Trajectory Planning Using the Ferguson Curve Model and Curvature Theory of a Ruled Surface

[+] Author and Article Information
B. S. Ryuh, G. R. Pennock

School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907

J. Mech. Des 112(3), 377-383 (Sep 01, 1990) (7 pages) doi:10.1115/1.2912618 History: Received May 01, 1989; Online June 02, 2008


The trajectory of a robot end-effector is completely described by a ruled surface and a spin angle about the ruling of the ruled surface. In this way the differential properties of motion of the end-effector are obtained from the well-known curvature theory of a ruled surface. The robot can then be programmed so that the end-effector will follow the prescribed trajectory with high accuracy. In the case where the ruled surface cannot be described by an explicit analytic function, the ruled surface may be represented by a geometric modeling technique. Since a ruled surface can be expressed in terms of a single parameter, a curve generating technique is used to represent the ruled surface. The technique presented in this paper is the Ferguson curve model which guarantees that the trajectory will pass through all of the set points and will have curvature continuity at each set point. To illustrate the proposed method of robot trajectory planning, a practical example is included in the paper.

Copyright © 1990 by The American Society of Mechanical Engineers
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