ankle joint center
The ankle joint center is determined in a similar manner to the knee joint center (see
Knee joint center on page 53).
Static ankle joint center calculation on page 55
Dynamic ankle joint center calculation on page 57
Static ankle joint center calculation
In static trials with a KAD, the KAX marker is used to define the plane of the knee axis,
and the plane of the ankle axis is assumed to be parallel to this. A value for Tibial
Torsion can be entered, and the plane of the in which the Ankle joint center lies will be
rotated by this amount relative to the plane containing the KAX marker.
Thus the AJC is found using the modified chord function, such that it has a distance
equal to the ankle offset from the ANK marker (AO), and such that the ANK-AJC line
forms an angle equal to the Tibial Torsion with the projection of the KAX-AJC line into
the plane perpendicular to the KJC-AJC line. Note that Tibial Torsion is thus considered
as an external rotation of the ankle axis relative to the knee axis.
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The shank marker rotation offset is then calculated by projecting its position onto the
same plane. Note that this value takes into account the value of the tibial torsion, and
in general, you would expect it to be slightly less than the value for Tibial Torsion, if the
TIB wand marker is conventionally placed.
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Dynamic ankle joint center calculation
In the dynamic trial, and static trials without a KAD, the ankle joint center is calculated
from the knee joint center, shank wand marker and ankle marker with the ankle offset
and shank rotation offset using the modified chord function. Thus the ankle joint
center is at a distance of ankle offset from the ankle marker, and the angle between
the KJC-AJC-ANK plane and the KJC-AJC-TIB plane is equal to the tibia rotation offset.
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Tibia
Tortioned tibia on page 58
Untortioned tibia on page 58
Tortioned tibia
The tibial rotation offset as determined by the static trial already takes into account
the tibial torsion. Thus a Tortioned Tibia is defined with an origin at the AJC, the Z Axis
in the direction from the AJC to the KJC, the Y axis leftwards along the line between
the AJC and ANK marker, and the X axis generally forwards. This is representative of the
distal end of the tibia.
Untortioned tibia
A second tibia is also generated representing the tibia before tibial torsion is applied, by
rotating the X and Y axes of the Tortioned Tibia round the Z axis by the negative of the
tibial torsion (i.e. externally for +ve values). This represents the proximal end, and is
used to calculate the knee joint angles.
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Foot
Static foot on page 59
Dynamic foot on page 61
Static foot calculation
The heel marker is used in the static trial, and the model effectively makes two
segments. For both segments, the AJC is used as the origin.
The main foot segment is constructed using the TOE-HEE line as the primary axis. If the
settings for the model have the foot flat check box selected (ie you have selected Left
Foot and/or Right Foot in the Assume Horizontal properties for the Process Static Plugin Gait Model pipeline operation), then HEE is moved vertically (along the global Z axis)
to be at the same height as TOE. This line is taken as the Z axis, running forwards along
the length of the foot. The direction of the Y axis from the untortioned tibia is used to
define the secondary Y axis. The X axis thus points down, and the Y axis to the left.
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A second foot segment is constructed, using the TOE-AJC as the primary axis, and
again the Y axis of the untortioned tibia to define the perpendicular X axis and the foot
Y axis (the 'uncorrected' foot).
The Static offset angles (Plantar Flexion offset and Rotation offset) are then calculated
from the 'YXZ' Cardan Angles between the two segments (rotating from the
'uncorrected' segment to the heel marker based foot segment). This calculation is
performed for each frame in the static trial, and the mean angles calculated. The static
plantar-flexion offset is taken from the rotation round the Y axis, and the rotation
offset is the angle round the X axis. The angle round the Z axis is ignored.
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Dynamic foot calculation
In the dynamic trial, the foot is calculated in the same way as for the 'uncorrected' foot.
The resulting segment is then rotated first round the Y axis by the Plantar Flexion
offset. Then the resulting segment is rotated around its X axis by the rotation offset.
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Upper body kinematics
Upper body fixed values on page 62
Head on page 63
Thorax on page 63
Shoulder joint center on page 64
Clavicle on page 64
Elbow joint center on page 65
Wrist joint center on page 66
Humerus on page 66
Radius on page 66
Hand on page 67
Upper body fixed values
A shoulder offset value is calculated from the Subject measurement value entered, plus
half the marker diameter. Elbow, wrist and hand offset values are also calculated from
the sum of the respective thickness with the marker diameter divided by two.
A progression frame is independently calculated in just the same way as for the lower
body. C7 is tested first to determine if the subject moved a distance greater than the
threshold. If not, the other thorax markers T10 CLAV and STRN are used to determine
the general direction the thorax was facing in from a mean of 10% of the frames in the
middle of the trial.
Note that in principle it could be possible to arrive at different reference frames for the
upper and lower body, though the circumstances would be extreme.
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Head
The head origin is defined as the midpoint between the LFHD and RFHD markers (also
denoted 'Front').
The midpoint between the LBHD and RBHD markers ('Back') is also calculated, along
with the 'Left' and 'Right' sides of the head from the LFHD and LBHD midpoint, and the
RFHD and RBHD midpoint respectively.
The predominant head axis, the X axis, is defined as the forward facing direction (Front
- Back). The secondary Y axis is the lateral axis from Right to Left (which is
orthogonalized as usual).
For the static processing, the YXZ Euler angles representing the rotation from the head
segment to the lab axes are calculated. The Y rotation is taken as the head Offset
angle, and the mean of this taken across the trial.
For the dynamic trial processing, the head Offset angle is applied around the Y axis of
the defined head segment.
Thorax
The orientation of the thorax is defined before the origin. The Z axis, pointing upwards,
is the predominant axis. This is defined as the direction from the midpoint of the STRN
and T10 to the midpoint of CLAV and C7. A secondary direction pointing forwards is the
midpoint of C7 and T10 to the midpoint of CLAV and STRN. The resulting X axis points
forwards, and the Y axis points leftwards.
The thorax origin is then calculated from the CLAV marker, with an offset of half a
marker diameter backwards along the X axis.
