Topology Optimization Methods Of Compliant Mechanisms Based On PRBM And Jacobian Matrix

Systematic conceptual design is one of the development trends of modern mechanisms.The future conceptual design of mechanisms will no longer just synthesize a mechanism with desired function, but synthesize a mechanism with desired function and optimized performance simultaneously. Thus, it is important to develop relative theories and methods of conceptual design. Heading in this direction, this paper focuses on the conceptual design methodology of compliant mechanisms. Two conceptual design methods considering topology performance are proposed for the simple hinge-based compliant mechanisms and multiple degree-of-freedom(DOF) compliant parallel mechanisms(CPMs).(1) The two popular conceptual design methods of compliant mechanisms are discussed.The rigid-body replacement method cannot create new topology and select the best topology for a particular problem. The topology optimization method can synthesize the optimal topology for a specific problem, but currently focuses on the simple distributed compliant mechanisms.This paper proposes a new idea that introduces topology optimization into the design scope(the above-mentioned two kinds of compliant mechanisms) of the rigid-body replacement method.(2) A new topology optimization method based on the pseudo-rigid-body model(PRBM)is proposed for the simple hinge-based compliant mechanisms. This method begins with topology optimization of pseudo-rigid-body mechanisms, then turns the optimal pseudo-rigid-body mechanism into hinge-based compliant mechanisms. By utilizing new topology expression scheme and topology analysis method, the topology optimization is extended to the hinge-based compliant mechanisms.(3) A Jacobian-based topology optimization method is proposed for the multi-DOF CPMs. Traditional topology optimization methods realize multiple outputs by predefining multiple specific output displacements, which can not be applied to multi-DOF topology optimization.To solve this problem, the Jacobian matrix is introduced into the field of topology optimization. The Jacobian matrix describes all the DOF of CPM’s mobile platform in a unified and concise form, and contains the information of CPM’s DOF and direct kinematics. By optimizing the CPM’s Jacobian matrix, one can synthesize a compliant mechanism with desired DOF(mechanism’s funcion) and optimized direct kinematics(mechanism’s performance).(4) To realize the topology optimization of multi-DOF CPMs, multiple design domains connected to the mobile platform in parallel are used to synthesize the compliant limbs of CPM.By establishing the relationships between the design domains of compliant limbs and the whole performances of CPM, the topology optimization problem of CPM is regarded as finding out the optimal limb topologies in multiple design domains to make the CPM possess desired DOF and optimized kinematic performance.(5) The Jacobian-based topology optimization method is used to optimally synthesize the2-DOF and 3-DOF planar CPMs, and is extended to 3D CPMs. The validity of the proposed method is verified by the design result and experimental result. In addition, the CPMs designed by the proposed method possess distributed topology, which is a new kind of CPM’s topology.This paper tries to introduce the idea of topology optimization into the conceptual design of simple hinge-based compliant mechanisms and CPM, and provides new conceptual design methodologies considering topology performance for those mechanisms. As a result, the proposed methods will enrich the topology optimization methodology and expand its application range.