Designing hybrid flexure systems and elements using Freedom and Constraint Topologies

Abstract. In this paper we introduce the principles necessary to synthesize hybrid flexure systems and elements. Flexure systems consist of rigid bodies that are joined together by flexure elements that elastically deform to guide the system's rigid bodies with desired degrees of freedom (DOFs). The principles introduced here for synthesizing hybrid flexure systems and elements are extensions of the Freedom and Constraint Topologies (FACT) synthesis approach. FACT utilizes a comprehensive library of geometric shapes from which designers can rapidly consider and compare a multiplicity of flexure concepts that achieve any desired set of DOFs. Prior to this paper, designers primarily used these shapes to synthesize parallel and serial flexure systems and elements. With this paper, designers may now use these same shapes to synthesize more general flexures that consist of various combinations of parallel and serial systems and elements (i.e., hybrid configurations). As such, designers can access a larger body of flexure solutions that satisfy demanding design requirements. Instructions for helping designers utilize or avoid the advantages and challenges of over-, under-, and exact-constraint are also provided. Hybrid systems and elements are analysed and designed as case studies.