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Technical Brief

Equivalent Linkages and Dead Center Positions of Planar Single-Degree-of-Freedom Complex Linkages

[+] Author and Article Information
Jun Wang

Professor
School of Mechanical Engineering,
HuBei University of Technology,
Wuhan 430068, HuBei, China
e-mail: junwang@mail.hbut.edu.cn

Kwun-Lon Ting

Professor
Fellow ASME
Center for Manufacturing Research,
Tennessee Technological University,
Cookeville, TN 38501
e-mail: kting@tntech.edu

Daxing Zhao

Professor
School of Mechanical Engineering,
HuBei University of Technology,
Wuhan 430068, HuBei, China
e-mail: zdx007@126.com

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received May 2, 2013; final manuscript received November 14, 2014; published online March 11, 2015. Assoc. Editor: Xilun Ding.

J. Mechanisms Robotics 7(4), 044501 (Nov 01, 2015) (6 pages) Paper No: JMR-13-1086; doi: 10.1115/1.4029187 History: Received May 02, 2013; Revised November 14, 2014; Online March 11, 2015

This paper proposes a simple and general approach for the identification of the dead center positions of single-degree-of-freedom (DOF) complex planar linkages. This approach is implemented through the first order equivalent four-bar linkages. The first order kinematic properties of a complex planar linkage can be represented by their instant centers. The condition for the occurrence of a dead center position of a single-DOF planar linkage can be designated as when the three passive instantaneous joints of any equivalent four-bar linkage become collinear. By this way, the condition for the complex linkage at the dead center positions can be easily obtained. The proposed method is a general concept and can be systematically applied to analyze the dead center positions for more complex single-DOF planar linkages regardless of the number of kinematic loops or the type of the kinematic pairs involved. The velocity method for the dead center analysis is also used to verify the results. The proposed method extends the application of equivalent linkage and is presented for the first time. It paves a novel and straightforward way to analyze the dead center positions for single-DOF complex planar linkages. Examples of some complex planar linkages are employed to illustrate this method in this paper.

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Copyright © 2015 by ASME
Topics: Linkages
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References

Figures

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Fig. 2

Equivalent four-bar linkage

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Fig. 1

Stephenson type II six-bar linkage and one equivalent linkage

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Fig. 3

A dead center position of Stephenson type II linkage

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Fig. 4

A dead center position for a single flier eight-bar linkage [4,17]

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Fig. 5

A dead center position for a symmetrical eight-bar linkage and its equivalent linkage

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Fig. 6

A dead center position for the double butterfly eight-bar linkage

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Fig. 7

(a) A Stephenson type III six-bar linkage, (b) a dead center position of Stephenson type III six-bar linkage, and (c) a dead center position Stephenson type III six-bar linkage

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