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Research Papers

Slider-Cranks as Compatibility Linkages for Parametrizing Center-Point Curves

[+] Author and Article Information
David H. Myszka

 University of Dayton, Dayton, OH 45469dmyszka@udayton.edu

Andrew P. Murray

 University of Dayton, Dayton, OH 45469murray@notes.udayton.edu

J. Mechanisms Robotics 2(2), 021007 (Apr 19, 2010) (7 pages) doi:10.1115/1.4001096 History: Received April 30, 2009; Revised September 09, 2009; Published April 19, 2010; Online April 19, 2010

In synthesizing a planar 4R linkage that can achieve four positions, the fixed pivots are constrained to lie on a center-point curve. It is widely known that the curve can be parametrized by a 4R compatibility linkage. In this paper, a slider-crank is presented as a suitable compatibility linkage to generate the center-point curve. Furthermore, the center-point curve can be parametrized by the crank angle of a slider-crank linkage. It is observed that the center-point curve is dependent on the classification of the slider-crank. Lastly, a direct method to calculate the focus of the center-point curve is revealed.

Copyright © 2010 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

The displacement pole is the center of pure rotation from position j to position k

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Figure 2

Compatibility linkage can be used to generate a feasible center point

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Figure 3

Like the poles, Q points are on the center-point curve

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Figure 4

The principal focus can be located through a graphical construction

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Figure 5

A feasible center-point views opposite sides in equal, or supplementary, angles

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Figure 6

Two compatibility linkages with different P1 and P4 vertices

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Figure 7

A slider-crank that serves as a compatibility linkage

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Figure 8

Slider-crank compatibility linkage from example 1

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Figure 9

Slider-crank compatibility used to graphically generate a feasible center point

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Figure 10

A center-point curve is generated from a slider-crank compatibility linkage

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Figure 11

The slider-crank compatibility linkage from example 2

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Figure 12

The slider-crank compatibility linkage from example 3

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Figure 13

The slider-crank compatibility linkage from example 4

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Figure 14

Two compatibility linkage with different vertices from example 5

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Figure 15

An RPRP compatibility linkage from example 5

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