Abstract
A novel topology optimization approach is proposed in this paper for the design of three rotational degree-of-freedom (DOF) spatially compliant mechanisms, combining the Jacobian isomorphic mapping matrix with the solid isotropic material with penalization (SIMP) topological method. In this approach, the isomorphic Jacobian matrix of a 3-UPC (U: universal joint, P: prismatic joint, C: cylindrical joint) type parallel prototype manipulator is formulated. Subsequently, the orthogonal triangular decomposition and differential kinematic method is applied to uncouple the Jacobian matrix to construct a constraint for topology optimization. Firstly, with respect to the 3-UPC type parallel prototype manipulator, the Jacobian matrix is derived to map the inputs and outputs to be used for initializing the topology optimization process. Secondly, the orthogonal triangular decomposition with the differential kinematic method is used to reconstruct the uncoupled mapping matrix to derive the 3-UPC type parallel prototype manipulator. Finally, a combination of the solid isotropic material with penalization (SIMP) method and the isomorphic mapping matrix is applied to construct the topological model. A typical three rotational DOF spatially compliant mechanism is reported as a numerical example to demonstrate the effectiveness of the proposed method.
Highlights
Compliant mechanisms are widely used in precision manufacturing as they do not show problems such as clearance, friction and wear [1]
The results show that the natural frequency is higher than the same compliant mechanism with the hinge replacement method proposed in the literature [17]
A topology optimization approach was proposed for the design of three rotational degree-of-freedom (DOF) spatially compliant mechanisms
Summary
Compliant mechanisms are widely used in precision manufacturing as they do not show problems such as clearance, friction and wear [1]. The whole structural stiffness maximization is not satisfied by this method, while compliant mechanisms are limited in use to micro positioning due to their spatial multi-DOF (degree-of-freedom) motion characteristics [5,6,7]. Previous works [13,14,15,16] highlighted how research into compliant mechanisms is divided into two main directions: large stroke with multi-DOF and micro/nano scale displacement with multi-DOF. The latter scope is further divided into lumped compliance (often referred to as the pseudo-rigid-body-model, PRBM) and distributed compliance (often referred to as topology optimization), as reported in [17].
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