Robotic devices with high performance in precision and speed are required in many industrial sectors and even in applications such as medical ones (micro manipulation of internal tissues or laparoscopy) or in entertainment. This paper presents some constructive geometric structures which can be used to design force controllers for robotic manipulators and general mechanisms. The approach is based on the well-known geometric control of system dynamics. In such a framework which uses elements of the invariant subspace theory, some typical problems in robotics can be mathematically formalized and analyzed. A generalized linear model is used and a careful analysis is made. The main result of the paper consists of proposing an explicit new subspace structure for grasping internal forces in robotic manipulations and general mechanisms.