Synthesizing Parallel Flexures That Mimic the Kinematics of Serial Flexures Using Freedom and Constraint Topologies

Abstract

The principles of the freedom and constraint topologies (FACT) synthesis approach are adapted and applied to the design of parallel flexure systems that mimic degrees of freedom (DOFs) primarily achievable by serial flexure systems. FACT provides designers with a comprehensive library of geometric shapes. These shapes enable designers to visualize the regions wherein compliant flexure elements may be placed for achieving desired DOFs. By displacing these shapes far from the point of interest of the stage of a flexure system, designers can compare a multiplicity of concepts that utilizes the advantages of both parallel and serial systems. A complete list of which FACT shapes mimic which DOFs when displaced far from the point of interest of the flexure system's stage is provided as well as an intuitive approach for verifying the completeness of this list. The proposed work intends to cater to the design of precision motion stages, optical mounts, microscopy stages, and general purpose flexure bearings. Two case studies are provided to demonstrate the application of the developed procedure.