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Shoulder joint center
The clavicles are considered to lie between the thorax origin, and the shoulder joint
centers. The shoulder joint centers are defined as the origins for each clavicle. Note
that the posterior part of the shoulder complex is considered too flexible to be modeled
with this marker set.
Initially a direction is defined, which is perpendicular to the line from the thorax origin
to the SHO marker, and the thorax X axis. This is used to define a virtual shoulder
'wand' marker.
The chord function is then used to define the shoulder joint center (SJC) from the
Shoulder offset, thorax Origin, SHO marker and shoulder 'wand'.
Clavicle
The clavicle segment is defined from the direction from the joint center to the thorax
origin as the Z axis, and the shoulder wand direction as the secondary axis. The X axis
for each clavicle points generally forwards, and the Y axis for the left points upwards,
and the right clavicle Y axis points downwards.
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Elbow joint center
A construction vector direction is defined, being perpendicular to the plane defined by
the shoulder joint center, the elbow marker (LELB) and the midpoint of the two wrist
markers (LWRA, LWRB).
The elbow joint center is defined using the chord function, in the plane defined by the
shoulder joint center, the elbow marker and the previously defined construction vector.
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Wrist joint center
After the elbow joint center is calculated, the wrist joint center (WJC) is calculated. In
this case the chord function is not used. The wrist joint center is simply offset from the
midpoint of the wrist bar markers along a line perpendicular to the line along the wrist
bar, and the line joining the wrist bar midpoint to the elbow joint center.
Humerus
After the wrist joint center is defined, the Humerus is calculated with its origin at the
EJC, a principal Z axis from EJC to SJC, and a secondary line approximating to the X axis
between the EJC and the WJC.
Radius
The radius origin is set at the wrist joint center. The principal axis is the Z axis, from the
WJC to the EJC. The secondary line approximating to the Y axis is taken as the Y axis of
the Humerus segment.
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Hand
The hand is defined by first defining its origin. The chord function is used again for this,
with the WJC, FIN marker and Hand Offset. The midpoint of the wrist bar markers is
used to define the plane of calculation.
The principal Z axis is then taken as the line from the hand origin to the WJC, and a
secondary line approximating the Y axis is defined by direction of the line joining the
wrist bar markers.
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Angle outputs
The output angles for all joints are calculated from the YXZ Cardan angles derived by
comparing the relative orientations of the two segments.
The knee angles are calculated from the femur and the Untortioned tibia segments,
whilst the ankle joint angles are calculated from the Tortioned tibia and the foot
segment.
In the case of the feet, since they are defined in a different orientation to the tibia
segments, an offset of 90 degrees is added to the flexion angle. This does not affect
the Cardan angle calculation of the other angles since the flexion angle is the first in
the rotation sequence.
The progression angles of the feet, pelvis, thorax and head are the YXZ Cardan
calculated from the rotation transformation of the subject's Progression Frame for the
trial onto each segment orientation.
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Kinetic modeling
The kinetic modeling parts of the model simply assign masses and radii of gyration to
the segments defined in the kinematic model. An estimate of the position of the center
of mass is required in the segment. This is defined as a point at a given proportion
along a line from the distal joint center (normally the origin of the segment) towards
the proximal joint center of a "typical" segment. The masses of each segment are
calculated as a proportion of the total body mass. The principal axes moments of
inertia are calculated from (mass) normalized radii of gyration from these tables too. In
general the moment is considered to be zero around the longitudinal axis of most
segments. Since experimental data were not available, estimates have been made for
the radii of gyration of the pelvis and thorax. You can change these values in the
Properties pane of the Process Dynamic Plug-in Gait Model pipeline operation.
The following diagram shows the kinetic hierarchy.
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Note that the clavicles are not considered to have mass in themselves, so reactions for
the humerus segments are consider to act directly on the thorax.
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The feet are only 'connected' to the forceplates where forceplate measurements and
marker data indicate a match. Only one segment is chosen to be in contact with a
given forceplate for each frame.
Note also that the "untortioned" tibiae are used for the kinetic modeling. This means
that where the KAD and a tibial torsion have been used, and the proximal frame is
chosen to reference the ankle moments, the flexion and abduction moments will not
correspond to the axes used to calculate the ankle angles. Having said that, the axes
are calculated with a "floating axis" definition, so even for corresponding segments the
axes will not be coincident.
Even though the "untortioned" tibiae are used for the reference frames, a difference in
moments will be observed if the trial is processed with a different tibial torsion. When
the tibial torsion is applied in the static trial, the ankle joint center is moved backwards,
then the "untortioned" tibia is calculated by rotating the tortioned tibia round the Z
axis, keeping the ankle joint center in position. Thus, for a given trial, as tibial torsion is
increased, and the joint center is rotated backwards around the ankle marker, the ankle
flexion moment will generally become more positive.
Segment
CoM
Mass
Radius of gyration
Pelvisa
0.895
0.142
0.31
Femur
0.567
0.1
0.323
Tibia
0.567
0.0465
0.302
Foot
0.5
0.0145
0.475
Humerus
0.564
0.028
0.322
Radius
0.57
0.016
0.303
Handb
0.6205
0.006
0.223
Thoraxc
0.63
0.355
0.31
Headd
see below
0.081
0.495
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a) Pelvis: The center of mass is defined along a line from the midpoint of the hip joint
centers, to the center of the top surface of the Lumbar 5 vertebra. For simplified
scaling, this distance is defined as 0.925 times the distance between the hip joint
centers, and the Lumbar5 is defined as lying directly on the Z axis (derived by
inspection from the bone mesh used in Polygon). The radius of gyration for the pelvis is
an estimate, and is applied round all three axes.
b) Hand: The length of the hand in this model is defined as the distance from the wrist
joint center to the finger tip. An estimate of 0.75 is taken as the proportion of this
length to the "Knuckle II" reference point referred to in the Dempster data on page 104.
c) Thorax: The thorax length is taken as the distance between an approximation to the
C7 vertebra and the L5 vertebra in the Thorax reference frame. C7 is estimated from the
C7 marker, and offset by half a marker diameter in the direction of the X axis. L5 is
estimated from the L5 provided from the pelvis segment, but localized to the thorax,
rather than the pelvis. The positions are calculated for all frames in the trial, and
averaged to give the mean length. The Center of mass is deemed to lie at a proportion
of 0.63 along this line.
d) Head: The center of mass of the head is defined as being 0.52 * the distance from
the front to the back of the head along the X axis from the head origin (the midpoint of
the front head markers). The length of the head used for the inertial normalization is
the distance from this point to the C7 vertebra (the mean position localized to the head
segment). The inertia value for the head is applied around all three axes.
