Completely Specified Displacements of a Rigid Body and Their Application in the Direct Kinematics of In-Parallel Mechanisms

In this paper we study the type of completely specified displacements of a rigid body where the distances of six points on the body, between their final and initial positions, have been specified. A method is presented to calculate the screws associated with these displacements. It is shown that there are 24 different screws at the most that will bring the rigid body from the initial to its final position to satisfy the six distances. If the six points are co-planar or symmetrical with respect to a plane then the number of screws reduces to 16. The method to calculate the screws associated with these completely specified displacements, is used to obtain a simple algebraic solution to the direct kinematics problem of a special type of in-parallel mechanisms: the mechanisms where the moving and the fixed platforms are the same.

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