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

Closedform 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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