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Research Papers

Design Optimization of Compliant Mechanisms Consisting of Standardized Elements

[+] Author and Article Information
Gang-Won Jang

School of Mechanical and Automotive Engineering, Kunsan National University, Kunsan, Jeonbuk 573-701, Korea

Myung-Jin Kim

School of Mechanical and Aerospace Engineering and National Creative Research Initiatives Center for Multiscale Design, Seoul National University, Shinlim-Dong, San 56-1, Kwanak-Gu, Seoul 151-742, Korea

Yoon Young Kim1

School of Mechanical and Aerospace Engineering and National Creative Research Initiatives Center for Multiscale Design, Seoul National University, Shinlim-Dong, San 56-1, Kwanak-Gu, Seoul 151-742, Koreayykim@snu.ac.kr

In this paper, we distinguish “intersection” from “joint.” An intersection means a spatial common position where neighboring beam elements are connected, and a joint is a very short part connecting the intersection to the ground beam element. One intersection has as many joints as it has connected beam elements.

1

Corresponding author.

J. Mech. Des 131(12), 121006 (Nov 12, 2009) (8 pages) doi:10.1115/1.4000531 History: Received December 03, 2008; Revised October 14, 2009; Published November 12, 2009; Online November 12, 2009

We developed a design method to configure optimal compliant mechanisms consisting of standardized elements such as semirigid beams, hubs, and joints. In the proposed design approach, mechanism compliance is based upon elastic deformations of joint elements made of short elastic beams. To set up the design problem as an optimization problem, a standard ground beam-based topology optimization method is modified to handle compliant mechanisms comprised of design variable-independent semirigid beams and design variable-dependent elastic joints. In the proposed method, unlike structural stiffness maximization problems, intermediate values should appear to allow elastic deformations in the joints. With our approach, reconfiguration design from one existing compliant mechanism to another can be formulated wherein the number of beam element relocation operations is also minimized. This formulation can be useful in minimizing the time and effort required to convert one mechanism to another.

Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

Prototypes: (a) before and (b) after deformation of the force inverter in Fig. 7, and (c) before and (d) after deformation of the orthogonal type force converter in Fig. 1

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Figure 2

Consideration of joint stiffness: (a) infinite stiffness corresponding to a rigid connection and (b) flexible stiffness (proposed)

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Figure 3

Proposed ground structure consisting of ground beams and joint elements

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Figure 4

A joint element of length li and width bi connecting ground beams

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Figure 5

Force inverter design problem (Young’s modulus E=210 GPa, ground beam width b¯=100 μm, beam thickness t=100 μm, F=1 N, input spring stiffness kin=100 N/m, and output spring stiffness kout=100 N/m)

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Figure 6

Optimization history of the force inverter design problem

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Figure 7

Optimized force inverter: (a) elastic hinge information (the numbers in parenthesis denote the values of design variables) and (b) deformed shape

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Figure 8

Optimized force inverter: (a) elastic hinge information (the numbers in parenthesis denote the values of design variables) and (b) the location of elastic hinges

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Figure 9

Normalized output displacement with respect to γ̂

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Figure 10

Effect of the mass evaluation parameter s on optimized results

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Figure 11

Optimized force inverter (a) without any mass constraint and (b) with a 40% mass constraint

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Figure 12

Design domain of an orthogonal type force converter (kin=kout=100 N/m, 20% mass usage constraint)

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Figure 13

Optimized result of an orthogonal type force inverter: (a) joint values, (b) deformed shape, and (c) location of elastic hinges

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Figure 14

Design domain of a gripper (kin=kout=100 N/m, 15% mass usage constraint) with different gripping points (a)–(c)

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Figure 15

Optimized results of grippers: (a) the optimized topology, (b) the deformed shape, and (c) the location of elastic hinges

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Figure 16

Optimized results for the problem depicted in Fig. 1: (a) result using Eq. 2 with uniform initial design variables and (b) result using Eq. 10 with the layout in Fig. 1 as an initial layout

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Figure 17

Optimized results for the problem depicted in Fig. 1: (a) result using Eq. 2 with uniform initial design variables and (b) result using Eq. 10 with the layout in Fig. 1 as an initial layout

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