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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 is found. For an even number of struts, the same essential concepts used to generate the six-strut case can be employed to generate OGSPs with eight struts, ten struts, etc. Next, 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. As an illustrative example, these methods are applied to the design of the attachment of vibration isolation and precision pointing system for the space based laser.