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Research Papers

Nonsingular Spherically Constrained Clemens Linkage Wrist

[+] Author and Article Information
Paul Milenkovic

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

An alternative derivation using multiple spherical triangles is given by Henderson and Taimina, http://kmoddl.library.cornell.edu/tutorials/08/

J. Mechanisms Robotics 3(1), 011014 (Feb 10, 2011) (8 pages) doi:10.1115/1.4003415 History: Received March 19, 2009; Revised December 22, 2010; Published February 10, 2011; Online February 10, 2011

The parallel connection of a revolute-spherical-revolute Clemens linkage with a revolute-universal joint (RU) spherical linkage realizes a two-axis spherical pointing device suitable for use in a robot wrist. The design is derived from a Clemens linkage constant-velocity coupling having a spherical constraint. A novel transverse orientation of the RU linkage facilitates control of the pointing direction through actuation of a pair of revolute joints at the base of the device, a capability not otherwise required when this type of mechanism is employed as a constant-velocity coupling. As the mechanism is confined to spherical space, spherical trigonometry and related geometric reasoning may be employed in the analysis of mobility and actuation. The analysis derives the forward and inverse kinematic relations, showing that the mechanism allows a full 180 deg of deflection of the pointer from the center before encountering a singularity.

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Copyright © 2011 by American Society of Mechanical Engineers
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References

Figures

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Figure 2

Rotation sequence of symmetrically actuated UU linkage

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Figure 3

Pointer velocity vectors for unit-rate joint actuation

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Figure 4

Determining yaw and pitch half-angles from stereographic projection of rotation sequence midpoint

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Figure 5

All-revolute realization of RSR∥RU pointing mechanism

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Figure 6

Similar triangles establishing symmetric yaw actuation

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Figure 7

Pitch deflection through actuation of the base joint of the RU linkage

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Figure 8

Top view of kinematic model of two-axis wrist: (top) yaw deflection of −100 deg and (bottom) yaw deflection of −100 deg combined with pitch actuation of −100 deg

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Figure 9

Isometric view of CAD model of two-axis wrist with pushrod drive: (top) yaw deflection −100 deg and (bottom) yaw deflection of −100 deg combined with pitch actuation of −100 deg

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Figure 1

Relationship between spherical triangle and rotated coordinate frames

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