Loading...
Please wait, while we are loading the content...
Similar Documents
Computational Aspects of the Design of Micro-Mechanical Hinged Structures
| Content Provider | Semantic Scholar |
|---|---|
| Author | Karl-Friedrich Shringer, B. |
| Copyright Year | 2001 |
| Abstract | We are investigating computational aspects of engineering design problems that are amenable to tractable algorithmic solution. Our work focuses on parametric design of micro-mechanical hinged structures, which allow the construction of three-dimensional micromechanical devices. They are particularly attractive to design automation, because of (i) the highly specialized and automated production process, which constrains and guides geometric design, (ii) the possibly high number of devices produced simultaneously in one manufacturing process, (iii) and the rather simple geometry and functionality of the devices. Micro-mechanical hinged structures consist of platelock pairs. Each plate can rotate about a single axis defined by a pair of hinges. When rotating out of the wafer plane, the plate has to push a spring loaded lock out of the way. The lock is designed such that when the plate reaches a certain angle (typically r/2), the lock snaps down into a slot in the plate, yielding a rigid three-dimensional structure. For parametric design we utilize generalized configuration space. Besides parameters for each degree of kinematic freedom, generalized configuration space ineludes design parameters, e.g. the length of a plate. Assumptions on geometry and physics, such as purely rectangular geometry, quasi-static motion (no inertial or Coriolis forces), and Coulomb friction implement constraints imposed by our specific problem domain. We exploit these constraints to develop an efficient algorithm for analyzing and designing hinged structures. First we recognize that the configuration space of a plate-lock pair is C = [0, r] ~. It can be shown that the conditions for contact can be modeled *This paper describes research done in the Robotics and Vision Laboratory and the Computer Science Department at Cornell University. Support for our robotics research is provided in part by the National Science Foundation under grants No. IRI-8802390, IRI-9000532 and by a Presidential Young Investigator award to Bruce Donald, and in part by the Air Force Office of Sponsored Research, the Mathematical Sciences Institute, Intel Corporation, and AT&T Bell Laboratories. as low-degree polynomial curves in C, allowing fast exact simulation without numerical integration. Furthermore the configuration space of the platelock pair can be subdivided into a small number of qualitatively equivalent states, each of which represents one edge-edge, edge-vertex, or vertex-vertex contact pair in a cross-section model of the plate-lock pair. For example, all configurations where a vertex VL of the lock is in contact with an edge ep of the plate would form one state. Again, states can be identified by simple algebraic relations on the geometric parameters. All configurations inside a state obey the same equations, while a state change can be seen as a discontinuity in the behavior of the system. State transitions are possible only when their corresponding regions in C-space are adjacent, and they depend on kinematics and dynamics of the plate-lock pair. So our model for micro-mechanical hinges can be represented as a behavior graph whose vertices correspond to configurations with equivalent contact, and whose dges describe the conditions for transitions between different states. The functionality of the structure can be determined by analyzing the behavior graph. Similar designs may have isomorphic graphs, but may differ in the conditions for state transitions, so that the structures differ in properties like stability or ease of assembly. Structures with different graphs may still have similar functionality, as long as start and end state of the graphs are equivalent. Design algorithms for these structures will make extensive use of the behavior graphs for analysis and simulation of the designed parts. Because the equations governing each state are simple, and fast simulation is possible, we are optimistic about developing algorithms which can optimize design parameters for a given behavior graph, and which search for specific behavior graphs of a given parameterized structure. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://www.aaai.org/Papers/Symposia/Fall/1992/FS-92-03/FS92-03-020.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
