Publication

On the computation of the direct kinematics of parallel spherical mechanisms using Bernstein polynomials

Conference Article

Conference

IEEE International Conference on Robotics and Automation (ICRA)

Edition

2001

Pages

3332-3337

Doc link

http://dx.doi.org/10.1109/ROBOT.2001.933132

File

Download the digital copy of the doc pdf document

Abstract

Solving the direct kinematics of parallel spherical mechanisms with l legs is basically solving systems of l-1 second-order multinomials. This paper presents a recurrent expression for the control points of these multinomials when expressed in the Bernstein form. This result allows one to propose a technique for solving the direct kinematics of these mechanisms that takes advantage of the sub-division and convex hull properties of polynomials in the Bernstein form. Contrary to other numerical approaches, the one presented here is clearly less involved and, although it can be classified within the same category as interval-based techniques, it does not require any interval arithmetic computation.

Categories

robots.

Scientific reference

C. Bombín, L. Ros and F. Thomas. On the computation of the direct kinematics of parallel spherical mechanisms using Bernstein polynomials, 2001 IEEE International Conference on Robotics and Automation, 2001, Seül, Corea del Sud, pp. 3332-3337, IEEE.