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Research Papers

The Spring-Connected Rigid Block Model Based Automatic Synthesis of Planar Linkage Mechanisms: Numerical Issues and Remedies

[+] Author and Article Information
Sang Jun Nam

 Samsungtechwin R&D Center, Seongnam-si, Gyeonggi, 463-400, Korea

Gang-Won Jang

Faculty of Mechanical and Aerospace Engineering,  Sejong University, Seoul 143-747, Korea

Yoon Young Kim1

Mem. ASMEWCU Multiscale Design Division, School of Mechanical and Aerospace Engineering,  Seoul National University, Seoul 151-742, Koreayykim@snu.ac.kr

1

Corresponding author.

J. Mech. Des 134(5), 051002 (Apr 03, 2012) (11 pages) doi:10.1115/1.4006266 History: Received September 02, 2011; Revised February 21, 2012; Published April 03, 2012

Because it is difficult to select in advance an appropriate linkage for converting an input motion to a desired output motion, a linkage synthesis method that does not require any baseline linkage would be preferred. To this end, an optimization-based linkage synthesis method that employs a spring-connected rigid block model has recently been suggested and applied for open-path problems. The objective of this study is to expand the method for the synthesis of more complex linkage mechanisms such as closed-loop linkages. Because the direct application of the method originally developed for open-path problems causes several numerical difficulties for closed-loop problems, an alternative optimization-based synthesis formulation is proposed in this investigation. The effectiveness of the suggested formulation is verified through several case studies including the synthesis of mechanisms generating closed paths.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Overview of the automatic linkage-mechanism synthesis in Ref. [1]: (a) problem definition to find a planar linkage mechanism for converting a given input motion to a desired output motion without relying on any baseline linkage; (b) design domain discretized by spring-connected rigid blocks; and (c) linkage-connection simulation by using SBMs with different spring-stiffness values (kmax: maximum (strong) spring stiffness, kmin: minimum (very weak) spring stiffness)

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Figure 2

(a) A four-bar linkage modeled by SBM. (b) The motion of the SBM in (a).

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Figure 3

(a) The modified SBM proposed in this work. (b) A block surrounded by 12 springs. (c) An example of floating-block anchoring.

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Figure 4

Motions of SBMs having (a) proper degrees of freedom, (b) redundant degrees of freedom, and (c) deficient degrees of freedom (*: current path of the output point, o: target path)

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Figure 5

Flowchart of the optimization process using the proposed formulation

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Figure 6

Linkage-mechanism synthesis problem: (a) a target mechanism having a closed path and (b) the employed SBM discretized by 5 × 5 blocks

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Figure 7

Iteration histories of the objective function, F, and the value of nk for the synthesis problem in Fig. 6

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Figure 8

Iteration history for the strain energy, S, and the squared displacement by external forces, D

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Figure 9

Output paths of the intermediate and final SBMs for the synthesis problem in Fig. 6

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Figure 10

Motions of the converged SBM and the identified linkage mechanism for the synthesis problem in Fig. 6

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Figure 11

Definitions of synthesis problems having different paths at the output point, Q

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Figure 12

Comparison between the output motions of the converged SBMs and those of the identified linkage mechanisms for the synthesis problems in (a) Fig. 1, (b) Fig. 1, and (c) Fig. 1

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Figure 13

Motion histories at several iterations for the problem defined in Fig. 1

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Figure 14

(a) Problem definition to synthesize a straight-line mechanism by using SBM. (b) Output motions of the converged SBM and the identified six-bar linkage. (c) Path of the output point of the identified mechanism.

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