F. Bulca, M. Husty, J. Angeles, P.J. Zsombor-Murray The kinematic analyses of the double tetrahedral mechanism as a paradigm of highly constrained parallel mechanisms is the starting point for this project. In this regard we apply the functional matrix concept to the degree of freedom analysis of this and other highly constrained mechanisms. Husty's example, in the use of kinematic mapping techniques to characterize the dextrous as well as entire workspace of a planar three legged R-R-R manipulator, is extended to treat spherical and spatial mechanisms of similar type so as to develop a systematic way to find the workspaces of platform mechanisms, in general. The Bennett, and other overconstrained 5R and 6R mechanisms as well as the double tetrahedron will be dealt with as specific instances of special cases.