Physik Instrumente PI TEC66 Kinematics Of Multi Axis Tip Tilt Systems

PI-TEC66-Kinematics-of-Multi-Axis-TipTilt-Systems Piezo Positioning Systems with Parallel Kinematics

User Manual: Physik Instrumente Piezo Positioning Systems with Parallel Kinematics

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Kinematics of Multi-Axis Tip/Tilt Systems

Piezo tip/tilt mirror systems from PI are based on parallel kinematics with a single movable
platform for all directions of motion. The systems achieve a higher linearity than can be
attained by switching two single-axis systems in succession, as is the case with galvanoscanners, for example, and therefore, are very compact.

Horse head nebula
(Photo: Brian Lula)

The tilt angle and
the travel in Z are
calculated using the
following formulas:

θX

θY = 2A –

θY

(B+C)
2a

θX =

(B-C)
b

Z=

(A+B+C)
3

A, B, C is the linear
displacement of the
relevant actuators.

Arrangement of the actuators of a tripod piezo drive

They allow for an optical beam deflection up
to 100 mrad, extremely short response times
from milliseconds to microseconds and resolutions down to nanoradians.

The platform is driven by two pairs of piezo
actuators located in 90° angles to one another.
Four actuators are controlled differentially in
pairs, depending on the tilt direction. The tilt
axes θX and θY are arranged orthogonally so
that a coordinate transformation is not necessary.

PI offers a large range from compact systems
for laser beam steering up to large units used
for astronomy.

This concludes in an excellent stability in linear
and angular positioning for a wide temperature range.

Tip/Tilt System with Tripod Piezo Drive
The platform is driven by three piezo actuators
that are located in 120° angles to one another.
By means of coordinate transformation, the
motion can be split among the different actuators.

Just as the tripod, the differential version guarantees an optimum angular stability over a
large temperature range. For position controlled versions, the differential evaluation of
two sensors per axis provides an improved
linearity and resolution.

In addition to tilting, the platform may also be
used linearly in Z direction, which is important,
for example, for correcting optical path lengths
(phase shifters).

WWW.PI.WS

Piezo

Tip/Tilt System with Differential Piezo Drive
(Tetrapod)

Piezo

Piezo-actuated tip/tilt mirrors and platforms
are suitable both for highly dynamic operation,
such as tracking, scanning, image stabilization,
elimination of drift and vibration, and for static
positioning of optical systems and samples.

Principle of a tilt system with
differential piezo drive

Dynamics of a Piezo Tip/Tilt Mirror

The maximum operating frequency of a piezo
tip/tilt system strongly depends on its mechanical resonant frequency. The properties
of amplifier, controller and sensor are also
important. To estimate the effective resonant
frequency of the system – a combination of
platform and mirror – it is necessary to calculate the moment of inertia of the mirror substrate first.
Moment of inertia of a rotationally symmetric
mirror:
IM = m

[

2R2 + H2
12

+

(

H
2

)]

IM = m

[

12

+

+T

( )]
H
2

f' = m

f0
1 + IM/I0

Resonant frequency of a piezo tip/tilt system
with mirror
with:

2

Moment of inertia of a rectangular mirror:

L2 + H2

The resonant frequency of the system is calculated with resonant frequency of the platform
(see technical data) and moment of inertia of
the mirror substrate using the following formula:

2

+T

with:
m = mirror weight [g]
IM = moment of inertia of a mirror
[g × mm²]
L = mirror length orthogonally to tilt axis
[mm]
H = mirror thickness [mm]
T = distance of pivot point to platform surface
(see technical data of individual models)
[mm]
R = mirror radius [mm]

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f' = resonant frequency of platform with mirror [Hz]
f0 = resonant frequency of platform without
mirror [Hz]
I0 = moment of inertia of platform (see technical data) [g × mm²]]
IM = moment of inertia of mirror
[g × mm²]

|

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Although the information in this document has been compiled with
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we cannot guarantee for the information being complete, correct and
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TEC66 Kinematics of Multi-Axis Tip/Tilt Systems 10/2017 Subject to change without notice. © Physik Instrumente (PI) GmbH & Co. KG 2017

MOTION



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