This paper investigates the geometric and structural characteristics involved in the control of rather general manipulation systems, consisting of multiple cooperating linkages, interacting with a reference member of the mechanism (the 'object') by means of contacts on any available part of their links. Object grasp and manipulation by the human hand is taken as a paradigmatic example for this class of manipulators. This paper reports on some recent results on the analysis and control of these mechanisms, based on a geometric analysis of a local approximation of system dynamics. A special attention is devoted to the force control by an algebraic output feedback.