This paper presents the dynamic model of a kinematically-redundant planar parallel manipulator and an optimization method to minimize the actuator torques when the end-effector is subjected to a wrench while following a trajectory. A previous study proposed a kinetostatic approach to solve the same problem. The objective of the work presented here was to verify if the kinetostatic assumption was valid.The inclusion of the dynamic model in the optimization produced some undesirable oscillations and required the use of a different objective function. It is shown that for the application considered, the kinetostatic approach provided an acceptable solution.
The load-carrying capacity of manipulators is often considered to be the same throughout their workspace. However, the actual capacity of manipulators largely depends on their posture, their velocity, their acceleration and the limits of their actuators. In this paper, a method is proposed to increase the payload capacity of manipulators through trajectory optimisation. This optimisation is performed on a task basis and therefore, the load-carrying capacity varies from task to task. An extensive analysis of the method is conducted based on its application on a planar RR serial two degree-of-freedom manipulator. This analysis evaluates the ability of the method to find feasible trajectories and compares the results with those obtained using Bang-bang type methods. It is shown that, although the trajectories produced by the proposed method are not time optimal, the method is much more versatile and much simpler to implement than its Bang-bang counterparts.
In this work, the dexterous workspace of a general geometry 3-PRRR kinematically redundant planar parallel manipulator with six actuated joints, three of which are redundant, is determined. The 3-PRRR manipulator is an adaptation of the 3-RRR manipulator with a redundant prismatic actuator added to each leg. Obtaining the dexterous workspace by discretizing a large area around the manipulator and determining if each point is in the workspace is relatively simple though computationally inefficient. This work proposes a geometrical method to determine the dexterous workspace of a 3-PRRR planar parallel manipulator. With this method, an exact solution of the workspace boundaries is obtained. The geometrical method uses the four-bar mechanism analogy to determine the dexterous workspace. Though the method is applied to a 3-PRRR planar manipulator, it can be readily applied to any n-PRRR planar manipulator, where n is the number of chains.
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