An overlapped plane model and topology optimization for planar mechanism synthesis

•A novel model without domain discretization for planar mechanism synthesis.•The model reduces design variables and ensures better coverage of solution space.•A new optimization formulation improves efficiency and enhances solution diversity.•New mechanisms are obtained in several classical mechanism synthesis problems. In this paper, a model without domain discretization, and a new optimization formulation for given target paths, are proposed for planar mechanism synthesis based on topological optimization. The proposed model consists of overlapped planes and unified joints. The overlapped planes have the same size as the synthesis domain, and any two of these planes are connected with a unified joint. The unified joint parameterized by only one design variable can represent three states, namely disconnected, connected with prismatic joints, and connected with revolute joints. Compared to models in terms of discrete elements, the new model not only allows more possible connections between rigid bodies and thus expands solution space but also drastically reduces the number of design variables by removing redundant elements. In the proposed formulation, the number of unified joints is defined as a constraint instead of the target path error, which further reduces computational time but enhances the diversity of synthesized solutions. Three four-bar mechanisms synthesis problems are presented, where mechanisms of an oval-shaped path, 8-shaped path, and an irregular path are respectively generated. As the fourth example, we synthesized several six-bar mechanisms for vehicle suspensions with small wheel alignment parameter variations. It is thus demonstrated that the proposed model and formulation are applicable and efficient to planar mechanism synthesis, and more mechanisms can be generated to track the target paths.