RESEARCH ARTICLE

On the location of the secondary instantaneous poles in two-degree-of-freedom spherical mechanisms

  • Soheil ZARKANDI
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  • Department of Mechanical Engineering, Babol Noshirvani University of Technology, Babol, Iran

Received date: 25 Dec 2013

Accepted date: 12 Jan 2014

Published date: 05 Mar 2014

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg

Abstract

As the instant centers in planar mechanisms, the instantaneous poles (or instant poles, in brief) can be used for kinematic analysis in spherical mechanisms. One of the mandatory steps in this analysis is the determination of the location of these poles. This paper presents a theorem showing analytically that the locus of an unknown secondary instant pole in two-degree-of-freedom (2-DOF) spherical mechanisms is a great circle (GC). The exact location of the pole on its GC is obtained based on the configuration of the mechanism and velocity ratio of the two inputs. Moreover, using the results of the theorem, a geometrical technique is presented to determine the GC of the pole.

Cite this article

Soheil ZARKANDI . On the location of the secondary instantaneous poles in two-degree-of-freedom spherical mechanisms[J]. Frontiers of Mechanical Engineering, 2014 , 9(1) : 34 -40 . DOI: 10.1007/s11465-014-0290-1

1
Di GregorioR. A general algorithm for analytically determining all the instantaneous pole axis locations in single-DOF spherical mechanisms. Journal of Mechanical Engineering Science, 2011, 225(9): 2062-2075

2
ChiangC H. Kinematics of Spherical Mechanisms. New York: Cambridge University Press, 1988

3
ZarkandiS. A new geometric method for singularity analysis of spherical mechanisms. Robotica, 2011, 29: 1083-1092

4
HainK. Applied Kinematics. 2nd ed. New York: McGraw-Hill Book Co., 1967

5
UickerJ J, PennockG R, ShigleyJ E. Theory of Machines and Mechanisms. 3rd ed. New York: Oxford University Press, 2003

6
HuntK H. Kinematic Geometry of Mechanisms. Oxford University Press, 1978

7
Di GregorioR. A novel geometric and analytic technique for the singularity analysis of one-dof planar mechanisms. Mechanism and Machine Theory, 2007, 42(11): 1462-1483

8
Di GregorioR. A novel method for the singularity analysis of planar mechanisms with more than one degree of freedom. Mechanism and Machine Theory, 2009, 44(1): 83-102

9
FosterD E, PennockG R. Graphical methods to locate the secondary instant centers of single-degree-of-freedom indeterminate linkages. ASME Journal of Mechanical Design, 2005, 127(2): 249-256

10
GosselinC, AnglesJ. Singularity analysis of closed-loop kinematic chains. IEEE Transactions on Robotics and Automation, 1990, 6(3): 281-290

11
Di GregorioR. An algorithm for analytically calculating the positions of the secondary instant centers of indeterminate linkages. Journal of Mechanical Design, 2008, 130(4): 042303 (9 pages)

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