This contribution deals with a new analysis of a rigid body manipulation system. It is based on the well–knowngeometric control of system dynamics. In such a framework some typical problems in robotics are mathematicallyformalized and analyzed. The outcomes are so general that it is possible to speak of structural properties in roboticmanipulation. The problem of non-interacting force/motion control is investigated. A generalized linear model is usedand 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 decoupledlinear 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 tospeed up the dynamic of the considered mechanism.