Semi-numerical solution to 6/6-Stewart-platform kinematics based on symmetry

Abstract

Abstract. The direct and inverse kinematics of the 6/6-Stewart-platform architecture drawn opposite is considered. A fast and self-contained numerical algorithm is designed to compute the kinematic transformations. The design exploits the geometric symmetry of the construction by reducing the involved polynomial equations in a systematic fashion. The two special cases of constant orientation and of constant position are solved in closed form.

Certified Solving and Synthesis on Modeling of the Kinematics. Problems of Gough-Type Parallel Manipulators with an Exact Algebraic Method

“…Thus, the algebraic system involves 30 equations and 12 variables. (2), quaternions can express mobile platform rotation, [Lazard 1993, Mourrain 1993b, Egner 1996, Murray et al 1997. The quaternion representation includes 4 variables {q 0 ; q 1 ; q 2 ; q 3 } where the vector q = q 1 i +q 2 j +q 3 k defines the platform specific rotation axis and q 0 = cos(α/2) determines the coordinate expressing the rotation α along that axis.…”

A Geometric Newton-Raphson Method for Gough-Stewart Platforms

“…For a general Gough-Stewart platform, there are up to 40 possible solutions, [10,6,9,11,1,14]. Many workers have used numerical methods for this problem, for example [4,15,2,7,3,8]. Most of this work concerns finding all solutions and uses general numerical techniques which do not take account of the geometry of the group of rigid-body displacements.…”