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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

## Abstract

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.

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## Figures

Figure 3

Common perpendiculars between the screw axis and two homologous lines

Figure 4

Overdetermined system

Figure 5

Approximation of the pitch

Figure 6

Instant center method in 2D

Figure 7

Instantaneous screw axis for line displacements

Figure 8

The path of a moving line (a ruled surface)

Figure 9

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

Figure 2

Three-dimensional Reuleaux’s method

Figure 1

Reuleaux’s method

Figure 10

Instantaneous screw axis and central normals of the trajectory ruled surface

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