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Research Papers

Full Rotatability and Singularity of Six-Bar and Geared Five-Bar Linkages

[+] Author and Article Information
Kwun-Lon Ting

Center for Manufacturing Research, Tennessee Technological University, Cookeville, TN 38501kting@tntech.edu

Jun Wang

Center for Manufacturing Research, Tennessee Technological University, Cookeville, TN 38501jwang22@tntech.edu

Changyu Xue

Center for Manufacturing Research, Tennessee Technological University, Cookeville, TN 38501cxue21@tntech.edu

Kenneth R. Currie

Center for Manufacturing Research, Tennessee Technological University, Cookeville, TN 38501kcurrie@tntech.edu

J. Mechanisms Robotics 2(1), 011011 (Jan 11, 2010) (9 pages) doi:10.1115/1.4000517 History: Received April 11, 2008; Revised August 28, 2009; Published January 11, 2010

Full rotatability identification is a problem frequently encountered in linkage analysis and synthesis. The full rotatability of a linkage refers to a linkage, in which the input may complete a continuous rotation without the possibility of encountering a dead center position. In a complex linkage, the input rotatability of each branch may be different. This paper presents a unified and comprehensive treatment for the full rotatability identification of six-bar and geared five-bar linkages, regardless of the choice of input joints or reference link. A general way to identify all dead center positions and the associated branches is discussed. Special attention and detail discussion is given to the more difficult condition, in which the input is not given through a joint in the four-bar loop or to a gear link. A branch without a dead center position has full rotatability. Using the concept of joint rotation space, the branch of each dead center position, and hence, the branch without a dead center position can be identified. One may find the proposed method to be generally and conceptually straightforward. The treatment covers all linkage inversions.

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Copyright © 2010 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

A Stephenson six-bar linkage

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Figure 2

Intersection between the I/O and JRS boundary

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Figure 3

Nonintersection between the I/O curve and JRS boundary

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Figure 4

Input versus output curves between θ8 versus θ2

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Figure 5

A geared five-bar linkage

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Figure 6

Branches of a geared five-bar linkage

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Figure 7

A Stephenson six-bar chain

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Figure 8

Branch identification with θ2 versus θ3 in Fig. 1

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Figure 9

I/O curve of θ8 versus θ7 in Fig. 7

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Figure 10

I/O curve of θ5 versus θ3

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Figure 11

I/O curve of θ5 versus θ1

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Figure 12

I/O curve of θ5 versus θ2

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Figure 13

Four branches of a Stephenson six-bar linkage

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