Design and Prototyping of a Spherical Parallel Machine Based on 3-CPU Kinematics

The article has described an innovative spherical parallel wrist developed at the Polytechnic University of Marche in Ancona, revisiting all the main design steps, from kinematic synthesis up to physical prototyping. Machine kinematics has been worked out in closed form and all the singularity surfaces have been analysed: it has been pointed out that the mechanism does not possess inverse kinematics singularities, while direct kinematics singularities and translation singularities lie on the same closed surface. The inner space, where motion paths can be safely planned, has been identified and unfortunately it cannot be enlarged by kinematics optimisation because machine's Jacobian does not depend on geometrical parameters. For this reason, it was decided to drive machine design by dynamic optimisation concepts and an inverse dynamics model has been developed: the study of machine's dynamic manipulability, by means of different algebraic tools, led to the final design of the wrist, that has been also verified with structural analysis packages. The availability of the dynamic model, on the other hand, will be useful for the development of model based control systems, able to exploit the high potentials of direct drive actuation: a first dynamic analysis, moreover, shows that simplified models could be used, since the non-diagonal terms of mass matrix are much smaller than diagonal terms and platform's inertia could be neglected, at least when manipulator is far from singular configurations. All design steps have been performed in a virtual prototyping environment, that allowed to take into consideration simultaneously the constraints of the mechanics and the problems of the controller, allowing to assess the performances of the closed-loop system. The physical prototyping of the machine, however, allowed to validate the good properties envisaged during the design phase but also to experience the disadvantages of the concept itself: they are mainly due to the scarce accessibility of the centre of the spherical motion, which is common to most parallel wrists, and to the difficult assembly, which requires a precise alignment of joints axes: this problem has been partially overcome by the manufacturing of specific fixtures that are characterised by very high accuracy and are used while assembling the machine. The machine has been moved so far only through motors drives and a conventional PID position controller is actually being developed: more advanced control systems, able to exploit the high dynamics of the design and the power of direct actuation, will be studied soon.