At a platform singularity, a parallel manipulator loses constraint. Adding redundant actuation in an existing leg or new leg can eliminate these types of singularities. However, redundant manipulators have been designed with little attention to frame invariant techniques. In this dissertation, physically meaningful measures for closeness to singularities in non-redundant manipulators are developed. Two such frameworks are constructed. The first framework is a constrained optimization problem that unifies seemingly unrelated existing measures and facilitates development of new measures. The second is a clearance propagation technique based on workspace generation. These closeness measures are expanded to include redundancy and thus can be used as objective functions for designing redundant actuation. The constrained optimization framework is applied to a planar three degree of freedom redundant parallel manipulator to show feasibility of the technique.