This paper develops new, analytical methods to find a large class of orthogonal Gough-Stewart platforms (OGSPs) having desired properties at their home position. In contrast, prior methods have been computationally intensive, relying on numerical search techniques. By exploiting symmetry, 27 equations are reduced to only two. The new techniques are directly applicable to clean-sheet design of micro-manipulators, vibration isolators, and Cartesian stiffness matrices. In addition, straightforward methods for retro-fitting existing OGSPs are illustrated. Because the new theory greatly simplifies OGSP formulas about a single point, it is expected that these results will also prove to be very useful when numerically designing gross motion platforms