Computational Aspects of the Design of Micro Mechanical Hinged Structures

Towards Design Automation of MEMS (1990-1992)

Team Members

Karl F. Böhringer, Bruce R. Donald (Cornell)


We are interested in determining the shape of micro mechanical hinged structures, given specifications of their parameterized geometry and their functionality. Interactions between mechanism components are reflected in their configuration space (C-space). Each pair of components in contact is responsible for a surface region in C-space. Adjacency relationships of these regions define a C-space graph whose nodes represent contact states of the mechanism, and whose edges represent physically feasible state transitions. Parameterized components result in parameterized regions, and thus parameterized C-space graphs.

Functionality requirements may dictate properties of parts of the C-space graph, e.g. a certain start or an end state, or a certain path of states. We describe an algorithm that determines values of design parameters such that given functional requirements are satisfied.

Figure 1: Micromechanical hinged plate (top and side view). Picture thanks to Kris Pister. Figure 2: Micromechanical hinged mechanism rotating out of the wafer plane (top and side view). Picture thanks to Kris Pister.


Figure 3: The figures show a parameterized C-space from two different points of view. The corresponding mechanism has two degrees of freedom (x and y axis), and one design parameter (z axis). Different horizontal slices of this graph may have very different shapes. This means that the corresponding designs exhibit different functionality.

Selected Publications

  • Rama Prasad, Karl F. Böhringer, Noel C. MacDonald, "Design, Fabrication, and Characterization of SCS Latching Snap Fasteners for Micro Assembly." ASME International Mechanical Engineering Congress and Exposition (IMECE), no. DSC-16A-1, San Francisco, California, November 12-17, 1995. Paper.
  • Karl F. Böhringer, "A Computational Approach to the Design of Micromechanical Hinged Structures." ACM SIGGRAPH Symposium on Solid Modeling and Applications, pp. 457-458, Montréal, Québec, Canada, May 1993 (extended abstract / poster).
  • K.-F. Böhringer, "Application of Computational Topology to the Design of Microelectromechanical Structures." Proceedings of the NSF Design and Manufacturing Systems Grantees Conference, Charlotte, North Carolina (January 1993). Paper.

A complete list of our publications (many of them available online) can be found here.


  • NSF IRI-8802390, IRI-9000532 and by a Presidential Young Investigaor award to Bruce Donald
  • Air Force Oce of Sponsored Research, the Mathematical Sciences Institute, Intel Corporation, and AT&T Bell Laboratories

© Karl F. Böhringer, Department of Electrical Engineering, Box 352500, Seattle, WA 98195-2500, USA