Spanning tree and free form wide curve theories for compliant mechanism synthesis.

摘要

Compliant mechanisms (CMs) take advantage of elastic deformation to transmit motion, force, or energy. With the elimination or significant reduction of rigid joints, CMs provide many advantages in their performance, manufacturing, and maintenance. During this decade, CMs have become an important type of mechanisms with well-recognized potential. The synthesis of CMs presents much challenge because of their intrinsic limitations such as limited range of motion, low load-bearing capability, fatigue failure, and plastic deformation. These limitations need to be overcome or avoided in the synthesis process. This dissertation presented reliable and effective methods to synthesize CMs.;CMs are typically single-piece elastic structures. Their configurations are commonly described by topology, shape, and size. Topology determines the material connectivity among different ports in CMs. Shape refers to the locations of different ports and the connection curves between ports. Size specifies the cross-sectional properties of the connections in CMs. The synthesis process of CMs is characterized by the optimal selection of suitable topology, shape, and size to make them best perform the desired functions. In this dissertation, a spanning tree based topology synthesis and free form wide curve based shape and size synthesis approaches were presented. The reliability and effectiveness of these approaches were verified by examples.;The introduced spanning tree theory establishes the mathematical foundation for CM topology identification, selection, and optimization. Valid topologies are easy to describe and invalid topologies easy to weed out. The topology synthesis results are well-defined. No jagged or fuzzy connections exist in the solutions, and no intuitive interpretations are needed to the final solutions. The topology synthesis results are practical for further shape and size optimization or for direct fabrication and use. Free form wide curve theory provides a mathematically vigorous representation for CM shape and size. Variable shape and size of CMs are described by limited control parameters of wide curves. The presented shape and size synthesis approach makes complete geometric description of CMs straightforward, smooth transition of intersecting connections convenient, and performance evaluation effective. The CM synthesis methods presented in this dissertation can be readily broadened to different CM applications and extended to general structural design.