0
Research Papers

Type Synthesis of Single-Loop Overconstrained 6R Spatial Mechanisms for Circular Translation

[+] Author and Article Information
Xianwen Kong

School of Engineering and Physical Sciences,
Heriot-Watt University,
Edinburgh EH14 4AS, UK
e-mail: X.Kong@hw.ac.uk

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received May 25, 2013; final manuscript received July 20, 2014; published online August 18, 2014. Assoc. Editor: Philippe Wenger.

J. Mechanisms Robotics 6(4), 041016 (Aug 18, 2014) (8 pages) Paper No: JMR-13-1101; doi: 10.1115/1.4028130 History: Received May 25, 2013; Revised July 20, 2014

To discover single-degree-of-freedom (DOF) single-loop overconstrained mechanisms is still an open problem. This paper deals with the type synthesis of single DOF single-loop overconstrained 6RMCTs (6R spatial mechanisms for circular translation). These mechanisms provide alternatives to planar parallelograms and are also associated with self-motion of several translational parallel mechanisms. 6RMCTs are to be obtained using a construction approach in combination with the approaches to the type synthesis of parallel mechanisms. By imposing certain conditions on the hybrid overconstrained 6R (plano-spherical, plano-Bennett, double-spherical, and spherico-Bennett) mechanisms, Bricard plane symmetric mechanism, and Bricard line symmetric mechanism, six special cases of 6RMCTs are obtained. By combining planar parallelograms with these special mechanisms, the general cases of 6RMCTs are then constructed. Finally, 4R2H, 2R4H, and 6H mechanisms for circular translation are obtained from the above 6RMCTs by replacing one or more pairs of R (revolute) joints with parallel axes each with a pair of H (helical) joints with parallel axes and the same pitch. This work contributes to the research on overconstrained six-bar mechanisms and further reveals that the research areas of parallel mechanisms and single-loop overconstrained mechanisms are closely related.

Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.

References

Waldron, K. J., 1968, “Hybrid Overconstrained Linkages,” J. Mech., 3(2), pp. 73–78. [CrossRef]
Baker, J. E., 1979, “The Bennett, Goldberg and Myard Linkages—In Perspective,” Mech. Mach. Theory, 14(4), pp. 239–253. [CrossRef]
Mavroidis, C., and Roth, B., 1995, “Analysis of Overconstrained Mechanisms,” ASME J. Mech. Des., 117(1), pp. 69–74. [CrossRef]
Dietmaier, P., 1995, “A New 6R Space Mechanism,” 9th World Congress on the Theory of Machines and Mechanisms, Milano, Italy, August 29–September 5, Vol. 1, pp. 52–56.
Wohlhart, K., 1991, “Merging Two General Goldberg 5R Linkages to Obtain a New 6R Space Mechanism,” Mech. Mach. Theory, 26(2), pp. 659–668. [CrossRef]
Six, K., and Kecskeméthy, A., 1999, “Steering Properties of a Combined Wheeled and Legged Striding Excavator,” 10th World Congress on the Theory of Machines and Mechanisms, Oulu, Finland, June 20–24, Vol. 1, pp. 135–140.
Zsombor-Murray, P. J., and Gfrerrer, A., 2002, “‘Robotrac’ Mobile 6R Closed Chain,” CSME Forum 2002, Kingston, Canada, May 21–24, Paper No. 02-05
Baker, J. E., 2003, “Overconstrained Six-Bars With Parallel Adjacent Joint-Axes,” Mech. Mach. Theory, 38(2), pp. 103–117. [CrossRef]
Chen, Y., and You, Z., 2008, “An Extended Myard Linkage and Its Derived 6R Linkage,” ASME J. Mech. Des., 130(5), p. 052301. [CrossRef]
Baker, J. E., 2010, “Using the Single Reciprocal Screw to Confirm Mobility of a Six-Revolute Linkage,” Proc. Inst. Mech. Eng., 224(10), pp. 2247–2255. [CrossRef]
Pfurner, M., 2012, “A New Family of Overconstrained 6R-Mechanisms,” Proceedings of EUCOMES 08, M.Ceccarelli, ed., Springer, Dordrecht, Netherlands, pp. 117–124. [CrossRef]
Hervé, J. M., 2011, “A New Four-Bar Linkage Completing Delassus' Findings,” Trans. Can. Soc. Mech. Eng., 35(1), pp. 57–62. Available at http://www.tcsme.org/Papers/Vol35/Vol35No1Paper4.pdf
Cui, L., and Dai, J. S., 2011, “Axis Constraint Analysis and Its Resultant 6R Double-Centered Overconstrained Mechanisms,” ASME J. Mech. Rob., 3(3), p. 031004. [CrossRef]
Hegedüs, G., Schicho, J., and Schröcker, H.-P., 2012, “Construction of Overconstrained Linkages by Factorization of Rational Motions,” Latest Advances in Robot Kinematics, J.Lenarčič, and M.Husty, eds., Springer, Dordrecth, Netherlands, pp. 213–220. [CrossRef]
Chen, Y., and You, Z., 2012, “Spatial Overconstrained Linkage—The Lost Jade,” Explorations in the History of Machines & Mechanisms, T.Koetsier, and M.Ceccarelli, eds., Springer, Dordrecht, Netherlands, pp. 535–550. [CrossRef]
Kong, X., and Gosselin, C., 2007, Type Synthesis of Parallel Mechanisms, Springer, Berlin. [CrossRef]
Kong, X., and Gosselin, C., 2004, “Type Synthesis of Three-Degree-of- Freedom Spherical Parallel Manipulators,” Int. J. Rob. Res., 23(3), pp. 237–245. [CrossRef]
Kong, X., and Yang, T.-L., 1996, “Dimensional Type Synthesis and Special Configuration of Analytical 6-SPS Parallel Manipulators,” High-Tech Letters (in Chinese), 6, pp. 17–20. Available at http://www.cqvip.com/QK/97187X/199606/2297788.html
Li, Z., and Schicho, J., 2013, “Classification of Angle-Symmetric 6R Linkages,” Mech. Mach. Theory, 70, pp. 372–379. [CrossRef]
Li, Z., and Schicho, J., 2014, “Three Types of Parallel 6R Linkages,” Computational Kinematics, F.Thomas, and A.Perez Gracia, eds., Springer, Dordrecht, Netherlands, pp. 111–119. [CrossRef]
Kong, X., and Huang, C., 2009, “Type Synthesis of Single-DOF Single-Loop Mechanisms With Two Operation Modes,” ASME/IFToMM International Conference on Reconfigurable Mechanisms and Robots (ReMAR 2009), London, June 22–24, pp. 136–141.

