A planar mechanism synthesis approach based on flexible joint model

A flexible joint model and the corresponding mechanism synthesis approach is proposed in this paper 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 paper 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 used for limiting the DOF of relative movement to simulate the functions of different joints. 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 numerical parameter optimization problem by using strain energy in the flexible joint model and solved by the sequential quadratic programming algorithm. To address inaccuracies in the calculation of degrees of freedom for the Grübler-Kutzbach formulation, a supplementary constraint function based on strain energy of flexible joint is proposed. To demonstrate the validity of the proposed approach several mechanism synthesis problems are presented.