The quality index for a redundant 4-4 in-parallel manipulator is presented. The device consists of a square platform and a square base connected by eight linearly actuated 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 corrdinates of the eight leg lines. In this paper it is proved that for the redundant 4-4 parallel manipulator the quality index for a platform of side a to be a maximum, the base has side sq root a and the perpendicular distance between the platform and the base is a/sq root. It is shown that the quality index can be used as ameasure of static stability. This information is valuable for the practical design of the parallel redundant manipulator.
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