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Research Papers: Mechanisms and Robotics

Distributed Shape Optimization of Compliant Mechanisms Using Intrinsic Functions

[+] Author and Article Information
Chao-Chieh Lan1

Department of Mechanical Engineering, National Cheng Kung University, No. 1 University Road, Tainan 701, Taiwancclan@mail.ncku.edu.tw

Yung-Jen Cheng

Department of Mechanical Engineering, National Cheng Kung University, No. 1 University Road, Tainan 701, Taiwan

1

Corresponding author.

J. Mech. Des 130(7), 072304 (May 20, 2008) (10 pages) doi:10.1115/1.2890117 History: Received May 27, 2007; Revised December 11, 2007; Published May 20, 2008

A compliant mechanism transmits motion and force by deformation of its flexible members. It has no relative moving parts and thus involves no wear, lubrication, noise, or backlash. Compliant mechanisms aim to maximize flexibility while maintaining sufficient stiffness so that satisfactory output motion may be achieved. When designing compliant mechanisms, the resulting shapes sometimes lead to rigid-body type linkages where compliance and rotation is lumped at a few flexural pivots. These flexural pivots are prone to stress concentration and thus limit compliant mechanisms to applications that only require small-deflected motion. To overcome this problem, a systematic design method is presented to synthesize the shape of a compliant mechanism so that compliance is distributed more uniformly over the mechanism. With a selected topology and load conditions, this method characterizes the free geometric shape of a compliant segment by its rotation and thickness functions. These two are referred as intrinsic functions and they describe the shape continuously within the segment so there is no abrupt change in geometry. Optimization problems can be conveniently formulated with cusps and intersecting loops naturally circumvented. To facilitate the optimization process, a numerical algorithm based on the generalized shooting method will be presented to solve for the deflected shape. Illustrative examples will demonstrate that through the proposed design method, compliant mechanisms with distributed compliance will lessen stress concentration so they are more robust and have a larger deflected range. It is expected that the method can be applied to design compliant mechanisms for a wide variety of applications.

Copyright © 2008 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Schematic of a compliant link

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Figure 2

Effect of number of polynomial terms on the link shape

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Figure 4

Control points and design domain

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Figure 5

Multiple shooting method

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Figure 6

A link in a compliant mechanism

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Figure 7

Schematic of a compliant gripper

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Figure 8

Optimal shape for the gripper (m=2)

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Figure 9

Convergence of optimal shapes for m=1,3,5

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Figure 10

Convergence of optimal shapes for k=1,3,5(m=5)

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Figure 11

Iteration history for m=k=5

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Figure 12

Optimal shapes obtained by using Bezier curves

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Figure 13

Schematic of a rotational stage

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Figure 14

Optimal shape of the parallel mechanism (m=5)

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Figure 15

Optimal shape of the parallel mechanism (m=0)

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Figure 16

Comparison of stress distribution (Δθ=6deg)

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Figure 17

CAD model of the monolithic stapler

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Figure 18

Schematic of compliant segments

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Figure 19

Optimal shapes of the stapler (m=k=5)

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Figure 20

The monolithic stapler

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Figure 21

Effects of E∕G and h∕L on δs∕δb with δb=0.2L

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Figure 22

Effects of δb on δs for various h∕L with E∕G=3

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