This paper investigates the geometric and structural characteristics involved in the control of general mechanisms and manipulation systems. These systems consist of multiple cooperating linkages that interact with a reference member of the mechanism (the "object") by means of contacts on any available part of their links. Grasp and manipulation of an object by the human hand is taken as a paradigmatic example for this class of manipulators. Special attention is devoted to the output specification and its controllability. An example design of a force controller using algebraic output feedback is presented at the end of this paper. In this example, a matrix representing a static output feedback is designed. The coefficients of this matrix are the weights for the sensed outputs. With the approach proposed in this paper, a robust decoupling is obtained between the output feedback and the contact forces and joint positions.