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Whole body center of mass
The center of mass is calculated whenever the head or thorax segment is present. A
weighted sum of all the centers of mass of all the segments is made, where segments
are defined by markers. The sum is still made if segments, such as the hands, for
example, do not have markers. The center of mass is the center of mass of all the
modeled segments.
Caution
Note that this center of mass algorithm has not been clinically tested, and
may be misleading in some clinical situations. In particular, the thorax
segment is modeled kinetically as a rigid body which includes the mass of the
abdomen (which is not independently modeled). The markers which define the
thorax are at the top of the thorax, and the center of mass is assumed to be
on a line directed towards the L5 vertebra. Any bending of the trunk in the
upper lumbar region will cause this assumption to fail, which may cause a
significant error in the position of the center of mass for the whole body.
The projection of the center of mass onto the floor is made simply by setting the Z
value to zero.
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Plug-in Gait output angles
The output angles for all joints are calculated from the YXZ Cardan angles derived by
comparing the relative orientations of the segments proximal (parent) and distal (child)
to the joint.
The knee angles are calculated from the femur and the Untorsioned tibia segments,
while the ankle joint angles are calculated from the Torsioned tibia and the foot
segment.
In the case of the feet, because they are defined in a different orientation to the tibia
segments, an offset of 90 degrees is added to the flexion angle. This does not affect
the Cardan angle calculation of the other angles because the flexion angle is the first
in the rotation sequence.
The progression angles of the feet, pelvis, thorax and head are the YXZ Cardan
calculated from the rotation transformation of the subject's progression frame for the
trial onto each segment orientation.
The following topics provide further details.
Angle definitions on page 75
Plug-in Gait kinematic variables on page 78
Upper body angles as output from Plug-in Gait on page 88
Lower body angles as output from Plug-in Gait on page 93
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Angle definitions
Plug-in Gait uses Cardan angles, modified in the case of the ankle angles, to represent
both:
Absolute rotations of the pelvis and foot segments and
Relative rotations at the hip, knee, and ankle joints
These angles can be described either as a set of rotations carried out one after the
other (ordered).
For more information about the use of Cardan angles to calculate joint kinematics,
refer to Kadaba, Ramakrishnan and Wooten (1990) and Davis, Õunpuu, Tyburski and
Gage (1991) (see Plug-in Gait references).
The rotations are measured about anatomical axes in order to simplify their
interpretation.
For more information on joint angle descriptions, including the issues of gimbal lock
and Codman's Paradox, see:
Ordered rotations on page 75
Angle goniometric description on page 76
Ordered rotations
To describe an angle using ordered rotations, the following are true:
One element is 'fixed'. For absolute rotations the laboratory axes are fixed. The
proximal segment axes are fixed for relative rotations.
The second element 'moves'. This means the segment axes move for absolute
rotations and distal segment moves for relative rotations.
A joint angle is then defined using the following ordered rotations:
The first rotation (flexion) is made about the common flexion axis. The other two
axes, abduction and rotation, are afterwards no longer aligned in the two elements.
The second rotation (abduction) is made about the abduction axis of the moving
element. The third rotation (rotation) is made about the rotation axis of the moving
element.
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Angle goniometric description
In addition to using ordered rotations, joint angles can also be described using
goniometric information. Using goniometric definitions, a joint angle is described by
the following:
Flexion is about the flexion axis of the proximal (or absolute) element.
Rotation is about the rotation axis of the distal element.
Abduction axis 'floats' so as always to be at right angles to the other two.
Cardan angles work well unless a rotation approaching 90 degrees brings two axes into
line. When this happens, one of the possible rotations is lost and becomes
unmeasurable. Fortunately, this does not frequently occur in the joints of the lower
limbs during normal or pathological gait. However this may occur in the upper limb and
particularly at the shoulder. For more information, see Gimbal lock on page 76 and
also Codman's Paradox on page 76 below.
Gimbal lock
Gimbal lock occurs when using Cardan (Euler) angles and any of the rotation angles
becomes close to 90 degrees, for example, lifting the arm to point directly sideways or
in front (shoulder abduction about an anterior axis or shoulder flexion about a lateral
axis respectively). In either of these positions the other two axes of rotation become
aligned with one another, making it impossible to distinguish them from one another, a
singularity occurs and the solution to the calculation of angles becomes unobtainable.
For example, assume that the humerus is being rotated in relation to the thorax in the
order Y,X,Z and that the rotation about the X-axis is 90 degrees.
In such a situation, rotation in the Y-axis is performed first and correctly. The X-axis
rotation also occurs correctly BUT rotates the Z axis onto the Y axis. Thus, any rotation
in the Y-axis can also be interpreted as a rotation about the Z-axis.
True gimbal lock is rare, arising only when two axes are close to perfectly aligned.
Codman's Paradox
The second issue however, is that in each non-singular case there are two possible
angular solutions, giving rise to the phenomenon of "Codman's Paradox" in anatomy
(Codman, E.A. (1934). The Shoulder. Rupture of the Supraspinatus Tendon and other
Lesions in or about the Subacromial Bursa. Boston: Thomas Todd Company), where
different combinations of numerical values of the three angles produce similar physical
orientations of the segment. This is not actually a paradox, but a consequence of the
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non-commutative nature of three-dimensional rotations and can be mathematically
explained through the properties of rotation matrices (Politti, J.C., Goroso, G.,
Valentinuzzi, M.E., & Bravo, O. (1998). Codman's Paradox of the Arm Rotations is Not a
Paradox: Mathematical Validation. Medical Engineering & Physics, 20, 257-260).
