Mobility Analysis of Interconnected Hybrid Flexure Systems Using Screw Algebra and Graph Theory

This paper introduces a general method for determining the mobility analysis of flexure systems of any complexity, including those that can’t be broken into parallel and serial flexure subsystems. Such systems are called interconnected hybrid flexure systems because they possess limbs with intermediate bodies that are connected by flexure systems or elements. The method in this paper utilizes screw algebra and graph theory to enable designers to determine the freedom spaces (i.e., the geometric shapes that represent all the ways a body is permitted to move) for all the bodies joined together by compliant flexure elements within interconnected hybrid flexure systems. Although many flexure-based precision motion stages, compliant mechanisms, and microarchitectured materials possess topologies that are highly interconnected, the theory for performing a mobility analysis of such interconnected flexure systems using traditional screw theory does not currently exist. The theory introduced here lays the foundation for an automated tool that can rapidly generate the freedom spaces of every rigid body within a general flexure system without having to perform traditional computationally expensive finite element analysis. Case studies are provided in the paper to demonstrate the utility of the proposed theory.