Publication

Closure polynomials for strips of tetrahedra

Conference Article

Conference

International Conference on Advances in Robot Kinematics (ARK)

Edition

15th

Pages

303-312

Doc link

http://dx.doi.org/10.1007/978-3-319-56802-7_32

File

Download the digital copy of the doc pdf document

Abstract

A tetrahedral strip is a tetrahedron-tetrahedron truss where any tetrahedron has two neighbors except those in the extremes which have only one. Unless any of the tetrahedra degenerate, such a truss is rigid. In this case, if the distance between the strip endpoints is imposed, any rod length in the truss is constrained by all the others to attain discrete values. In this paper, it is shown how to characterize these values as the roots of a closure polynomial whose derivation requires surprisingly no other tools than elementary algebraic manipulations. As an application of this result, the forward kinematics of two parallel platforms with closure polynomials of degree 16 and 12 is straightforwardly solved.

Categories

robots.

Author keywords

Position analysis, closed-form solutions, Distance Geometry, spatial linkages.

Scientific reference

F. Thomas and J.M. Porta. Closure polynomials for strips of tetrahedra, 15th International Conference on Advances in Robot Kinematics, 2016, Grasse, France, in Advances in Robot Kinematics, Vol 4 of Springer Proceedings in Advanced Robotics, pp. 303-312, 2018, Springer.