The e ect of redundant sensors in the solution of the direct kinematics of general parallel manipulators is studied here, for purposes of on-line implementation. We describe three measurement conditions under which the kinematic relations are linear and hence, a linear decoupling of the position and orientation of the direct kinematics is possible. For each condition, a decoupling equation is derived and used to reduce the direct kinematics to an orientation problem only. The latter is solved by resorting to the polar-decomposition theorem. The numerical accuracy and e ciency of the procedure are also investigated.