Codman proposed that the completely elevated humerus could be shown to be in
either extreme external rotation or in extreme internal rotation by lowering it either in
the coronal or sagittal plane respectively, without allowing any rotation about the
humeral longitudinal axis.
To demonstrate Codman's Paradox, complete the following steps:
1. Place the arm at the side, elbow flexed to 90 degrees and the forearm internally
rotated across the stomach.
2. Elevate the arm 180 degrees in the sagittal plane.
3. Lower the arm 180 degrees to the side in the coronal plane.
Observe that the forearm now points 180 degrees externally rotated from its
original position with no rotation about the humeral longitudinal axis actually
having occurred.
4. Note the difficulty in describing whether the fully elevated humerus was
internally or externally rotated.
This ambiguity can cause switching between one solution and the other, resulting in
sudden discontinuities. A combination of gimbal lock and Codman's Paradox can lead
to unexpected results when joint modeling is carried out. In practice, the shoulder is
the only joint commonly analyzed that has a sufficient range of motion about all
rotation axes for these to be an issue. Generally, if you are aware of the reasons for the
inconsistent data, you can manipulate any erroneous results by adding 180 or 360
degrees.
As Plug-in Gait uses Cardan (Euler) angles in all cases to calculate joint angles, they are
subject to both Gimbal Lock in certain poses, and the inconsistencies that occur as a
result of Codman's Paradox.
Plug-in Gait includes some steps to minimize the above effects by trying to keep the
shoulder angles in consistent and understandable quadrants. This is not a complete
solution however, as the above issues are inherent when using Cardan (Euler) angles
and clinical descriptions of motion.
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Plug-in Gait kinematic variables
When gait cycle events have been defined, derived kinematic quantities are calculated
and written to file.
Note that throughout this section, axes are described as follows:
Transverse axes are those axes which pass from one side of the body to the other;
Sagittal axes pass from the back of the body to the front; and
Frontal axes pass in a direction from the center of the body through the top of the
head.
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List of kinematic variables calculated by Plug-in Gait
The following table lists all the kinematic variables calculated by Plug-in Gait. It
includes information describing each variable in terms of ordered rotations or
goniometric definitions.
For example, knee rotation is a relative angle measured between the thigh as the
proximal segment and the shank as the distal segment. Its 'goniometric' axis is fixed to
the shank as the distal segment. Incidentally, this angle, although always calculated, is
often omitted from reports because it is so difficult to measure with precision.
Foot rotation and foot progression, also known as foot alignment, are not expressed in
terms of goniometric axes, since the ankle angles are not calculated as strict Cardan
angles. Both rotations measure the alignment of the foot. The first is relative to the
shank, and the second is measured as an absolute angle in the laboratory's transverse
plane.
Absolute angles are measured relative to laboratory axes with the sagittal and
transverse axes automatically selected according to the direction of walking. In Plug-in
Gait, the laboratory axis closest to the subject's direction of progression is labeled the
laboratory sagittal axis.
Each variable is listed in the following table:
Angle
Goniometric
Description
Absolute
Pelvic tilt is normally calculated about the laboratory's
rotation
Pelvic tilt
transverse axis. If the subject's direction of forward
progression is closer to the laboratory's sagittal axis,
however, then pelvic tilt is measured about this axis.
The sagittal pelvic axis, which lies in the pelvis
transverse plane, is normally projected into the
laboratory sagittal plane. Pelvic tilt is measured as the
angle in this plane between the projected sagittal
pelvic axis and the sagittal laboratory axis. A positive
value (up) corresponds to the normal situation in
which the PSIS is higher than the ASIS.
Pelvic
obliquity
Absolute
Pelvic obliquity is measured about an axis of rotation
perpendicular to the axes of the other two rotations.
This axis does not necessarily correspond with any of
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Angle
Goniometric
Description
rotation
the laboratory or pelvic axes. Pelvic obliquity is
measured in the plane of the laboratory transverse
axis and the pelvic frontal axis. The angle is measured
between the projection into the plane of the
transverse pelvic axis and projection into the plane of
the laboratory transverse axis (the horizontal axis
perpendicular to the subject's axis of progression). A
negative pelvic obliquity value (down) relates to the
situation in which the opposite side of the pelvis is
lower.
Pelvic
Absolute
rotation
Pelvic rotation is calculated about the frontal axis of
the pelvic co-ordinate system. It is the angle
measured between the sagittal axis of the pelvis and
the sagittal laboratory axis (axis closest to subject's
direction of progression) projected into the pelvis
transverse plane. A negative (external) pelvic rotation
value means the opposite side is in front.
Hip flexion
Relative
/extension
Hip flexion is calculated about an axis parallel to the
pelvic transverse axis which passes through the hip
joint centre. The sagittal thigh axis is projected onto
the plane perpendicular to the hip flexion axis. Hip
flexion is then the angle between the projected
sagittal thigh axis and the sagittal pelvic axis. A
positive (Flexion) angle value corresponds to the
situation in which the knee is in front of the body.
Hip ab
/adduction
Relative
Hip adduction is measured in the plane of the hip
flexion axis and the knee joint centre. The angle is
calculated between the long axis of the thigh and the
frontal axis of the pelvis projected into this plane. A
positive number corresponds to an adducted (inwardly
moved) leg.
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Angle
Goniometric
Description
Relative
Hip rotation is measured about the long axis of the
rotation
Hip
rotation
thigh segment and is calculated between the sagittal
axis of the thigh and the sagittal axis of the pelvis
projected into the plane perpendicular to the long axis
of the thigh. The sign is such that a positive hip
rotation corresponds to an internally rotated thigh.
Knee
Relative
The sagittal shank axis is projected into the plane
flexion
perpendicular to the knee flexion axis. Knee flexion is
/extension
the angle in that plane between this projection and
the sagittal thigh axis. The sign is such that a positive
angle corresponds to a flexed knee.
