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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

Yan, H. S., and Wu, L. L., 1989, “On the Dead-Center Positions of Planar Linkages Mechanisms,” ASME J. Mech. Des., 111(1), pp. 40–46. [CrossRef]
Soni, A. H., 1974, Mechanism Synthesis and Analysis, McGraw-Hill, New York.
Ting, K. L., 1993, “Branch and Dead Position Problems of N-Bar Linkages,” Advances in Design Automation, DE-Vol.65-2, American Society of Mechanical Engineers, Design Engineering Division (Publication), New York, pp. 459–465.
Pennock, G. R., and Kamthe, G. M., 2006, “Study of Dead-Centre Positions of Single-Degree-of-Freedom Planar Linkages Using Assur Kinematic Chains,” J. Proc. Inst. Mech. Eng., Part C, 220(9), pp. 1057–1074. [CrossRef]
Shen, H. P., Ting, K. L., and Yang, T. L., 2000, “Singularities Analysis of Basic Kinematic Chains and Complex Multiloop Planar Linkages,” ASME Design Engineering Technical Conferences and Computers and Information in Engineering Conference (DETC'00), Baltimore, MD, Sept. 10–13.
Shai, O., and Polansky, I., 2006, “Finding Dead-Point Positions of Planar Pin-Connected Linkages Through Graph Theoretical Duality Principle,” ASME J. Mech. Des., 128(3), pp. 599–609. [CrossRef]
Gregorio, R. D., 2007, “A Novel Geometric and Analytic Technique for the Singularity Analysis of One-DOF Planar Mechanisms,” Mech. Mach. Theory, 42(12), pp. 1462–1483. [CrossRef]
Zlatanov, D., Fenton, R. G., and Benhabib, B., 1994, “Singularity Analysis of Mechanisms and Robots Via a Velocity-Equation Model of the Instantaneous Kinematics,” IEEE International Conference on Robotics and Automation, San Diego, CA, May 8–13, pp. 986–991. [CrossRef]
Zlatanov, D., Fenton, R. G., and Benhabib, B., 1998, “Identification and Classification of the Singular Configurations of Mechanisms,” Mech. Mach. Theory, 33(6), pp. 743–760. [CrossRef]
Tsai, C.-C., and Wang, L. T., 2006, “On the Dead-Centre Position Analysis of Stephenson Six-link Linkages,” J. Proc. Inst. Mech. Eng., Part C, 220(9), pp. 1393–1404. [CrossRef]
Ting, K. L., Wang, J., Xue, C., and Currie, K. R., 2010, “Full Rotatability of Stephenson Six-Bar and Geared Five-Bar Linkages,” ASME J. Mech. Rob., 2(1), p. 011011. [CrossRef]
Wang, J., Ting, K., and Xue, C., 2010, “Discriminant Method for the Mobility Identification of Single Degree-of-Freedom Double-Loop Linkages,” Mech. Mach. Theory, 45(5), pp. 740–755. [CrossRef]
Hain, K., 1967, Applied Kinematics, 2nd ed., McGraw-Hill, New York.
Dijksman, E. A., 1984, “Geometric Determination of Coordinated Centers of Curvature in Network Mechanisms Through Linkage Reduction,” Mech. Mach. Theory, 19(3), pp. 289–295. [CrossRef]
Dijksman, E. A., 1977, “Why Joint-Joining is Applied on Complex Linkages,” Second IFToMM International Symposium on Linkages and Computer Aided Design Methods, Vol. I1, SYROM'77, Bucharest, Romania, June 16–21, Paper 17, pp. 185–212.
Uicker, J. J., Pennock, G. R., and Shigley, J. E., 2003, Theory of Machines and Mechanisms, 3rd ed., Oxford University, New York.
Pennock, G. R., and Kinzel, E. C., 2004, “Path Curvature of the Single Flier Eight-Bar Linkage,” ASME J. Mech. Des., 126(3), pp. 268–274. [CrossRef]
Foster, D. E., and Pennock, G. R., 2003, “A Graphical Method to Find the Secondary Instantaneous Centers of Zero Velocity for the Double Butterfly Linkage,” ASME J. Mech. Des., 125(2), pp. 268–274. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Stephenson type II six-bar linkage and one equivalent linkage

Grahic Jump Location
Fig. 2

Equivalent four-bar linkage

Grahic Jump Location
Fig. 3

A dead center position of Stephenson type II linkage

Grahic Jump Location
Fig. 4

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

Grahic Jump Location
Fig. 5

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

Grahic Jump Location
Fig. 6

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

Grahic Jump Location
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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