Design Optimization of MEMs Motion Arrays through Dynamic Simulation Dan Reznik, Stan Brown, and John Canny EECS Dept., UC-Berkeley Recently submitted ICRA'97 Paper

A Micro-Actuated Motion Array is a type of Micro Electro-Mechanical (MEM) device designed for the sensorless manipulation of objects a few milimiters in diameter. MEMs devices have been proposed for a number of applications including micromechanisms [1] and video displays [2].

Bohringer et al. [3] have designed and fabricated a motion array consisting of several thousand torsional resonators tiling up a surface of a few square cm in area. Each resonator oscillates at a frequency of a few KHz. Both linear and motion-pixel designs have been built. The former design can be used as a microscale conveyor-belt for part feeding while the latter can be used to synthesize arbitrary motion fields. For example, a squeeze-type field, made up of two opposing linear fields, has been suggested by Goldberg [4] for part orientation applications.

Difficulties in both implementation and testing of microscale motion arrays have been reflected in the lack of experimental results published as of yet. In particular, little is know about (1) the effectiveness of these devices for all but the simplest experiments, and (2) how their performance is affected by both operating conditions (e.g., part weight, part shape) and design parameters (e.g., resonator shape/density, oscillation frequencies, etc.). We address the above difficulties by proposing dynamic simulation as a viable tool for evaluating Bohringer's design effectiveness over a range of operating parameters. We make use of Mirtich's Impulse dynamic simulator [5] for the purposes of modeling and computation. The questions we ask are the following:

• Do the nominal dimension/weight/force specifications used in Bohringer's design actually work in the context of dynamic simulation? Namely, is the linear array design capable of moving a part dropped on its surface, and is a squeeze-type motion array capable of the part-orienting behavior described in [4]?
• If the above designs are successful, what are the measured feed and part orientation rates?
• How is the performance (e.g., the feed rate) of a motion array affected over variations of design and operating conditions, such as resonator shapes, part weights and array layout?

The first simulation, consisted of a 4 row x 8 column resonator array -- all resonators were aligned along a single direction. A part measuring .9 x .6 mm and weighing 1.8 micrograms was dropped on one end of the array. Within 3 ms, the part was transferred from the starting end to the opposing end of the array, confirming this design's conveyor belt-like behavior. Three snapshots of the simulation are shown Figure 1. A feed rate of 0.83 mm/sec was measured by dividing the length traversed by the part over the period of time simulated.

Figure 1: 4x8 resonator array

A second simulation was tried to evaluate if a small change in the geometry of a resonator would improve the feed rate. The idea consisted in moving the resonator's ridge inward by 12.5% of the resonator's length so as to increase the amount of horizontal energy transfered to the part at every collision with the ridge. In Figure 2 snapshots of this simulation are shown. Namely, two 4x8 arrays are placed side by side and identical parts are dropped at identical initial locations over each one of the arrays. The parts then race against each other, each one on their respective array. Simulation results show that the new resonator design achieves an almost 50% increase in feed rate!

Figure 2: feed rate vs. resonator designs

A third simulation was performed to assess the effect of part weight on the feed rate of a linear array. Namely, the first experiment was compared to an identical one for which the part weight is double from 1.8 to 3.6 micrograms. As shown in Figure 3, we verified a decrease of 25% in feed rate for the heavier part. We also found that a part weighing half as much as the original (i.e., 0.9 micrograms) would also be fed at a slower rate, implying that an optimal weight must exist which maximizes the feed rate for a given array.

Figure 3: feed rate vs. part weight

A final simulation was performed for which the original array layout is compared with one for which the resonator tiling is columnwise interleaved -- in particular, the interleaved design is the actual one implemented by Bohringer et. al. [3]. As shown in Figure 4, it was observed that the new design had no measurable impact on the feeding rate.

Figure 4: feed rate vs. tiling pattern

Table 1 below summarizes the feed rates measured for each of the above experiments.

A 12x8 resonator array was constructed to synthesize a squeeze field. The 6x8 resonators on the left portion of this array were oriented opposite to the 6x8 resonator group on the right side, thus creating a squeeze motion field. Simulations were run for both a square and a concave part. In both cases the parts were dropped away from the field's central line. These experiments are shown in Figures 5 and 6. Both simulations showed that the fields did propel the part towards the center of the array until the part's center of mass was roughly over the dividing line. However, the behavior of the part after the initial alignment phase was not as stable as predicted by squeeze-field theory. In particular, for the concave part, a stable orientation was never achieved. For these simulations we measured two quantities, shown in Table 2: (i) the time to bring the part's center of mass to the array's center and (ii) the time to stable part orientation.

Figure 5: reorienting square part w/ squeeze field

Figure 6: reorienting concave part w/ squeeze field

Our purpose in designing dynamic simulations of MEMS motion arrays was to (i) determine the utility of simulation as a verification tool for the effectiveness of MEMs and (ii) measure performance with the intent of design improvement and parameter tuning (e.g., what is the optimal choice for a part's weight?).

Our experiments involving both linear and squeeze motion arrays indicate that the designs proposed by Bohringer are effective in performing both linear part motion and part reorientation. Simulation results for the squeeze arrays could probably be improved by increasing the array resolution. For future work we would like to relate the measured parameters such as feed rate and orientation time to the physics of the process, e.g., oscillating frequencies, resonator shapes, mean trajectory of the part between collision, etc. We would also like to justify why certain resonator shapes are better than others, and possibly propose optimal array and resonator designs.

1. R. Yeh, E. Kruglick, and K. Pister, "Surface-micromachined components for articulated microrobots", IEEE Journal of Micro Electro Mechanical Systems, 5(1):10--17, March 1996.
2. L. Hornbeck, "128x128 deformable mirror device", IEEE Transactions on Electron Devices, ED(30):539--xxx, March 1983.
3. K. Bohringer, B. Donald, R. Mihailovich, and N. MacDonald, "Sensorless manipulation using massively parallel microfabricated actuator arrays", IEEE International Conference on Robotics and Automation, San Diego, CA, May 1994.
4. K. Goldberg, "Orienting polygonal parts without sensors", Algorithmica, 10(3):201--225, August 1993.
5. B. Mirtich and J. Canny, "Impulse-based simulation of rigid bodies", Symposium on Interactive 3D Graphics, New York, NY, 1995, ACM Press.
6. D. Berkowitz and J. Canny, "Designing Parts Feeders Using Dynamic Simulation", IEEE International Conference on Robotics and Automation, Minneapolis, MN, April, 1996.