This paper presents a new approach to the velocity and acceleration analyses 3DOF parallel manipulators. Building on the definition of the „acceleration motor‟, the forward and inverse velocity and acceleration equations are formulated such that the relevant analysis can be integrated under a unified framework that is based on the generalized Jacobian. A new Hessian matrix of serial kinematic chains (or limbs) is developed in an explicit and compact form using Lie brackets. This idea is then extended to cover parallel manipulators by considering the loop closure constraints. A 3- PRS parallel manipulator with coupled translational and rotational motion capabilities is analyzed to illustrate the generality and effectiveness of this approach.