Kinematics and Dynamics Modeling of Spherical Parallel Manipulator

Spherical parallel manipulators have been proposed for accurate and fast performance. In this paper, kinematics and dynamics of a spherical three degrees-of-freedom parallel manipulator are studied. First, both direct and inverse kinematics are solved by using a new geometric approach and defining a new appropriate set of coordinates. Then, based on the derived kinematics equations and Jacobian matrices of links, according to Lagrange method, the explicit dynamics formulation of the manipulator is developed. The obtained dynamics has been verified by using MSC.ADAMS and MATLAB Software, simultaneously. This explicit verified model is highly important to design and implement various model based control algorithms. So, a Fuzzy Adaptive PID controller is designed to show the controller's operation on the manipulator. Discussing the obtained results reveal the merits and importance of the proposed modeling.