Analytical Determination of a Sphere Inside Which the Stewart Platform Translates Without Suffering Any Leg Interference

Abstract

This paper presents a formulation to identify a sphere in the fixed-orientation workspace of a Stewart platform manipulator, such that no pair of legs of the platform would suffer an interference between them, if the geometric centre of the moving platform remained inside this sphere. Identification of such a sphere is an important step in the design and analysis of such manipulators. The geometric formulation leads to certain algebraic equations, and finally to the solution of a degree 8 univariate equation. The mathematical formulation is applied to two different situations, and the results obtained are verified by comparison with those obtained from an established open-source library designed to detect interference between solids.