This contribution deals with a new analysis of a rigid body manipulation system. It is based on the well-known geometric control of system dynamics. In such a framework some typical problems in robotics are mathematically formalized and analyzed. The outcomes are so general that it is possible to speak of structural properties in robotic manipulation. The problem of non-interacting force/motion control is investigated. A generalized linear model is used and a careful analysis is made. The main result consists in proposing a task-oriented choice of the controlled outputs, for which the structural non-interaction property holds for a wide class of manipulation systems. Moreover, a decoupled linear model predictive control is proposed which uses a pre-selecting matrix to speed up the dynamics of the mechanisms. The pre-selecting matrix enables to considers subspaces which correspond to the eigenvectors of decoupled system to speed up the dynamic of the considered mechanism.