Design Spatial Compliant Mechanisms: A Three-Dimensional Dynamic Compliance Matrix Method

Abstract Spatial compliant mechanisms have attracted considerable attention due to their wide applications in multi-degree-of-freedom manipulators and robotics. A three-dimensional dynamic compliance matrix method (DCM) with a small order of 6 × 6 is proposed to formulate the frequency-domain compliance of spatial compliant mechanisms. By treating a serial–parallel spatial compliant mechanism as an assembly of flexure hinge/beam members and rigid bodies, the scheme of compliance matrix summation for serial chains and stiffness/mass matrix summation for parallel branches is introduced by virtue of mass separating and grounding. Lumped mass matrices of spatial flexure hinges/beams and rigid bodies in the global coordinate frame are derived. Compliance-related kinetostatic and dynamic indexes, such as the degrees-of-freedom and constraint, parasitic motion errors, natural frequencies, and dynamic response functions, are discussed with the practical design of a piezoelectric 2R1T nanopositioner. The proposed three-dimensional DCM enables both kinetostatic compliance calculation and dynamic analysis of spatial compliant mechanisms through a pseudo-static matrix summation operation with much small order, avoiding the complexity of inner force analysis and kinematic calculation. Comparative finite element simulation and experimental validation demonstrate the advantages of the proposed approach.