The compliance matrix method for the kinetostatic analysis of flexure-based compliant parallel mechanisms: Conventions and general force–displacement cases

Abstract

In this paper, we present the mathematical formulation of the Compliance Matrix Method (CMM) for the kinetostatic analysis of Flexure-Based Compliant Mechanisms (FBCM). The formulation is achieved by integrating the different approaches found in literature, as an attempt of unification of the CMM. The CMM is combined with inverse kinematics in an analytical process, to be used in the kinetostatic analysis of Flexure-Based Compliant Parallel Mechanisms (FBCPM) with multiple actuation forces where the output displacements are not coincident, neither are parallel, with the input forces. This analytical process allows the total compliance matrix of the FBCPM to be obtained, which relates the input forces (commonly applied on the legs) with the output displacements (commonly desired in the moving platform). The effectiveness of the analytical process presented here, is validated using two FBCPM with Two-Dimensional and Three-Dimensional architectures as examples. Then, the analytical results are validated with Finite Element Analysis by comparing the capability of the FBCPM to follow complex trajectories: circular and angular trajectories for the 2D-FBCPM, and a spherical spiral trajectory for the 3D-FBCPM, showing excellent agreement (less than 5%).