Computational Aspects of the Design of Micro Mechanical Hinged Structures

Joint work with Bruce Donald.
We are interested in determining the shape of micro mechanical hinged structures [3], 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.

The figures above 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.


  1. K.-F. Böhringer, A Computational Approach to the Design of Micromechanical Hinged Structures. Proceedings of the ACM SIGGRAPH Symposium on Solid Modeling and Applications, Montréal, Québec, Canada (May, 1993).
  2. 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).

    Also of interest:

  3. K. S. J. Pister, M. W. Judy, S. R. Burgett, and R. S. Fearing, Microfabricated Hinges. SAA, 33(3):249-256 (1992).
  4. Rama Prasad, K.-F. Böhringer, and N. C. MacDonald, Design, Fabrication, and Characterization of SCS Latching Snap Fasteners for Micro Assembly, To appear in Proc. ASME International Mechanical Engineering Congress and Exposition (IMECE'95), San Francisco, California (November 1995).