Substructure compliance matrix model of planar branched flexure-hinge mechanisms: Design, testing and characterization of a gripper

• Matrix method for the quasi-static response of planar flexible-hinge mechanisms
• Substructuring of structurally- and kinematically-branched configurations
• Displacement-amplified gripper with circularly corner-filleted flexure hinges

This paper proposes an analytical compliance-based matrix method to model the quasi-static, small-displacement response of planar branched flexure-hinge over-constrained mechanisms. It studies structurally- and kinematically-branched flexible mechanisms comprising several chains that are connected in complex series-parallel configurations and that are acted upon by multiple external/reaction loads. These architectures are substructured or decomposed into simpler chains whose compliances are evaluated from known individual segment compliances. The substructured-chain compliances are subsequently combined with external loads to solve for unknown displacements and reactions and to further evaluate parameters relevant to the mechanism behavior. The method is applied to the design and analysis of a novel displacement-amplified gripper with right circularly corner-filleted flexure hinges. The mechanism's mechanical amplification, stiffness, and grip force are evaluated when either full or partial compliance (flexure-based only) is assumed. The analytical model predictions are confirmed by finite element analysis and by experimental testing of a proof-of-concept prototype. Subsequent analytical-model simulation highlights the relationships between the main geometric parameters and the gripper's performance qualifiers.