Dynamic model of a 3T1R parallel kinematics machine

This paper presents the dynamic model of a parallel kinematic manipulator (PKM) able to generate the Sch¨onflies motion of its moving platform. The motion consists of a spatial translation (3T) with a rotation about a fixed axis (1R). The PKM consists of a fixed base connected to a moving platform by four kinematic chains with four prismatic actuators at the base. The model was developed in the framework of the Lagrange formulation according to a multibody approach with an augmented formulation without the need of solving the kinematics in terms of the independent coordinates. The model has been used to solve both the inverse and forward problems. In the former the trajectory of the moving platform is treated as a servo-constraint reducing the PKM as a kinematically driven mechanism, in the latter the constraint equations at acceleration level are adjoined to the equations of motion leading to a differential-algebraic equations. Finally, the dynamic model was validated via a solid model simulation.