For a platform connected to its base through two chains forming a single loop, the instantaneous mobility may be expressed by a set of motion screws that is in the intersection of the sets of motion screws for each of the two chains. A recent work shows that the platform remains mobile after differential displacement along all mobile paths if the Lie closures of the screw sets of the two chains are each within the span of the union of screw sets of those chains. If this union span is one dimension short of containing the Lie closures of the two chains, a quadratic form determines whether the reference pose is at a constraint singularity and resolves the mobile paths at that singularity. Those results are now extended to a platform manipulator with more than two chains, using a recursive procedure for updating velocity, acceleration, and higher-order descriptions of platform mobility after adding successive chains. The new analytical technique characterizes the bifurcation of the mobility at constraint singularity of 3RSR, 3RER, and 3UPU platform mechanisms proposed for use in constant-velocity couplings, robotic wrists, and translational manipulators.
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August 2010
Research Papers
Mobility of Multichain Platform Mechanisms Under Differential Displacement
Paul Milenkovic
Paul Milenkovic
Department of Electrical and Computer Engineering,
e-mail: phmilenk@wisc.edu
University of Wisconsin-Madison
, Madison, WI 53706
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Paul Milenkovic
Department of Electrical and Computer Engineering,
University of Wisconsin-Madison
, Madison, WI 53706e-mail: phmilenk@wisc.edu
J. Mechanisms Robotics. Aug 2010, 2(3): 031004 (9 pages)
Published Online: July 14, 2010
Article history
Received:
July 26, 2008
Revised:
December 23, 2009
Online:
July 14, 2010
Published:
July 14, 2010
Citation
Milenkovic, P. (July 14, 2010). "Mobility of Multichain Platform Mechanisms Under Differential Displacement." ASME. J. Mechanisms Robotics. August 2010; 2(3): 031004. https://doi.org/10.1115/1.4001725
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