Kinetostatic modeling of complex compliant mechanisms with serial-parallel substructures: A semi-analytical matrix displacement method

Kinetostatic analysis of compliant mechanisms are crucial at the early stage of design, and it can be difficult and laborsome for complex configurations with distributed compliance. In this paper, a kinetostatic modeling method for flexure-hinge-based compliant mechanisms with hybrid serial-parallel substructures is presented to provide accurate and concise solutions by combining the matrix displacement method with the transfer matrix method. The transition between the elemental stiffness matrix and the transfer matrix of flexure hinges/flexible beams is straightforward, enabling the condensation of a hybrid serial-parallel substructure into one equivalent two-node element simple. A general kinetostatic model of the whole compliant mechanisms is first established based on the equilibrium equation of the nodal force. Then, a condensed two-port mechanical network representing the input/output force-displacement relations of single-degree-of-freedom (DOF) compliant mechanisms and the Jacobian matrix for multi-DOF compliant mechanisms are respectively built. Comparison of the proposed method with the compliance matrix method in previous literature, finite element analysis and experiment for three exemplary mechanisms reveals good prediction accuracy, suggesting its feasibility for fast performance evaluation and parameter optimization at the initial stage of design.