DETERMINATION OF CLOSED-FORM MATHEMATICAL EXPRESSION OF VOLUME OF CONSTANT ORIENTATION WORKSPACE FOR GOUGH–STEWART PLATFORM

Raghav Rajaram P.,∗ Aravind G.,∗ Gokul Narasimhan S.,∗ and Anjan K. Dash∗

Keywords

Closed-form expression, constant orientation workspace, geometrical method, Gough–Stewart platform, workspace volume

Abstract

Gough–Stewart platform is the most celebrated 6-Degrees of freedom (DOF) parallel manipulator. However, till now there is no report of a closed-form mathematical expression of volume of constant orientation workspace of this 6-DOF manipulator. The difficulty is in determining a closed-form mathematical expression of the intersection volume of six spheres. In this paper, a new geometrical approach is proposed to determine all possible shapes of the workspace with variation in the parameters of a Gough–Stewart platform (with regular hexagon platforms) at zero orientation. This gives rise to a look-up table which can tell the designer the shape of the workspace when he varies the geometric parameters. A total of nine unique shapes have been identified and classified into six procedures for determination of volume. For four such procedures, closed-form mathematical expression of the volume of the constant orientation workspace is determined which is a very novel contribution in the domain of Gough–Stewart platform/6-DOF parallel manipulators. This plays a crucial role in determining the optimal parameters of a Gough–Stewart platform for a given desired workspace volume required at zero orientation. A case study is discussed where an optimal Gough–Stewart platform is proposed for a given workspace volume with minimal number of singularities.

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