Dynamic modeling of parallel manipulators

Parallel manipulators, which consist of two rigid bodies (a base and a platform) connected by six serial kinematic chains (connectors), offer distinct advantages when compared to their serial counterparts. The motion of the platform with respect to the base is controlled by the displacement of the six parallel connectors which generate a very stiff and accurate manipulator capable of handling high payloads with minimal positioning errors. These characteristics have generated great interest in the use of this type of manipulator in applications such as machining processes and automated assembly operations.;It is clearly desirable to develop a comprehensive dynamic model for effectively designing and controlling the parallel manipulators.;The major objective of this research is to derive explicit equations of motion for parallel manipulators. This will provide the means to understand their dynamic behavior and enable the design of more efficient devices capable of fast and accurate motions while handling heavy payloads. As far as the author is aware, this is the first time the explicit equations of motion have been derived (as opposed to numerical solutions). They were derived using Kane's Method which proved to be well suited to the intricate kinematics of parallel manipulators, and verified with the Newton-Euler formulation. Subsequently, the equations were used for a inverse dynamic simulation, which calculated the actuator forces required for producing a desired motion of a given design whilst supporting a workpiece in a machining operation. Various geometric parameters, inertial properties and motion profiles were used for testing in order to understand some of the effects on the dynamic behavior.;The equations of motion indicate a high degree of coupling between the connectors caused by the gravitational, tangential, Coriolis and centrifugal accelerations acting upon the system. A most important result of the inverse dynamic simulations is that even for feed rates in excess of the limits of existing technology (1200 inches/min), the only significant coupling was due to gravity; the other coupling effects were negligible. This suggests the possibility of using mass balancing to reduce the coupling effects between the connectors and in the process creating faster and more accurate parallel manipulators.