Kinematics of the Spatial 3-upu Parallel Robot

Parallel robots are closed-loop structures presenting very good potential in terms of accuracy, stiffness and ability to manipulate large loads. One of the main bodies of the mechanism is fixed and is called the base, while the other is regarded as movable and hence is called the moving platform of the manipulator. Generally, the number of actuators is typically equal to the number of degrees of freedom and each leg is controlled at or near the fixed base [1]. Compared with traditional serial manipulators, the following are the potential advantages of parallel architectures: higher kinematical accuracy, lighter weight and better structural stiffness, stable capacity and suitable position of actuator’s arrangement, low manufacturing cost and better payload carrying ability. Accuracy and precision in the direction of the tasks are essential since the positioning errors of the tool could end in costly damage [2]. Important efforts have been devoted to the kinematics and dynamic investigations of parallel robots. Among these, the class of manipulators known as Stewart-Gough platform, used in flight simulators, focused great attention (Stewart [3]; Di Gregorio and Parenti Castelli [4]). The prototype of the Delta parallel robot developed by Clavel [5] at the Federal Polytechnic Institute of Lausanne and by Tsai and Stamper [6] at the University of Maryland, as well as the Star parallel manipulator (Hervé and Sparacino [7]), are equipped with three motors, which train on the mobile platform in a three-degrees-of-freedom general translational motion. Angeles [8], Wang and Gosselin [9] analysed the kinematics, dynamics and singularity loci of Agile Wrist spherical robot with three revolute