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Journal of Zhejiang University SCIENCE A 2007 Vol.8 No.7 P.1084~1090

http://doi.org/10.1631/jzus.2007.A1084


A generalization of Kempe’s linkages


Author(s):  MAO De-can, LUO Yao-zhi, YOU Zhong

Affiliation(s):  Space Structure Research Center, Zhejiang University, Hangzhou 310027, China; more

Corresponding email(s):   luoyz@zju.edu.cn

Key Words:  Double-loop, Kempe&rsquo, s linkages, Transformation matrices, Deployable structures


MAO De-can, LUO Yao-zhi, YOU Zhong. A generalization of Kempe’s linkages[J]. Journal of Zhejiang University Science A, 2007, 8(7): 1084~1090.

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DOI - 10.1631/jzus.2007.A1084


Abstract: 
A new, general type of planar linkages is presented, which extends the classical linkages developed by Kempe consisting of two single-looped kinematic chains of linkages, interconnected by revolute hinges. Together with a locking device, these new linkages have only one degree of freedom (DOF), which makes them ideal for serving as deployable structures for different purposes. Here, we start with a fresh matrix method of analysis for double-loop planar linkages, using 2D transformation matrices and a new symbolic notation. Further inspection for one case of kempe&rsquo;s linkages is provided. Basing on the inspection, by means of some novel algebraic and geometric techniques, one particularly fascinating solution was found. Physical models were built to show that the derivation in this paper is valid and the new mechanisms are correct.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

Reference

[1] Baker, J.E., Yu, H.C., 1983. Re-examination of a Kempe linkage. Mechanism and Machine Theory, 18(1):7-21.

[2] Beggs, J.S., 1966. Advanced Mechanism. Macmillan Company, New York.

[3] Darboux, G., 1879. Recherches sur un système articulé. Bull. Sci. Math. Soc. 2s, 3:151-192.

[4] Denavit, J., Hartenberg, R.S., 1955. A kinematic notation for lower-pair mechanisms based on matrices. Trans. ASME, J. Appl. Mech., 22(2):215-221.

[5] Fontené, G., 1904. Nouvelles Ann. Math, 4:105.

[6] Hoberman, C., 1990. Reversibly Expandable Doubly-curved Truss Structures. US Patent 4,942,700.

[7] Hoberman, C., 1991. Radial Expansion Retraction Truss Structure. US Patent 5,024,031.

[8] Kempe, A.B., 1878. On conjugate four-piece linkages. Proc. Lond. Math. Soc. 1s, 9:133-147.

[9] Wohlhart, K., 2000. Double-Chain Mechanisms. In: Pellegrino, S., Guest, S.D. (Eds.), IUTAM-IASS Symposium on Deployable Structures: Theory and Applications. Springer.

[10] You, Z., Pellegrino, S., 1997. Foldable bar structures. International Journal of Solids and Structures, 34(15):1825-1847.

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