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Journal of Dynamic Systems, Measurement, and Control | Volume 133 | Issue 6 | Research Paper
Research Papers

Solution of the Forward Dynamics of a Single-loop Linkage Using Power Series

[+] Author and Article Information
Paul Milenkovic

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

J. Dyn. Sys., Meas., Control 133(6), 061002 (Sep 09, 2011) (9 pages) doi:10.1115/1.4004766 History: Received November 29, 2010; Revised May 06, 2011; Accepted May 10, 2011; Published September 09, 2011; Online September 09, 2011
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The kinematic differential equations express the paths taken by points, lines, and coordinate frames attached to a rigid body in terms of the instantaneous screw for the motion of that body. Such differential equations are linear but with a time-varying coefficient and hence solvable by power series. A single-loop kinematic chain may be expressed by a system of such differential equations subject to a linear constraint. A single matrix factorization followed by a sequence of substitutions of linear-system right-hand-side terms determines successive orders of the joint rate coefficients in the kinematic solution for this mechanism. The present work extends this procedure to the forward dynamics problem, applying it to a Clemens constant-velocity coupling expressed as a spatial 9R closed kinematic chain.
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Figures

Grahic Jump Location
+Clemens CV coupling at three representative postures
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Clemens CV coupling at three representative postures
Figure 1

Clemens CV coupling at three representative postures

Grahic Jump Location
+Plan view of Clemens CV coupling at initial posture
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Plan view of Clemens CV coupling at initial posture
Figure 2

Plan view of Clemens CV coupling at initial posture

Grahic Jump Location
+Dynamic response of Clemens CV coupling input shaft angle for three conditions
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Dynamic response of Clemens CV coupling input shaft angle for three conditions
Figure 3

Dynamic response of Clemens CV coupling input shaft angle for three conditions

Grahic Jump Location
+Dynamic response of Clemens CV coupling for torsion springs (K = 10) on pitch and yaw axes
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Dynamic response of Clemens CV coupling for torsion springs (K = 10) on pitch and yaw axes
Figure 4

Dynamic response of Clemens CV coupling for torsion springs (K = 10) on pitch and yaw axes

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