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Research Papers: Design Automation

Jacobian-Based Topology Optimization Method Using an Improved Stiffness Evaluation

[+] Author and Article Information
Mohui Jin

College of Engineering,
South China Agricultural University,
Guangzhou 510642, China
e-mail: jinmohui@163.com

Xianmin Zhang, Benliang Zhu

School of Mechanical and
Automotive Engineering,
South China University of Technology,
Guangzhou 510641, China

Zhou Yang

College of Engineering,
South China Agricultural University,
Guangzhou 510642, China

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received February 25, 2017; final manuscript received September 28, 2017; published online November 9, 2017. Assoc. Editor: James K. Guest.

J. Mech. Des 140(1), 011402 (Nov 09, 2017) (11 pages) Paper No: MD-17-1179; doi: 10.1115/1.4038332 History: Received February 25, 2017; Revised September 28, 2017

A Jacobian-based topology optimization method is recently proposed for compliant parallel mechanisms (CPMs), in which the CPMs' Jacobian matrix and characteristic stiffness are optimized simultaneously to achieve kinematic and stiffness requirement, respectively. Lately, it is found that the characteristic stiffness fails to ensure a valid topology result in some particular cases. To solve this problem, an improved stiffness evaluation based on the definition of stiffness is adopted in this paper. This new stiffness evaluation is verified and compared with the characteristic stiffness by using several design examples. In addition, several typical benchmark problems (e.g., displacement inverter, amplifier, and redirector) are solved by using the Jacobian-based topology optimization method to show its general applicability.

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Figures

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Fig. 1

General design domain for planar CPMs

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Fig. 2

A compliant system with single input and single output

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Fig. 3

Stiffness modeling schematic for the ith compliant limb

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Fig. 4

Design domain for 2DOF CPMs

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Fig. 5

Final topologies of 2DOF CPM for the case of GA* = −3 solved by (a) the C-stiffness (ω = 0.5) and (b) stiffness (ω = 0.5) formulations

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Fig. 6

Iteration history of the topology in Fig. 5(a): (a) objective value and (b) kinematics requirement f and stiffness requirement S

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Fig. 7

Iteration history of the topology in Fig. 5(b): (a) objective value and (b) kinematics requirement f and stiffness requirement S

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Fig. 8

Final topologies of 2DOF CPM for the case of GA* = 2.5 solved by (a) the C-stiffness and (b) stiffness (ω = 0.7) formulations

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Fig. 9

Final topology of 2DOF CPM obtained by using f2 and stiffness formulation

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Fig. 10

Design domain for a 3DOF CPM

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Fig. 11

Final topology of the 3DOF CPM solved by the C-stiffness formulation

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Fig. 12

Final topology of the 3DOF CPM solved by the stiffness formulation

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Fig. 13

Design domain for displacement inverter and amplifier

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Fig. 14

Final topologies of displacement inverter for the case of GA* = −3 solved by (a) the C-stiffness (ω = 0.5) and (b) stiffness (ω = 0.5) formulations

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Fig. 15

Final topologies of displacement amplifier for the case of GA* = 3 solved by (a) the C-stiffness and (b) stiffness (ω = 0.6) formulations

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Fig. 16

Final topology of displacement amplifier designed by using the MSE/SE formulation

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Fig. 17

Design domain for a displacement redirector

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Fig. 18

Final topologies of displacement redirector solved by (a) the C-stiffness (ω = 0.5) and (b) stiffness (ω = 0.5) formulations

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Fig. 19

Solutions obtained by using different element discretizations, and solved by the C-stiffness (left) and stiffness (right) formulations

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