Closure polynomials for strips of tetrahedra

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International Symposium on Advances in Robot Kinematics (ARK)





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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.



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 Symposium 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.