Figures

Grahic Jump Location
Fig. 1

Construction of a 6RMCT based on a plano-Bennett mechanism: (a) general plano-Bennett 6R mechanism and (b) specific plano-Bennett mechanism for circular translation

Grahic Jump Location
Fig. 2

Construction of a 6RMCT based on a plano-spherical mechanism: (a) general plano-spherical 6R mechanism, and (b) specific plano-spherical mechanism for circular translation

Grahic Jump Location
Fig. 3

6RMCT as a parallel mechanism

Grahic Jump Location
Fig. 4

A double-spherical 6R mechanism

Grahic Jump Location
Fig. 5

A specific double-spherical 6RMCT

Grahic Jump Location
Fig. 6

Construction of general double-spherical 6R based 6RMCT: (a) single-DOF 3-loop mechanism and (b) 6RMCT

Grahic Jump Location
Fig. 7

Bennett mechanism and spherico-Bennett mechanism: (a) Bennett mechanism and (b) spherico-Bennett mechanism

Grahic Jump Location
Fig. 8

A specific spherico-Bennett 6RMCT

Grahic Jump Location
Fig. 9

Construction of general spherico-Bennett mechanism based 6RMCT: (a) single-DOF 3-loop mechanism and (b) 6RMCT

Grahic Jump Location
Fig. 10

A general Bricard plane symmetric mechanism

Grahic Jump Location
Fig. 11

A specific Bricard plane symmetric 6RMCT

Grahic Jump Location
Fig. 12

Construction of general Bricard plane symmetric mechanism based 6RMCT: (a) single-DOF 2-loop mechanism and (b) 6RMCT

Grahic Jump Location
Fig. 13

A general Bricard line symmetric mechanism

Grahic Jump Location
Fig. 14

A specific Bricard line symmetric 6RMCT

Grahic Jump Location
Fig. 15

Construction of general Bricard line symmetric mechanism based 6RMCT: (a) single-DOF 2-loop mechanism and (b) 6RMCT

Grahic Jump Location
Fig. 16

Prototype of a double-spherical 6R based 6RMCT

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In