0
Research Papers

Three-Dimensional Generalizations of Reuleaux’s and Instant Center Methods Based on Line Geometry

[+] Author and Article Information
Jasem Baroon

Department of Mechanical Engineering, Kuwait University, Safat 13060, Kuwaitjbaroon@kuc01.kuniv.edu.kw

Bahram Ravani

Department of Mechanical and Aeronautical Engineering, University of California, Davis, CA 95616bravani@ucdavis.edu

J. Mechanisms Robotics 2(4), 041011 (Oct 07, 2010) (8 pages) doi:10.1115/1.4001727 History: Received September 04, 2008; Revised January 19, 2010; Published October 07, 2010; Online October 07, 2010

In kinematics, the problem of motion reconstruction involves generation of a motion from the specification of distinct positions of a rigid body. In its most basic form, this problem involves determination of a screw displacement that would move a rigid body from one position to the next. Much, if not all of the previous work in this area, has been based on point geometry. In this paper, we develop a method for motion reconstruction based on line geometry. A geometric method is developed based on line geometry that can be considered a generalization of the classical Reuleaux method used in two-dimensional kinematics. In two-dimensional kinematics, the well-known method of finding the instant center of rotation from the directions of the velocities of two points of the moving body can be considered an instantaneous case of Reuleaux’s method. This paper will also present a three-dimensional generalization for the instant center method or the instantaneous case of Reuleaux’s method using line geometry.

FIGURES IN THIS ARTICLE
<>
Copyright © 2010 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 1

Reuleaux’s method

Grahic Jump Location
Figure 2

Three-dimensional Reuleaux’s method

Grahic Jump Location
Figure 3

Common perpendiculars between the screw axis and two homologous lines

Grahic Jump Location
Figure 4

Overdetermined system

Grahic Jump Location
Figure 5

Approximation of the pitch

Grahic Jump Location
Figure 6

Instant center method in 2D

Grahic Jump Location
Figure 7

Instantaneous screw axis for line displacements

Grahic Jump Location
Figure 8

The path of a moving line (a ruled surface)

Grahic Jump Location
Figure 9

Velocities of two points on a line generator of a ruled surface

Grahic Jump Location
Figure 10

Instantaneous screw axis and central normals of the trajectory ruled surface

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.

Related Journal Articles
Related eBook Content
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