Generalized Shooting Method for Analyzing Compliant Mechanisms With Curved Members

[+] Author and Article Information
Chao-Chieh Lan

The George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0405

Kok-Meng Lee1

The George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0405kokmeng.lee@me.gatech.edu


Corresponding author.

J. Mech. Des 128(4), 765-775 (Oct 18, 2005) (11 pages) doi:10.1115/1.2202139 History: Received January 29, 2005; Revised October 18, 2005

We consider here a class of compliant mechanisms consisting of one or more flexible beams, the manipulation of which relies on the deflection of the flexible beams. As compared with traditional rigid-body mechanisms, compliant mechanisms have the advantages of no relative moving parts and thus involve no wear, backlash, noises, and lubrication. This paper presents a formulation based on shooting method (SM) and two numerical solvers for analyzing compliant mechanisms consisting of multiple flexible members that may be initially straight or curved. Five compliant mechanisms, which are chosen to illustrate both initially straight and curved members and different types of joint/contact conditions, are formulated to exemplify analyses using the generalized shooting method for a wide spectrum of applications. The advantages of the generalized SM over the finite difference FD and finite element FE methods are demonstrated numerically. Unlike FD or FE methods that rely on fine discretization of beam members to improve its accuracy, the generalized SM that treats the boundary value problem (BVP) as an initial value problem can achieve higher-order accuracy relatively easily, and hence is more efficient computationally. In addition, the computed results were validated experimentally. It is expected that the generalized SM presented here will offer designers a useful analysis tool, and will effectively facilitate the process of design and optimization of compliant mechanisms.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 2

Schematics and coordinate systems of a flexible beam

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Figure 3

A pair of connecting links

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Figure 4

Illustrative examples

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Figure 6

Numerical results for Example 2

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Figure 7

Deflection and contact forces for Example 3

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Figure 8

Convergence result for Example 3

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Figure 9

Planar spring mechanism

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Figure 10

Force-displacement relationships

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Figure 11

Compliant mechanism with initially curved links

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Figure 12

Verification of GSM

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Figure 13

% error (N=20 for both FDM and FEM)

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Figure 14

Experiment results

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Figure 15

CAD model of the rotating indexer

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Figure 16

Experiment setup

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Figure 1

Schematics of a series of compliant links

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Figure 5

Numerical results for Example 1



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