We present a new approach to compute quasi-static and dynamic equilibrium positions and orientations (if any) of 2D polygonal or curved parts placed on general shaped 2D force field configurations. On the theoretical side, the novelty of our approach is that it puts into practice a fundamental result of piecewise-linear topology-the simplicial approximation theorem-and suggests an implementation using tools and techniques borrowed from modern computational geometry.

The microelectromechanical systems (MEMS) field is proceeding at a rapid rate in designing and developing new ever smaller, ever higher performance sensor and actuator devices in silicon. These devices need to be assembled along with more conventional small devices into complete systems. Currently there are no automation systems capable of meeting the exacting requirements of handling these small and often fragile (until encapsulated) MEMS devices. This paper describes the latest results of our ongoing research on sensorless MEMS manipulator arrays. We use CMOS VLSI technology to construct automatic handling devices that scale with the technology curves of CMOS VLSI, and may offer a solution to the micro assembly problem. The intelligent motion surface (IMS), itself a MEMS device, has been designed to meet this challenge. This paper also introduces the CILIA software, a high-level programmable simulation software available to the research community via the WWW. The CILIA software decouples the design of applications requiring the use of manipulator arrays from the actual devices used to implement them, therefore offering a level of abstraction for the application designer, who can implement a set of motion plans independent of the MEMS device actually being used. Also, the CILIA software can be used to simulate both macro and micro manipulator array devices.