Publication

Ellipse distance geometry and the design of 3R robots

Conference Article

Conference

IFToMM World Congress on Mechanism and Machine Science (IFToMM)

Edition

16th

Pages

577-587

Doc link

http://dx.doi.org/10.1007/978-3-031-45705-0_56

File

Download the digital copy of the doc pdf document

Authors

Abstract

The study of the power of a point with respect to a circle and its application to orthogonal circles, bundles of circles, etc., has received a lot of attention in the past. In this paper, we show how the concept of conjugate ellipses generalizes the concept of orthogonal circles. It is also shown that it is possible to design 3R serial regional robots whose inverse kinematics can be reduced to the computation of the intersection between two conjugate ellipses which, in turn, can be reduced to the intersection of an ellipse and a line by relying on the concept of radical conic. The relevance of these findings is illustrated through an example.

Categories

automation.

Author keywords

Quartically-solvable robots, quadratically-solvable robots, 3R robots, distance geometry, ellipses

Scientific reference

F. Thomas and B. Bongardt. Ellipse distance geometry and the design of 3R robots, 16th IFToMM World Congress on Mechanism and Machine Science, 2023, Tokyo (Japan), Vol 147 of Mechanisms and Machine Science, pp. 577-587, 2023, Springer, Cham.