Parallel Kinematics Piezo Positioning Systems

Characteristics

In multi-axis Piezo Positioning Systems (also known as parallel kinematic) you will find the following characteristics.

  • Actuators act directly on a single moving platform, thus designed to be more compact compared to serial stacked or nested systems.
  • All axes are able to be designed with identical dynamic properties, which considerably reduces the moved mass.
  • Available with up to 6 degrees of freedom and offer high dynamics over all axes due to minimal mass inertia.
  • Errors and masses of the individual axes are not cumulated.

Fixed Reference Parallel Metrology

A parallel kinematics designed multi-axis stage enables direct parallel metrology. This means measuring all degrees of freedom of the moving platform in relation to a fixed reference. Unintended crosstalk of the motion into a different axis, e.g., as a result of force, can thus be detected and actively corrected in real time. Even at dynamic operation active guiding allows high trajectory fidelity in the nanometer range.

Multi-Axis Tip/Tilt Systems Kinematics

Parallel kinematics that has a single movable platform for all directions of motion is known as a Piezo tip/tilt mirror system. By switching two single-axis systems in succession (e.g., as with galvanoscanners) these systems can achieve a higher linearity whilst remaining extremely compact.

These type of platforms are suitable for both highly dynamic operation (scanning, tracking, image stabilization, vibration and elimination of drift) and static positioning of optical systems and specimens. They allow for an optical beam deflection up to 100 mrad, extremely short response times of a few microseconds and resolutions down to the nano-radian range. If a Piezo Tip/Tilt system is something you’re considering for your application we have a range of compact systems for laser beam control up to large units used for astronomy.

Tripod Piezo Drive Tip/Tilt System

Driven by three piezo actuators that are located in 120° angles to one another means that by coordinate transformation, the motion can be split among the different actuators.

The platform can also be used linearly in Z direction (for example correcting optical path lengths (phase shifters)).

Calculate the tilt angle and the travel range in Z with the equation below. The linear displacement of the corresponding actuators are A, B and C

Tetrapod – Differential Piezo Drive Tip/Tilt System

Two pairs of piezo actuators located at 90° angles to one another drives this type of platform (also know as a Tetrapod). Each set of pairs are controlled differentially depending on the tilt direction. A coordinate transformation is not necessary as the tilt axes θX and θY are arranged orthogonally.

The result is excellent position/angle stability over a large temperature range. A tetrapods guarantees optimum angular stability over a large temperature range. The differential evaluation of two sensors per axis provides improved linearity and resolution with position controlled versions.

Tripod Piezo Drive Actuator Arrangement
Tilt System with Differential Piezo Drive Principle

Piezo Tip/Tilt Mirror Dynamics

The mechanical resonant frequency, amplifier, controller and sensor of the piezo tip/tilt system will determine the maximum operating frequency. To estimate the effective resonant frequency of the  combination of platform and mirror the moment of inertia of the mirror substrate must be calculated first.

Inertia symmetric mirror momentum formula
Inertia rectangular mirror moment formula

Mirror weight (g)IM Moment of inertia of the mirror (g x mm2)Length of the mirror orthogonal to the tilt axis (mm) | Thickness of mirror (mm)Distance rotating point platform surface (see technical data of the individual models) (mm)Radius of mirror (mm)

The following equation gives the system’s resonant frequency which is calculated based on the resonant frequency of the platform (refer to each products individual specification) and the moment of inertia of the mirror substrate.

Resonant frequency of a piezo tilt system with mirror

f’ Resonant Frequency of the Platform With Mirror (Hz)f0Resonant frequency of platform without mirror (Hz) |I0 Moment of inertia of platform (see technical data of the individual models) (g × mm²) | IM Moment of inertia of mirror (g × mm²)

* This page is a rendition with permission from our Supplier, Physik Insturmente GmbH, Piezo Positioning Systems with Parallel Kinematics page.

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