It will be shown how to generate under-actuated manipulators by substituting non-holonomic spherical pairs (nS pairs) for (holonomic) spherical pairs (S pairs) in fully-parallel manipulators (FPMs). Through this pair substitution, an under-actuated manipulator, previously proposed by one of the authors, will be demonstrated to be generated from an inversion of the 6-3 FPM. Moreover, the kinetostatic analysis of this manipulator will be reconsidered to obtain a simple and compact formulation. This reformulated analysis can be used both in the design of the underactuated manipulator, and in its control.