Recursive matrix relations for kinematics of a three-prismatic-revolute- cylindrical (3-PRC) parallel kinematic machine (PKM) are established in this paper. Knowing the translational motion of the platform, we develop the inverse kinematical problem and determine the positions, velocities and accelerations of the robot's elements. Finally, compact matrix equations and graphs of simulation for displacements, velocities and accelerations of each of three legs are obtained.