Acceleration Analysis of 3-RPS Parallel Manipulators by Means of Screw Theory

According to the notation proposed by the International Federation for the Theory of Mechanisms and Machines IFToMM (Ionescu, 2003); a parallel manipulator is a mechanism where the motion of the end-effector, namely the moving or movable platform, is controlled by means of at least two kinematic chains. If each kinematic chain, also known popularly as limb or leg, has a single active joint, then the mechanism is called a fully-parallel mechanism, in which clearly the nominal degree of freedom equates the number of limbs. Tire-testing machines (Gough & Whitehall, 1962) and flight simulators (Stewart, 1965), appear to be the first transcendental applications of these complex mechanisms. Parallel manipulators, and in general mechanisms with parallel kinematic architectures, due to benefits --over their serial counterparts-such as higher stiffness and accuracy, have found interesting applications such as walking machines, pointing devices, multi-axis machine tools, micro manipulators, and so on. The pioneering contributions of Gough and Stewart, mainly the theoretical paper of Stewart (1965), influenced strongly the development of parallel manipulators giving birth to an intensive research field. In that way, recently several parallel mechanisms for industrial purposes have been constructed using the, now, classical hexapod as a base mechanism: Octahedral Hexapod HOH-600 (Ingersoll), HEXAPODE CMW 300 (CMW), Cosmo Center PM-600 (Okuma), F-200i (FANUC) and so on. On the other hand one cannot ignore that this kind of parallel kinematic structures have a limited and complex-shaped workspace. Furthermore, their rotation and position capabilities are highly coupled and therefore the control and calibration of them are rather complicated. It is well known that many industrial applications do not require the six degrees of freedom of a parallel manipulator. Thus in order to simplify the kinematics, mechanical assembly and control of parallel manipulators, an interesting trend is the development of the so called defective parallel manipulators, in other words, spatial parallel manipulators with fewer than six degrees of freedom. Special mention deserves the Delta robot, invented by Clavel (1991); which proved that parallel robotic manipulators are an excellent option for industrial applications where the accuracy and stiffness are fundamental characteristics. Consider for instance that the Adept Quattro robot, an application of the Delta robot, developed by Francois Pierrot in collaboration with Fatronik (Int. patent appl. WO/2006/087399), has a