Mobility Analysis of Flexure Mechanisms via Screw Algebra

Abstract

This paper presents a general framework for studying the mobility of flexure mechanisms with a serial, parallel or hybrid topology using the screw algebra. The current approach for mobility analysis of flexures is ad hoc and mostly done by intuition. In this methodology, we first build a library of commonly used flexure elements, flexure joints, and simple chains. We then apply the screw algebra to find their motion and constraint spaces in the form of twist and wrench matrices. To analyze a general flexure mechanism, we first apply a top-down approach to hierarchically subdivide it into multiple modules or building blocks down to the level of flexure structures that are already provided in the library. We then use a bottom-up routine to study the mobility of each module up to the level of the overall mechanism. Examples and case studies from simple flexure joints, chains to spatial compliant platforms are used to demonstrate the methodology. This systematic methodology is an important tool for guiding the qualitative design of flexure mechanisms.