This paper presents a totally general geometric approach to the study of robotics manipulators and the dynamics of general mechanisms. In particular, a parametrization of a pre-compensator based on structures of subspaces for a non-interacting controller is presented. With advances in technological development, robotics is increasingly being used in many industrial sectors, including medical applications (e.g., micro-manipulation of internal tissues or laparoscopy). Typical problems in robotics may be mathematically formalized and analyzed, resulting in outcomes so general that it is possible to speak of structural properties in robotic manipulation and mechanisms. This work investigates the design of a force/motion controller. A generalized linear model is used to perform a careful analysis, resulting in the proposed general geometric structure for the study of mechanisms. In particular, a lemma and a theorem are presented which offer a parametrization of a pre-compensator for a taskoriented choice of input subspaces. The existence of these input subspaces is a necessary condition for the structural non-interaction property.