Abstract
In this paper, kinematics and dynamics modeling of a typical 3-Degree of freedom (DOF) translational Parallel kinematic machine (PKM) is carried out. The kinematic structure of PKM consists of three limbs, connecting the base and the tool platform. Each limb consists of an arm and a forearm with joints Prismatic-revolute-revolute-revolute (PRRR). The arrangement of joints are in such a way that the tool platform will have pure translational motion along the Cartesian axes. Inverse kinematic relations that are necessary to find the slider positions and joint angles for a given position of tool platform are derived. The dynamics model is then derived based on Natural orhogonal complement (NOC). The inverse dynamics equations presented are used to compute actuator forces. The actuator forces using NOC are validated with those obtained based on Lagrangian method. The effect of slider, arm, and forearm inertia on the actuator forces is studied to know whether to neglect the arm and forearm inertias while computing the actuator forces for PKM. Finally, an attempt is made to find the optimal location of a circular trajectory using Genetic algorithms (GA) with minimization of Grand total actuator force (GTAF) as objective function.
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