This paper presents a geometric approach to the analysis and control of parallel mechanisms (rigid bodies connected by joint constraints with closed kinematic loops). In this framework, the control problem is naturally decomposed into two parts: trajectory (position and velocity) tracking and constraint force control. For trajectory tracking, it is shown that away from configuration space singularities, the constraint space is a submanifold of the ambient space and thus many well-established (e.g. stability proven) control algorithms for serial or tree mechanisms can be directly applied with a suitable choice of local coordinates (can be chosen as a projection from its joint space). While the problem of constraint force control depends on the choice of ambient space and its metric. Open loop or PI with dynamics compensation type controller can be used in the force control depending on the availability of force sensors.