Topology optimization of planar linkage mechanisms for path generation without prescribed timing

Abstract

The synthesis of planar linkage mechanisms by a topology optimization method has recently received much attention because both their numbers and dimensions can be simultaneously determined without baseline layouts. To synthesize a mechanism to produce a desired path at its end-effector, a desired path can be defined with or without prescribed timing. While earlier topology optimizations of mechanisms were all concerned with paths with prescribed timing, no study to deal with the topology optimization of mechanisms for path generation without prescribed timing is carried out in spite of its importance. The aim of this study is to propose and set up a gradient-based topology optimization formulation to synthesize planar linkage mechanisms that generate desired paths without prescribed timing. To this end, the desired path of the end-effector is expressed by the centroid distance function which is then represented by its Fourier descriptors. Then a topology optimization formulation using the Fourier descriptors is developed and the sensitivity analysis based on the Fourier descriptors is derived. Several numerical case studies are considered to verify the effectiveness of the proposed formulation. Some numerical issues appearing with the use of the Fourier descriptors are also investigated.