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Journal of Mechanisms and Robotics | Volume 2 | Issue 3 | Research Paper
Research Papers

Mobility of Multichain Platform Mechanisms Under Differential Displacement

[+] Author and Article Information
Paul Milenkovic

Department of Electrical and Computer Engineering, University of Wisconsin-Madison, Madison, WI 53706phmilenk@wisc.edu

J. Mechanisms Robotics 2(3), 031004 (Jul 14, 2010) (9 pages) doi:10.1115/1.4001725 History: Received July 26, 2008; Revised December 23, 2009; Published July 14, 2010; Online July 14, 2010
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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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Figures

Grahic Jump Location
+3RSR Clemens wrist in a nonsingular pose
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3RSR Clemens wrist in a nonsingular pose
Figure 1

3RSR Clemens wrist in a nonsingular pose

Grahic Jump Location
+3RSR Clemens wrist in the singular pose
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3RSR Clemens wrist in the singular pose
Figure 2

3RSR Clemens wrist in the singular pose

Grahic Jump Location
+3RER (3RRRRR) Myard CVC in a singular pose
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3RER (3RRRRR) Myard CVC in a singular pose
Figure 3

3RER (3RRRRR) Myard CVC in a singular pose

Grahic Jump Location
+3UPU (3RRPRR) SNU translational manipulator in a singular pose
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3UPU (3RRPRR) SNU translational manipulator in a singular pose
Figure 4

3UPU (3RRPRR) SNU translational manipulator in a singular pose

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