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This paper develops methods for generating classes of orthogonal Gough-Stewart platforms (OGSPs). First, a new, two-parameter class of six-strut OGSPs which leads to isotropic manipulators are found. Next, this class is extended to include redundant Gough-Stewart platforms (GSPs). For an even number of struts, the same algorithm used to generate the six-strut case can be employed. For an odd number of struts, similar essential concepts are used to derive seven-strut and nine-strut OGSPs. Maximization of fault tolerance is implemented for a nine-strut isotropic OGSP. By exploiting invariant properties of the inverse Jacobian, new methods for favorably altering the center of gravity, strut attachment surface, and strut spatial distribution are developed.