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.
Similar content being viewed by others
References
Di Gregorio R. 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
Chiang C H. Kinematics of Spherical Mechanisms. New York: Cambridge University Press, 1988
Zarkandi S. A new geometric method for singularity analysis of spherical mechanisms. Robotica, 2011, 29: 1083–1092
Hain K. Applied Kinematics. 2nd ed. New York: McGraw-Hill Book Co., 1967
Uicker J J, Pennock G R, Shigley J E. Theory of Machines and Mechanisms. 3rd ed. New York: Oxford University Press, 2003
Hunt K H. Kinematic Geometry of Mechanisms. Oxford University Press, 1978
Di Gregorio R. A novel geometric and analytic technique for the singularity analysis of one-dof planar mechanisms. Mechanism and Machine Theory, 2007, 42(11): 1462–1483
Di Gregorio R. 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
Foster D E, Pennock G 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
Gosselin C, Angles J. Singularity analysis of closed-loop kinematic chains. IEEE Transactions on Robotics and Automation, 1990, 6(3): 281–290
Di Gregorio R. 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)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Zarkandi, S. On the location of the secondary instantaneous poles in two-degree-of-freedom spherical mechanisms. Front. Mech. Eng. 9, 34–40 (2014). https://doi.org/10.1007/s11465-014-0290-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11465-014-0290-1