Topology Optimization of Spatially Compliant Mechanisms with an Isomorphic Matrix of a 3-UPC Type Parallel Prototype Manipulator

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...

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Bibliographic Details
Published in:Micromachines (Basel) 2018-04, Vol.9 (4), p.184
Main Authors: Zhu, Dachang, Zhan, Wanghu, Wu, Fupei, Simeone, Alessandro
Format: Article
Language:English
Subjects:
3-UPC type parallel prototype manipulator
compliant mechanisms
Decomposition
Degrees of freedom
isomorphic mapping matrix
Isotropic material
Jacobi matrix method
Jacobian matrix
Kinematics
Mapping
Mathematical models
solid isotropic material with penalization (SIMP)
Topology optimization
Universal joints
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Summary: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.
ISSN:2072-666X
2072-666X
DOI:10.3390/mi9040184