  This paper presents a unified approach for inverse and direct dynamics of
constrained multibody systems that can serve as a basis for analysis,
simulation, and control. The main advantage of the formulation of the dynamic
is that it does not require the constraint equations to be linearly
independent. Thus, a simulation may proceed even in the presence of redundant
constraints or singular configurations and a controller does not need to change
its structure whenever the mechanical system changes its topology or number of
degrees of freedom. A motion control scheme is proposed based on a projected
inverse-dynamics scheme which proves to be stable and minimizes the weighted
Euclidean norm of the actuation force. The projection-based control scheme is
further developed for constrained systems, e.g. parallel manipulators, which
have some joints with no actuators (passive joints). This is complemented by
the development of constraint force control. A condition on the inertia matrix
resulting in a decoupled mechanical system is analytically derived which
simplifies the implementation of the force control.
