Publication

Closed-form position analysis of variable geometry trusses

Journal Article (2017)

Journal

Mechanism and Machine Theory

Pages

14-21

Volume

109

Doc link

http://dx.doi.org/10.1016/j.mechmachtheory.2016.11.004

File

Download the digital copy of the doc pdf document

Abstract

Variable geometry trusses are composed, in general, of unit cells which can be modeled as bars connected by spherical joints. Under mild conditions, it has been shown that the only feasible cells are topologically equivalent to bipyramids. Unfortunately, using standard formulations, the closed-form position analysis of bipyramids is not a trivial task. Actually, it has only been achieved for bipyramids with up to 7 vertices, whose closure polynomial has been shown to be of order 24. In this paper, using a distance-based formulation and a kinematic inversion for fans of tetrahedra, the problem is solved for bipyramids with up to 11 vertices, whose closure polynomial is of degree 896. No other position analysis problem leading to such a high-order closure polynomial has been previously solved.

Categories

robots.

Author keywords

Variable Geometry Trusses, Position Analysis, Bipyramids,Fans of tetrahedra, Coordinate-free formulations, Distance-based formulations

Scientific reference

J.M. Porta and F. Thomas. Closed-form position analysis of variable geometry trusses. Mechanism and Machine Theory, 109: 14-21, 2017.