Knee ab
Relative
This is measured in the plane of the knee flexion axis
/adduction
and the ankle center, and is the angle between the
(Knee
long axis of the shank and the long axis of the thigh
valgus
projected into this plane.
/varus)
A positive number corresponds to varus (outward
bend of the knee).
Knee
Relative
rotation
Knee rotation is measured about the long axis of the
shank. It is measured as the angle between the
sagittal axis of the shank and the sagittal axis of the
thigh, projected into a plane perpendicular to the long
axis of the shank. The sign is such that a positive
angle corresponds to internal rotation. If a tibial
torsion value is present in the Session form, it is
subtracted from the calculated knee rotation value. A
positive tibial torsion value therefore has the effect of
providing a constant external offset to knee rotation.
Ankle dorsi
Relative
The foot vector is projected into the foot sagittal
/plantar
plane. The angle between the foot vector and the
flexion
sagittal axis of the shank is the foot dorsi/plantar
flexion. A positive number corresponds to dorsiflexion.
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Angle
Goniometric
Description
rotation
Foot
Relative
rotation
This is measured about an axis perpendicular to the
foot vector and the ankle flexion axis. It is the angle
between the foot vector and the sagittal axis of the
shank, projected into the foot transverse plane. A
positive number corresponds to an internal rotation.
Foot-based
This optional angle is defined similarly to ankle dorsi
dorsi
/plantar flexion, but it is measured in a plane
/plantar
containing the knee and ankle centers and the toe
flexion
marker.
Foot
Absolute
progression
This is the angle between the foot vector (projected
into the laboratory's transverse plane) and the sagittal
laboratory axis. A positive number corresponds to an
internally rotated foot.
Head tilt
Absolute
Head tilt is normally calculated about the laboratory's
transverse axis. If the subject's direction of forward
progression is closer to the laboratory's sagittal axis,
however, then head tilt is measured about this axis.
The sagittal head axis is normally projected into the
laboratory sagittal plane. Head tilt is measured as the
angle in this plane between the projected sagittal
head axis and the sagittal laboratory axis. A positive
value (up) corresponds to forward head tilt.
Head
obliquity
Absolute
Head lateral tilt is measured about an axis of rotation
perpendicular to the axes of the other two rotations.
This axis does not necessarily correspond with any of
the laboratory or head axes. Head lateral tilt is
measured in the plane of the laboratory transverse
axis and the head frontal axis. The angle is measured
between the projection into the plane of the
transverse head axis and projection into the plane of
the laboratory transverse axis (the horizontal axis
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Angle
Goniometric
Description
rotation
perpendicular to the subject's axis of progression). A
negative head obliquity value (down) relates to the
situation in which the opposite side of the head is
lower.
Head
Absolute
rotation
Head rotation is calculated about the frontal axis of
the head co-ordinate system. It is the angle measured
between the sagittal axis of the head and the sagittal
laboratory axis (axis closest to subject's direction of
progression) projected into the head transverse plane.
A negative (external) head rotation value means the
opposite side is in front.
Thorax tilt
Absolute
Thorax tilt is normally calculated about the
laboratory's transverse axis. If the subject's direction
of forward progression is closer to the laboratory's
sagittal axis, however, then thorax tilt is measured
about this axis. The sagittal thorax axis is normally
projected into the laboratory sagittal plane. Thorax tilt
is measured as the angle in this plane between the
projected sagittal thorax axis and the sagittal
laboratory axis. A positive value (up) corresponds to
forward thorax tilt.
Thorax
obliquity
Absolute
Thorax obliquity is measured about an axis of rotation
perpendicular to the axes of the other two rotations.
This axis does not necessarily correspond with any of
the laboratory or thorax axes. Thorax obliquity is
measured in the plane of the laboratory transverse
axis and the Thorax frontal axis. The angle is
measured between the projection into the plane of
the transverse thorax axis and projection into the
plane of the laboratory transverse axis (the horizontal
axis perpendicular to the subject's axis of progression.
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Angle
Goniometric
Description
rotation
As the thorax segment is defined with the frontal Z
axis point downward a positive (up) thorax obliquity
angle relates to the situation in which the opposite
side of the thorax is lower.
Thorax
Absolute
rotation
Thorax rotation is calculated about the frontal axis of
the thorax co-ordinate system. It is the angle
measured between the sagittal axis of the thorax and
the sagittal laboratory axis (axis closest to subject's
direction of progression) projected into the thorax
transverse plane. As the thorax segment is defined
with the frontal Z axis point downward a positive
(internal) thorax rotation value means the opposite
side is in front.
Neck
Relative
The sagittal head axis is projected onto the plane
flexion
perpendicular to the thorax sagittal axis. Neck flexion
/extension
is then the angle between the projected sagittal head
axis and the sagittal thorax axis around the fixed
transverse axis of the thorax. A positive (flexion) angle
value corresponds to the situation in which the head
is tilted forward.
Neck
Relative
The angle between the long axis of the head and the
lateral
long axis of the thorax around a floating transverse
flexion
axis.
Neck
rotation
Relative
Neck rotation is measured about the long axis of the
head. It is measured as the angle between the sagittal
axis of the head and the sagittal axis of the thorax,
around a floating frontal axis. As the thorax frontal
axis points downward while the head frontal axis
points upward, a positive angle therefore refers to
rotation of the head toward the opposite side.
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Angle
Goniometric
Description
Relative
Spine flexion is the angle between the sagittal thorax
rotation
Spine
flexion
axis and the sagittal pelvis axis around the fixed
/extension
transverse axis of the pelvis. A positive (flexion) angle
value corresponds to the situation in which the thorax
is tilted forward.
Spine
Relative
The angle between the long axis of the thorax and the
lateral
long axis of the pelvis, around a floating transverse
flexion
axis.
Spine
Relative
rotation
It is measured as the angle between the sagittal axis
of the thorax and the sagittal axis of the pelvis,
around a floating frontal axis. As the thorax frontal
axis points downward while the pelvis frontal axis
points upward, a positive angle therefore refers to
rotation of the thorax toward the opposite side.
