A Planar Mechanism Synthesis Approach Based on Flexible Joint Model

Abstract

Abstract. A flexible joint model and the corresponding mechanism synthesis approach are proposed in this article for simultaneously optimizing the topology and dimension configuration of planar mechanisms. The proposed approach leverages topology optimization, enabling the generation of diverse configurations without any predetermined baseline mechanism. The flexible joint model proposed in this article consists of a revolute joint and two orthogonal prismatic joints, which represent the relative motions of the adjacent rigid bodies in three degrees of freedom (DOF). The zero-length springs are employed to restrict the relative motion DOF, thereby emulating the functionality of different joint types. The flexible joint model allows for the configuration of the mechanism to be expressed using only a few parameters. The synthesis problem of the path-generating mechanism is converted into a numerical parameter optimization problem based on the strain energy of the flexible joint model and solved by the sequential quadratic programming (SQP) algorithm. To address inaccuracies in the calculation of degrees of freedom in the Grübler–Kutzbach (G–K) formulation, a supplementary constraint function based on the strain energy of the flexible joint is proposed. To demonstrate the validity of the proposed approach, several mechanism synthesis problems are solved by this approach.