0
TECHNICAL PAPERS

On the Effect of Dual Weights in Computer Aided Design of Rational Motions

[+] Author and Article Information
Anurag Purwar

Department of Mechanical Engineering, State University of New York, Stony Brook, NY 11794-2300purwar@design.eng.sunysb.edu

Qiaode Jeffrey Ge1

Department of Mechanical Engineering, State University of New York, Stony Brook, NY 11794-2300Qiaode.Ge@stonybrook.edu

1

Corresponding author.

J. Mech. Des. 127(5), 967-972 (Jan 27, 2005) (6 pages) doi:10.1115/1.1906263 History: Received April 09, 2004; Revised January 27, 2005

In recent years, it has become well known that rational Bézier and B-spline curves in the space of dual quaternions correspond to rational Bézier and B-spline motions. However, the influence of weights of these dual quaternion curves on the resulting rational motions has been largely unexplored. In this paper, we present a thorough mathematical exposition on the influence of dual-number weights associated with dual quaternions for rational motion design. By deriving the explicit equations for the point trajectories of the resulting motion, we show that the effect of real weights on the resulting motion is similar to that of a rational Bézier curve and how the change in dual part of a dual-number weight affects the translational component of the motion. We also show that a rational Bézier motion can be reparameterized in a manner similar to a rational Bézier curve. Several examples are presented to illustrate the effects of the weights on rational motions.

FIGURES IN THIS ARTICLE
<>
Copyright © 2005 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 1

(a) Screw motion with unit real weights ŵi=1+ε0; i=0,1. (b) Screw motion with nonunit real weights ŵ0=1+ε0, ŵ1=2+ε0.

Grahic Jump Location
Figure 2

(a) A rational Bézier motion of degree 6 with unit real weights, ŵi=1+ε0; i=0,…,3. (b) A rational Bézier motion with nonunit real weights ŵi=1+ε0; i=0,3 and ŵi=4+ε0; i=1,2.

Grahic Jump Location
Figure 3

(a) A rational Bézier motion of degree 6 ŵi=1+ε1; i=0,…,3. (b) A reparameterized rational Bézier motion ŵi=λi+ελi; λ=2 and i=0,…,3.

Grahic Jump Location
Figure 4

The effect of dual weights on screw interpolation.

Grahic Jump Location
Figure 5

The effect of dual weights on a rational Bézier motion.

Grahic Jump Location
Figure 6

(a) Key frames and the trajectory. (b) C2 spline interpolating motion for key-frames of (a).

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In