Multi-objective optimization of a 3-DOF translational parallel kinematic machine

In this paper, stiffness modelling and analysis of a typical 3-DOF parallel kinematic machine (PKM) that provides translational motion along X, Y and Z axes is presented. The mechanism consists of three limbs each having an arm and a forearm with prismatic-revoluterevolute-revolute joints (PRRR). The joint arrangement is in such a way that the moving or tool platform maintains same orientation in the entire workspace. Through inverse kinematics, the joint angles for a given position of tool platform necessary for the stiffness modelling and analysis are obtained. The stiffness modelling is based on the compliance matrices of arm and forearm of each limb. Typical non-dimensional performance indices, namely, workspace volume index (WVI), global translational stiffness index (GTSI), and global rotational stiffness index (GRSI), are introduced and used to study the influence of dimensions. Attempts are also made to find the optimal dimensions of the translational PKM using multi-objective optimization based on the genetic algorithms (MOGA) in MATLAB. The methodology presented and the results obtained are useful for predicting the performance capability of the PKM under study.