An Intrinsic and Geometric Framework for Synthesis and Analysis of Distributed Compliant Mechanisms.

Abstract

Traditional engineering designs associate strength with rigidity. As a result, most engineering systems that involve mechanical motion typically consist of rigid links connected with joints or interfaces. In contrast, nature achieves motion by exibility or compliance through elastic deformation. It maintains strength by distributing compliance throughout its geometry rather than localizing it. Incorporating distributed compliance in engineering designs yield monolithic systems that are cost-effective, lightweight, having reduced peak stress, and zero friction and wear. The principles of mechanics accurately predict the behavior of these compliant mechanisms, but yield little insight into their systematic synthesis. This thesis proposes a mathematical framework to represent problem specifcations and the mechanism behavior in terms of geometrically intuitive quantities that enable analysis and synthesis. Compliance representation is proposed for (i) single port mechanisms with a unique point of interest in terms of geometric quantities such as ellipses and vectors, and (ii) multiple port mechanisms with transmission of load and motion between distinct input(s) and output(s) is captured in terms of load ow. This geometric representation provides a direct mapping between the mechanism geometry and their behavior, and is used to characterize simple deformable members that form a library of building blocks. The design space spanned by the building block library guides the decomposition of a given problem specification into tractable sub-problems that can be each solved from an entry in the library. The effectiveness of this geometric representation aids user insight in design, and enables discovery of trends and guidelines to obtain practical conceptual designs. Furthermore, the thesis proposes an optimization technique for dimensional synthesis of conceptual designs to uniformly distribute stresses throughout its constituent members, thereby reducing peak stresses that lead to failure. The resulting metric used for renement enables an objective comparison and global ranking of various mechanism geometries and their actuation schemes based on their ability to store energy, or perform work before failure. The geometrically insightful conceptual synthesis methodology, optimization technique and global comparison of resulting designs furnish a pragmatic methodology for the synthesis of distributed compliant mechanisms. This methodology is successfully applied to obtain solutions for some practical applications.