Recursive matrix relations for the complete dynamics of a 3-PRP planar parallel robot are established in this paper. Three identical planar legs connecting to the moving platform are located in the same vertical plane. Knowing the motion of the platform, we develop first the inverse kinematical problem and determine the positions, velocities and accelerations of the robot. Further, the inverse dynamic problem is solved using an approach based on the principle of virtual work. Finally, some graphs of simulation for the input powers of three actuators and the internal joint forces are obtained.