The paper aims to analyze the equivalent kinematic chains of a family of three-degree-of-freedom (3-DOF) tripod mechanisms with planar-spherical bonds in order to determine the platform motions generated by the mechanisms, and then to develop a prototype of a 3-DOF 3-RPS type parallel mechanism, which can be used as a wrist robotic device. After a short introduction to mechanical generators of Lie subgroups of displacement, the mobility formula of a general 3-DOF tripod mechanism based on the modified Gru¨ebler’s criterion is given. Using displacement group theory theorems, the analyzed closed-loop system becomes finally equivalent to three contacts between a rigid assembly of three moving spheres onto three fixed planes. As an application of the above method, a prototype mechanism is designed and fabricated based on the kinematics analysis, the force capability and the simplicity.
High speed motion and positioning accuracy are the most important performance requirements of robot manipulators for the pick and place and assembly tasks. This paper focuses on the kinematic control system applied to a New Pavallel Manipulator (NPM) with fixed linear direct drive actuators specially designed for highspeed trajectory applications. For this, an optimal velocity based control method for high speed straight line trajectory of the NPM is proposed. The method is based on the maximum velocity zones analysis consisting of algebraic inequalities describing the constraints on the kinematics model. The proposed control algorithm is then implemented in o fline trajectory planning and in real time position servoing for kinematic control in the sense of achieving optimal trajectory performance. Digital PD control structure of the NPM is presented in order to satisjj the requirements in the actual manufacturing automation.The experimental straight line trajectory is satisfactory controlled by a speed of l.Sm/s without considering degree of accuracy.
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