The necessary and sufficient conditions for the full input rotatability in a spherical four-bar linkage are proved. The direct criterion is: for all twist angles α in the range [0, π], the excess (deficit) of the sum of the frame and input twist angles over (from) π should, in absolute value, be greater than that for the coupler and follower twist angles; the difference between the follower and input twist angles, in absolute value, should be greater than that for the coupler and follower twist angles. Application of the direct criterion to full rotatability of other links are discussed and some variations in the form of the criterion are developed.
Issue Section:
Research Papers
Topics:
Linkages
1.
Barker, C. R., and Lo, J., 1986, “Classification of Spherical Four-Bar Mechanisms,” ASME Paper 86-DET-144.
2.
Chiang, C. H., 1988, Kinematics of Spherical Mechanisms, Cambridge University Press.
3.
Duditza
F. L.
Dittrich
G.
1960
, “Die Bedingungen fu¨r die Umlauffa¨higkeit Spha¨rischer Viergliedriger Kurbelgetriebe
,” Industrie-Anzeiger
, Vol. 91
, No. 71
, pp. 1687
–1690
.4.
Freudenstein, F., 1965, “On the Determination of the Type of Spherical Four-Link Mechanisisms,” Contemporary Problems in the Theory of Machines and Mechanisms, USSR Academy of Sciences, pp. 193–196.
5.
Gosselin
C.
Angeles
J.
1987
, “Repre´sentation Graphique de la Re´gion de Mobilite´ des Me´canismes Plans et Sphe´riques a` Barres Articule¯es
,” Mechanism and Machine Theory
, Vol. 22
, No. 6
, pp. 557
–562
.6.
Gupta
K. C.
1985
, “Mobility Conditions for Planar Linkages Using Triangle Inequality and Graphical Interpretation (Discussion)
,” ASME JOURNAL OF MECHANISMS, TRANSMISSIONS AND AUTOMATION IN DESIGN
, Vol. 107
, pp. 399
–400
.7.
Gupta
K. C.
1986
, “Rotatability Considerations for Spherical Four-Bar Linkages with Applications to Robot Wrist Design
,” ASME JOURNAL OF MECHANISMS, TRANSMISSIONS AND AUTOMATION IN DESIGN
, Vol. 108
, No. 3
, pp. 387
–391
.8.
Ma, R., 1994, “Robot Wrists and Related Linkages—Kinematic Analysis and Synthesis,” Ph.D. disertation. University of Illinois at Chicago.
9.
Savage
M.
Hall
A. S.
1970
, “Unique Description of All Spherical Four-Bar Linkages
,” ASME JOURNAL OF ENGINEERING FOR INDUSTRY
, Vol. 6
, No. 3
, pp. 559
–563
.10.
Soni
A. H.
1970
, “Unique Description of All Spherical Four-Bar Linkages (Discussion)
,” JOURNAL OF ENGINEERING FOR INDUSTRY
, Vol. 6
, No. 3
, pp. 563
–566
.11.
Watanabe, K., 1988, Personal communications.
Copyright © 1995
by The American Society of Mechanical Engineers
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