Shoulder
Relative
Shoulder flexion is calculated about an axis parallel to
flexion
the thorax transverse axis. Shoulder flexion is the
/extension
angle between the projected sagittal-humerus axis
and the sagittal-thorax axis around the fixed
transverse axis. of the thorax. A positive (flexion)
angle value corresponds to the situation in which the
arm is in front of the body.
Shoulder ab
/adduction
Relative
The angle is calculated between the transverse axis of
the humerus and the transverse axis of the thorax
around a floating sagittal axis. A negative number
corresponds to an abducted (outwardly moved) arm.
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Angle
Goniometric
Description
Relative
Shoulder rotation is measured about the long axis of
rotation
Shoulder
rotation
the humerus segment and is calculated between the
sagittal axis of the humerus and the sagittal axis of
the thorax around a floating frontal axis. The sign is
such that a positive shoulder rotation corresponds to
an internally rotated humerus.
Elbow
Relative
Elbow flexion is the only kinematic parameter
flexion
calculated at the elbow as the segment definitions of
/extension
the Humerus and radius result in two of the axes
being shared. Elbow flexion is calculated between the
sagittal radius axis and the sagittal humerus axis
around the fixed transverse axis of the humerus. A
positive number indicates a flexion angle.
Wrist
Relative
Wrist flexion is the angle between the sagittal hand
flexion
axis and the sagittal radius axis around the fixed
/extension
transverse axis of the radius. A positive (flexion) angle
value corresponds to the situation in which the wrist
bends toward the palm.
Wrist ab
Relative
/adduction
The angle is calculated between the transverse axis of
the hand and the transverse axis of the radius around
a floating sagittal axis. A positive number corresponds
to the hand abducting toward the thumb.
Wrist
rotation
Relative
Wrist rotation is measured about the long axis of the
hand segment and is calculated between the sagittal
axis of the hand and the sagittal axis of the radius
around a floating frontal axis. The sign is such that a
positive wrist rotation corresponds to the hand
rotating in the direction of the thumb.
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For more information, see also:
Complete pelvis position description
A pelvis in which the three markers all lay in the horizontal plane and the line joining
the ASIS markers was parallel to a laboratory axis, would have zero tilt, obliquity and
rotation.
To visualize the pelvic angles, start with a pelvis in this neutral position, tilt it about the
transverse axis by the amount of pelvic tilt, rotate it about its (tilted) sagittal axis by the
amount of pelvic obliquity and rotate it about its (tilted and oblique) frontal axis by the
amount of pelvic rotation. The pelvis is now in the attitude described by those degrees
of tilt, obliquity and rotation.
The transverse and frontal plane kinematics of all joints are influenced by the
mathematics involved with embedded axes. The following is an example which
demonstrates the effect of using embedded axes to calculate "pelvic obliquity" in a
static trial: If a calibration device, designed with 15 degrees of pelvic tilt and level ASIS
markers, is statically rotated 20 degrees from a lab's axis of progression, a report
generated by Plug-in Gait will show 10 degrees of pelvic obliquity. For more clarification
about the effect of embedded axes on joint kinematics, refer to Kadaba, Ramakrishnan
and Wooten (1990).
Complete hip position description
A thigh whose long axis was parallel to the frontal pelvic axis, and in which the knee
flexion axis was parallel to the pelvic transverse axis, would be in the neutral position
(described by zeroes in all three angles). To move from this neutral position to the
actual thigh position described by the three angles, first flex the hip by the amount of
the hip flexion, then adduct by the amount of hip adduction, then rotate the thigh
about the (flexed and adducted) long axis of the thigh, and it is in the position
described by those three angles.
Complete knee position description
A neutral shank is positioned such that the shank is in line with the thigh and the ankle
flexion axis is parallel to the knee flexion axis. From this position, flex the knee by the
amount of knee flexion, bend inward by the amount of valgus/varus, and rotate by the
amount of knee rotation, to produce the actual position described by those three
angles.
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Upper body angles as output from Plug-in Gait
The following tables display the upper body segment angles from Plug-in Gait.
All upper body angles are calculated in rotation order YXZ.
As Euler angles are calculated, each rotation causes the axis for the subsequent
rotation to be shifted. X’ indicates an axis which has been acted upon and shifted by
one previous rotation, X’’ indicates a rotation axis which has been acted upon and
shifted by two previous rotations.
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Left upper body angles
Angles
LHeadAngles
LThoraxAngles
LNeckAngles
LSpineAngles
LShoulderAngles
LElbowAngles
Vicon Motion Systems Ltd.
Positive rotation
Axis
Direction
1
Backward Tilt
Prg.Fm. Y
Clockwise
2
Right Tilt
Prg.Fm. X'
Anti-clockwise
3
Right Rotation
Prg.Fm. Z''
Clockwise
1
Backward Tilt
Prg.Fm. Y
Clockwise
2
Right Tilt
Prg.Fm. X'
Anti-clockwise
3
Right Rotation
Prg.Fm. Z''
Clockwise
1
Forward Tilt
Thorax Y
Clockwise
2
Left Tilt
Thorax X'
Clockwise
3
Left Rotation
Thorax Z''
Clockwise
1
Forward Thorax Tilt
Pelvis Y
Anti-Clockwise
2
Left Thorax Tilt
Pelvis X'
Clockwise
3
Left Thorax Rotation
Pelvis Z''
Anti-Clockwise
1
Flexion
Thorax Y
Anti-clockwise
2
Abduction
Thorax X'
Anti-clockwise
3
Internal Rotation
Thorax Z''
Anti-clockwise
1
Flexion
Humeral Y
Anti-clockwise
2
-
Humeral X'
-
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Angles
LWristAngles
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Positive rotation
Axis
Direction
3
-
Humeral Z''
-
1
Ulnar Deviation
Radius X
Clockwise
2
Extension
Radius Y'
Clockwise
3
Internal Rotation
Radius Z''
Clockwise
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Right upper body angles
Angles
RHeadAngles
RThoraxAngles
RNeckAngles
RSpineAngles
RShoulderAngles
RElbowAngles
Vicon Motion Systems Ltd.
