Abstract

The quality index for a redundant 4-4 in-parallel manipulator with a square platform and a square base was obtained in [1]. Following this, the quality index for a redundant 4-8 manipulator with a square platform and an octagonal base was determined in [2]. In this paper the optimal quality index for a redundant 8-8 manipulator is determined. The device has an octagonal platform and a similar octagonal base connected by eight legs. The quality index is defined as a dimensionless ratio which takes a maximum value of 1 at a central symmetrical configuration that is shown to correspond to the maximum value of the square root of the determinant of the product of the manipulator Jacobian by its transpose. The Jacobian matrix is none other than the normalized coordinates of the eight leg lines. It is shown that the quality index can be used as a constructive measure of not only acceptable and optimum design proportions but also an acceptable operating workspace (in the static stability sense). The analysis of the redundant 8-8 manipulator described here can be used to model and design a self-deployable space structure that has a pair of flexible octagonal antenna platforms in the base and top platform.

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