Unified topology and joint types optimization of general planar linkage mechanisms

Abstract

We propose a gradient-based topology optimization method to synthesize a planar linkage mechanism consisting of links and revolute/prismatic joints, which converts an input motion to a desired output motion at its end effector. Earlier gradient-based topology optimization methods were mainly applicable to the synthesis of linkage mechanisms connected by revolute joints only. The proposed method simultaneously determines not only the topology of planar linkage mechanisms but also the required revolute and/or prismatic joint types. For the synthesis, the design domain is discretized into rectangular rigid blocks that are connected to each other by the newly proposed revolute and prismatic joint elements, the joint states of which vary depending on the corresponding design variables. The new concept of joint elements is materialized thorough an elaborately configured set of zero-length springs whose stiffnesses vary as the functions of the design variables. Therefore, any connectivity state among unconnected, rigidly connected, revolute joint, and prismatic joint states can be represented by properly adjusting the stiffnesses. After presenting our modeling, formulation, and sensitivity analysis, the developed method is tested with verification examples. Then the developed method is extended to be able include additional shape design variables and applied to solve a realistic problem of synthesizing a finger rehabilitation robotic device. We expect the developed method to play a critical role in synthesizing a wide class of general linkage mechanisms.