Positive rotation
Axis
Direction
1
Backward Tilt
Prg.Fm. Y
Clockwise
2
Left Tilt
Prg.Fm. X'
Clockwise
3
Left Rotation
Prg.Fm. Z''
Anti-clockwise
1
Backward Tilt
Prg.Fm. Y
Clockwise
2
Left Tilt
Prg.Fm. X'
Clockwise
3
Left Rotation
Prg.Fm. Z''
Anti-clockwise
1
Forward Tilt
Thorax Y
Clockwise
2
Right Tilt
Thorax X'
Anti-clockwise
3
Right Rotation
Thorax Z''
Anti-clockwise
1
Forward Thorax Tilt
Pelvis Y
Anti-Clockwise
2
Right Thorax Tilt
Pelvis X'
Anti-clockwise
3
Right Thorax Rotation
Pelvis Z''
Clockwise
1
Flexion
Thorax Y
Anti-clockwise
2
Abduction
Thorax X'
Clockwise
3
Internal Rotation
Thorax Z''
Clockwise
1
Flexion
Humeral Y
Clockwise
2
-
Humeral X'
-
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Angles
RWristAngles
Vicon Motion Systems Ltd.
Positive rotation
Axis
Direction
3
-
Humeral Z''
-
1
Ulnar Deviation
Radius X
Anti-clockwise
2
Extension
Radius Y'
Clockwise
3
Internal Rotation
Radius Z''
Anti-clockwise
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Lower body angles as output from Plug-in Gait
The following tables display the lower body segment angles from Plug-in Gait.
All lower body angles are calculated in rotation order YXZ except for ankle angles,
which are calculated in order YZX.
As Euler angles are calculated, each rotation causes the axis for the subsequent
rotation to be shifted. X’ indicates an axis which has been acted upon and shifted by
one previous rotation, X’’ indicates a rotation axis which has been acted upon and
shifted by two previous rotations.
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Left lower body angles
Angles
LPelvisAngles
LFootProgressAngles
LHipAngles
LKneeAngles
LAnkleAngles
Vicon Motion Systems Ltd.
Positive rotation
Axis
Direction
1
Anterior Tilt
Prg.Fm. Y
Anti-clockwise
2
Upward Obliquity
Prg.Fm. X'
Anti-clockwise
3
Internal Rotation
Prg.Fm. Z''
Clockwise
1
-
Prg.Fm. Y
-
2
-
Prg.Fm. X'
-
3
Internal Rotation
Prg.Fm. Z''
Clockwise
1
Flexion
Pelvis Y
Clockwise
2
Adduction
Pelvis X'
Clockwise
3
Internal Rotation
Pelvis Z''
Clockwise
1
Flexion
Thigh Y
Anti-clockwise
2
Varus/Adduction
Thigh X'
Clockwise
3
Internal Rotation
Thigh Z''
Clockwise
1
Dorsiflexion
Tibia Y
Clockwise
2
Inversion/ Adduction
Tibia X''
Clockwise
3
Internal Rotation
Tibia Z'
Clockwise
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Right lower body angles
Angles
RPelvisAngles
RFootProgressAngles
RHipAngles
RKneeAngles
RAnkleAngles
Vicon Motion Systems Ltd.
Positive rotation
Axis
Direction
1
Anterior Tilt
Prg.Fm. Y
Anti-clockwise
2
Upward Obliquity
Prg.Fm. X'
Clockwise
3
Internal Rotation
Prg.Fm. Z''
Anti-clockwise
1
-
Prg.Fm. Y
-
2
-
Prg.Fm. X'
-
3
Internal Rotation
Prg.Fm. Z''
Anti-clockwise
1
Flexion
Pelvis Y
Clockwise
2
Adduction
Pelvis X'
Anti-clockwise
3
Internal Rotation
Pelvis Z''
Anti-clockwise
1
Flexion
Thigh Y
Anti-clockwise
2
Varus/Adduction
Thigh X'
Anti-clockwise
3
Internal Rotation
Thigh Z''
Anti-clockwise
1
Dorsiflexion
Tibia Y
Clockwise
2
Inversion/ Adduction
Tibia X''
Anti-clockwise
3
Internal Rotation
Tibia Z'
Anti-clockwise
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Plug-in Gait output specification
The following topics provide definitions to enable you to reliably reconstruct the
segment co-ordinate systems using Plug-in Gait outputs in third-party modeling
software.
Global (laboratory) co-ordinate system on page 97
Pelvis on page 98
Femur on page 99
Tibia on page 100
Foot on page 101
Joint kinematic definitions on page 102
Joint kinetics on page 103
The Plug-in Gait model consists of seven segments (including the left and right side):
Pelvis
Femur (left and right)
Tibia (left and right)
Feet (left and right)
When Plug-in Gait Static calculations are performed, a scaling length for each of the 7
segments is written to the subject's .mp file.
The Plug-in Gait Dynamic process outputs joint kinematics and kinetics to a .c3d file,
which also defines them in terms of their order and sign conventions.
For information about the definition of the Plug-in Gait model itself and the algorithms
used to locate the segment co-ordinate systems and calculate the segment lengths
from skin fixed marker data, see Plug-in Gait kinematic and kinetic calculations on page
43. The marker names used here are from the standard Plug-in Gait marker
definitions. For precise definitions of their location, see Plug-in Gait models and
templates on page 5.
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Global (laboratory) co-ordinate system
The laboratory co-ordinate system is required here as a reference for the pelvis
kinematics. The lab system is also used later in the definition of the foot co-ordinate
frame.
The global Z axis defines the vertical, i.e. perpendicular to the lab floor.
The global X and Y axes are in the plane of the lab floor, with X often defining the
direction if normal walking along the laboratory walkway.
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Pelvis
The origin of the pelvis co-ordinate system in Plug-In Gait is the midpoint of the vector
connecting the two asis landmarks (LASI and RASI). The co-ordinate system of the
pelvis is reconstructed from the surface markers on the ASIS and PSIS landmarks, but
should be considered to be related to the bony geometry of the pelvis as follows.
