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Micromachines 2017, 8(9), 279; doi:10.3390/mi8090279

Multi-Objective Topology Optimization of a Compliant Parallel Planar Mechanism under Combined Load Cases and Constraints

1
School of Information Science and Technology, Jinan University, Guangzhou 510632, China
2
School of Mechanical and Electrical Engineering, Guangzhou University, Guangzhou 510006, China
3
Key Laboratory of Disaster Forecast and Control in Engineering, Ministry of Education of China, Jinan University, Guangzhou 510632, China
*
Authors to whom correspondence should be addressed.
Received: 1 July 2017 / Revised: 29 August 2017 / Accepted: 5 September 2017 / Published: 14 September 2017

Abstract

This paper focuses on a new type of configuration design of a compliant parallel mechanism (CPM) planar continuum structure and its characteristic analysis of vibration-inherent frequency for planar motion, which can suppress the impact of random vibration in ultra-precision positioning and manufacturing equipment and improve the inherent frequency response of the mechanism. Firstly, a vector-mapping isomorphism between the fully CPM and conventional isomorphic parallel mechanism was constructed with a kinematic differential Jacobian matrix. Then, the mathematical model of topology optimization was put forward considering the compromise programming on the static stiffness and mean vibration-inherent frequency of the mechanism as the design variable and the minimization of compliance as the objective function. A constraint of volume fraction was considered and multi-objective micro displacement mechanism topology optimization based on a prismatic-revolute-revolute (3-PRR) planar nano-positioning continuum structure was performed using the solid isotropic material with penalization (SIMP) technique, which combines the criteria of the optimization algorithm and the vector isomorphic mapping method. Multi-objective topology optimization of the continuum structure micro displacement mechanism was investigated and presented by optimizations with different initial rejection rates. The simulation results show that the stiffness and vibration suppression performance of the continuum structure were improved, whereas the positioning of differential kinematics characteristics of the 3-PRR micro displacement planar fully CPM and isomorphic prototype mechanism retain the same. The modal analysis also provides a rational configuration for the micro displacement mechanism dimensional design and its optimal modal parameters. The crossover oscillation in frequency response of the continuum structure was reduced and quickly converged in the optimization iterations. The performance of the optimized mechanism was verified by the experiments on a planar fully compliant micro displacement continuum structure based on Lead Zirconate Titanate (PZT) actuator. View Full-Text
Keywords: multi-objective topological optimization; differential vector isomorphic mapping; 3-PRR planar micro displacement; SIMP multi-objective topological optimization; differential vector isomorphic mapping; 3-PRR planar micro displacement; SIMP
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Wang, G.; Zhu, D.; Liu, N.; Zhao, W. Multi-Objective Topology Optimization of a Compliant Parallel Planar Mechanism under Combined Load Cases and Constraints. Micromachines 2017, 8, 279.

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