This paper shows how to generate under-actuated manipulators by substituting nonholonomic spherical pairs (nS pairs) for (holonomic) spherical pairs (S pairs) in ordinary (i.e. not under-actuated) manipulators. As a case study, an under-actuated manipulator, previously proposed by one of the authors, is demonstrated to be generated, through this pair substitution, from an inversion of the 6-3 fully-parallel manipulator (FPM). Moreover, the kinetostatic analysis of this under-actuated manipulator is reconsidered, and a simple and compact formulation is obtained. The results of this kinetostatic analysis can be used both in the design of the under-actuated manipulator, and in its control. Keywords: kinetostatics, non-holonomic constraint, ordinary manipulator, underactuated manipulator, parallel manipulator.