The Y axis is lateral (to the left) and is directed from the right hip joint centre (RHJC) to
the left hip joint centre (LHJC), where the HJC are defined as the centre of the
spherical part of the femoral head:
The Z axis is then perpendicular to Y and the vector between the sacrum (SACR) and
the midpoint of the asis landmarks:
where:
(The sacral marker is not always used, and this landmark can be calculated as being at
the midpoint of the vector connecting the LPSI and RPSI markers).
The X axis is naturally the cross product of the Y and Z pelvis axes:
In the Plug-in Gait model, the pelvis Y axis is assumed to be parallel to the vector
between the LASI and RASI markers, but the definition above is more suitable when
constructing a co-ordinate system from known hip joint centers.
The length of the pelvis segment calculated by the Plug-in Gait model is equal to the
inter-hip distance:
Plug-in Gait also outputs the inter-asis distance, which can also be used to assist in
reconstruction of the morphology of the pelvis.
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Femur
The accuracy/validity of the femoral coordinate system is affected by the estimation of
the knee joint center location as well as the knee flexion extension axis. These two
estimations are reliant upon your providing accurate marker placement and subject
measurements.
The co-ordinate axes are aligned with the long axis of the femurs and the knee flexion
axes as follows.
The Z axis of the femur is directed from the knee joint center to the hip joint center:
The X axis is anterior and is perpendicular to the knee flexion axis,
:
Finally, the Y axis is lateral (to the left for both legs) and is given by:
The scaling length of the femur is simply the distance from the knee joint center to the
hip joint center:
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Tibia
The Tibia effectively has two co-ordinate systems: a proximal one for calculating knee
joint angles and a distal one for calculating ankle joint angles.
Both segments have their origins at the ankle joint center (AJC) and are defined in a
manner similar to the femoral segments. Again, the location of the ankle joint center
and ankle flexion axis calculated by Plug-in Gait are reliant upon your providing
accurate marker placement and subject measurements.
Firstly, the proximal system uses the knee joint center, ankle joint center and the knee
flexion axis,
:
The distal coordinate system is then rotated about the long axis of the tibia (Z) such
that it is aligned with the ankle flexion axis,
:
The scaling length of the tibia is the distance from the ankle joint center to the knee
joint center:
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Foot
The origin of the foot segments of the Plug-in Gait model is located at the ankle joint
centers. The foot co-ordinate system is defined in a rather more complex manner
within the Plug-in Gait model than is necessary to recreate the motion of the bones
from the Plug-in Gait kinematics output.
Firstly, the system Z axis is equal to the vector from the toe to heel markers (HEE and
TOE), projected into the plane of the laboratory floor (X-Y plane):
Where:
The X axis is then perpendicular to this and the ankle flexion axis and is directed
vertically:
And finally, the Y axis is naturally the cross product of these two axes:
The scaling length of the foot is the distance from the ankle joint center to the toe
marker:
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Joint kinematic definitions
The following table specifies how the rotations within each of the joints of the model
are ordered as trajectories in the .c3d file.
Note
Angles are always given in the .c3d file as degrees.
For all of the joints, the joint co-ordinate system method of reporting kinematics has
been used to specify flexion, abduction, and rotation. It is difficult to give a consistent
definition of these angles for all of the joints due to the differing meaning of flexion
etc.
Instead, the axis in the proximal segment embedded co-ordinate system about which
each of the rotations takes place (together with the order these rotations should be
applied) is given in the following table showing Euler angle specification:
Joint
1st Component
2nd Component
3rd Component
Order
Global Pelvis
Tilt (Y)
Obliquity (X)
Rotation (-Z)
1,2,3
Left Hip
Flexion (-Y)
Adduction (-X)
Rotation (-Z)
1,2,3
Left Knee
Flexion (Y)
Adduction (-X)
Rotation (-Z)
1,2,3
Left Ankle
Flexion (-Y)1
Inversion (Z)
Rotation (X)
1,3,2
Right Hip
Flexion (-Y)
Adduction (X)
Rotation (Z)
1,2,3
Right Knee
Flexion (Y)
Adduction (X)
Rotation (Z)
1,2,3
Right Ankle
Flexion (-Y)1
Inversion (-Z)
Rotation (-X)
1,3,2
1. The feet segments are peculiar to the rest of the model, not only because of the
different rotation order, but also because the orientation of the foot at zero
degrees flexion is straight upwards, that is, the toe will point towards the knee.
An offset of +90 degrees should be applied in order to point the foot forwards.
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Joint kinetics
The output from Plug-in Gait also contains forces, moments and powers for each of the
segments.
Note
Forces, moments and powers are given in the .c3d file in Newtons, Newtonmeters and Watts respectively.
For both forces and moments, the reaction frame can be specified within Plug-in Gait
to be proximal, distal, or in the global frame.
For each of the forces, the components in the .c3d file match the co-ordinate
directions described in this document. For the moments, however, the order they are
stored in the .c3d file matches the rotation order shown in the table in Joint kinematic
definitions on page 102, and therefore do not correspond to any of the segment
embedded co-ordinate systems.
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The following table lists the components of the moments in terms of the axes about
which they act.
Joint
1st Component
2nd Component
3rd Component
Left hip
-Y
X
Z
Left knee
Y
X
Z
Left ankle (prox.)1
Y
X
Z
Left ankle (dist.)1
Y
Z
-X
Right hip
-Y
-X
-Z
Right knee
Y
-X
-Z
Right ankle (prox.)1
Y
-X
-Z
Right ankle (dist.)1
Y
-Z
X
1. Due to the differing alignment of the foot and tibia segment co-ordinate
systems, the components of the ankle moment differ depending on whether they
are represented in the proximal, distal or global co-ordinate systems.
References
Dempster, WT. (1955) Space requirements of the seated operator. WADC Technical
Report 55–159, Wright-Patterson Air Force Base, OH.
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