An Instant Center Approach Toward the Conceptual Design of Compliant Mechanisms

[+] Author and Article Information
Charles J. Kim1

 Bucknell University, Lewisburg, PA 17837

Sridhar Kota

 University of Michigan, Ann Arbor, MI 48109

Yong-Mo Moon

 Worcester Institute of Technology, Worcester, MA 01609


Formerly a graduate student at the University of Michigan, Ann Arbor, MI.

J. Mech. Des 128(3), 542-550 (Jul 29, 2005) (9 pages) doi:10.1115/1.2181992 History: Received April 11, 2005; Revised July 29, 2005

As with conventional mechanisms, the conceptual design of compliant mechanisms is a blend of art and science. It is generally performed using one of two methods: topology optimization or the pseudo-rigid-body model. In this paper, we present a new conceptual design methodology which utilizes a building block approach for compliant mechanisms performing displacement amplification/attenuation. This approach provides an interactive, intuitive, and systematic methodology for generating initial compliant mechanism designs. The instant center is used as a tool to construct the building blocks. The compliant four-bar building block and the compliant dyad building block are presented as base mechanisms for the conceptual design. It is found that it is always possible to obtain a solution for the geometric advantage problem with an appropriate combination of these building blocks. In a building block synthesis, a problem is first evaluated to determine if any known building blocks can satisfy the design specifications. If there are none, the problem is decomposed to a number of sub-problems which may be solved with the building blocks. In this paper, the problem is decomposed by selecting a point in the design space where the output of the first building block coincides with the second building block. Two quantities are presented as tools to aid in the determination of the mechanism's geometry – (i) an index relating the geometric advantage of individual building blocks to the target geometric advantage and (ii) the error in the geometric advantage predicted by instant centers compared to the calculated value from FEA. These quantities guide the user in the selection of the location of nodes of the mechanism. Determination of specific cross-sectional size is reserved for subsequent optimization. An example problem is provided to demonstrate the methodology's capacity to obtain good initial designs in a straightforward manner. A size and geometry optimization is performed to demonstrate the viability of the design.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 1

SISO geometric advantage problem statement with displacement at input and output specified

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Figure 2

(a) Beam with applied unit force [θ=(0,360°)], (b) Unit force mapped to displacement plot

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Figure 3

Compliance matrix maps unit force to displacement ellipse

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Figure 4

(a) PCV and IC of a C4B, (b) Displacement analysis of C4B using the instant center

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Figure 5

(i) CDB, (ii) If Point A is constrained as shown, the instant center may be determined in a similar fashion as the C4B

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Figure 6

Resulting geometric advantage (GA=B∕A) for specified PCV at input and output

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Figure 7

(a) Two C4B's concatenated, (b) one C4B and one CDB concatenated

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Figure 8

The selection of the DP and the PCV at the DP determine the locations of the instant center of the first and second stage (IC1 and IC2, respectively). The resulting geometric advantage is equal to (B∕A)(D∕C). It may be shown that given any DP, one may obtain an arbitrary GA by changing PCV at the DP.

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Figure 9

General C4B with moving junctions

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Figure 10

Problem specifications and corresponding geometric advantage index (nGA=0.5 in dotted black)

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Figure 11

(a) Building block with specified input, output, and instant center. The moving junction may be located anywhere in the design space. (b)GAerror for various moving junction locations.

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Figure 12

Mechanism requiring significant resizing to attain target geometric advantage

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Figure 13

Instant centers resulting from selection of the decomposition point

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Figure 14

(a) C4B building block for subproblem No. 1, (b) CDB building block for subproblem No. 2, (c) final concatenated conceptual design

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Figure 15

Deformed geometry of initial design

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Figure 16

(a) Size and geometry optimization results, (b) deformed mechanism from ANSYS

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Figure 17

Length and angle definitions

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Figure 18

Angle definitions to recast equations



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