Abstract
When using a Gough-Stewart Platform (GSP) for a vibration isolation or precision motion task, the geometry of that GSP is often chosen on an ad hoc basis. This can result in a number of problems: singularities or poor conditioning; inability to produce desired motions or forces; high dynamic coupling between axes; poor fault tolerance. This paper will show that the class of orthogonal GSPs has a number of useful properties. Denoting the mapping from Cartesian payload velocities to strut velocities as a 6x6 matrix M, orthogonal GSPs are those where either the rows or columns of M are orthogonal. In other words, either MM T or M T M are diagonal matrices. This paper will derive the properties of orthogonal GSPs wherein MM T is diagonal. In particular, it will first discuss the possible geometries that yield orthogonal GSPs. This will make it clear when these geometries are appropriate for a desired application. By re-arranging the rows and columns of M, a block diagonal form is found. Based on this block diagonal form, methods of designing Stewart platforms meeting desired position and force specifications are derived.
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