Modeling and generating parallel flexure elements

This work introduces the principles necessary to model and generate parallel flexure elements (i.e., compliant members or flexible joints) that may be used to synthesize next-generation precision flexure systems. These principles are extensions of the Freedom and Constraint Topologies (FACT) synthesis approach, which utilizes geometric shapes to help designers synthesize flexure systems that achieve desired degrees of freedom (DOFs). Prior to this paper, FACT was limited to the design of flexure systems that consisted primarily of simple wire or blade flexure elements only. In this paper, the principles are introduced that enable designers to use the same shapes of FACT to synthesize parallel flexure elements of any geometry, including new and often irregularly-shaped elements (e.g., hyperboloids or hyperbolic paraboloids). The ability to recognize such elements within the shapes of FACT, therefore, enables designers to consider a larger body of solution options that satisfy a broader range of kinematic, elastomechanical, and dynamic design requirements. Example flexure systems that consist of flexure elements, generated using this theory, are provided as case studies.