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MapleSim used to model motion of complex optical system

A team at Canadian Light Source used MapleSim as a modeling tool to determine the positioning of a six-strut kinematic mirror mount.

Canadian Light Source is a leading synchrotron research facility.

The model representing the six-strut kinematic mount was built in MapleSim. The equations describing the system were generated automatically from the model and were simplified by the Maple symbolic engine.

The results of the simulated motion of the motion actuators were used to get the induced position and orientation of the mirror. This information was then used as input for ray tracing.

“MapleSim is a highly useful simulation tool for complex systems and it can produce quick results with sufficient accuracy to be applicable to optical mounts that require precise positioning at the micron level,” said Alan Duffy at Canadian Light Source.

The motion of six-strut kinematic mounts is such that the arc of motion of the individual struts introduces cosine errors that cause minor coupling of otherwise independent axes.

As a result, the motion in any one direction may cause slight movement in another direction and also alter rotational orientation. Without a means of properly quantifying these changes in position and orientation, ray tracing results may not be truly accurate.

2-D schematic view of mirror tank subsystem with rigid body frames (i.e. displacements) attached to a rigid body.Figure A: 2-D schematic view of mirror tank subsystem with rigid body frames (i.e. displacements) attached to a rigid body.

MapleSim provided a means of inferring the actual positioning and orientation of these six-strut kinematic mounts as a function of the motors that control their movements.

A more realistic understanding of the operation of the six-strut system is useful for beamline alignment and improving performance.

The ultimate objective of the Canadian Light Source team is to create a real-time x-ray tracing of the system that uses the beamline control system to access the positions of optical components and then sends these as inputs to an x-ray tracing program.

The MapleSim model was built using domain specific palettes such as signal blocks or multi-body components. The struts were modeled using a 3-D rigid body, two rigid body frames, and two spherical joints from the multi-body library.

It was also possible to create an animation of the system in motion using STL files exported from CAD. Maple’s symbolic engine was utilised to perform model simplification, which allowed the governing equations to be reduced without any loss of fidelity.

2-D schematic view of strut subsystem (upper half) and 3-D graphical top-view of the constructed systemFigure B: 2-D schematic view of strut subsystem (upper half) and 3-D graphical top-view of the constructed system.

MapleSim allowed the re-use of systems by converting them to subsystems. The mirror tank is modeled as a rigid body with rigid body frames defining the displacement from the center of mass to the connection points where the struts are attached (left side of Figure A).

There is also an additional rigid body frame defining the displacement to the mirror pole (right side of Figure A).

An immediate application of the results is to use this positional information to mitigate cosine errors and improve ray tracing results and assist in alignment of the optical system.

3-D graphical view of MapleSim model in playback mode.Figure C: 3-D graphical view of MapleSim model in playback mode.

The simulation results were used to verify the vendor supplied look-up table (which provides mirror position and orientation as a function of motor actuator positions) and extend it to motor positions that were not included.

“MapleSim makes it easy to model the motion of a complex system without having to spend time deriving its equations of motion,” concluded Alan Duffy.

“It gave us accurate results, and fast simulations allowing us to see how the mirror would move in accordance with the motion of its actuators. MapleSim is an extremely useful and powerful modeling tool and has been very helpful.”

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