Kinematic Calibration of a Cartesian Parallel Manipulator

In this paper, a prototype Cartesian Parallel Manipulator (CPM) is demonstrated, in which a moving platform is connected to a fixed frame by three PRRR limbs. Due to the orthogonal arrangement of the three prismatic joints, it behaves like a conventional X-Y-Z Cartesian robot. However, because all the linear actuators are mounted at the fixed frame, the manipulator may be suitable for applications requiring high speed and accuracy. Using a geometric method and the practical assumption that three revolute joint axes in each limb are parallel to one another, a simple forward kinematics for an actual model is derived, which is expressed in terms of a set of linear equations. Based on the error model, two calibration methods using full position and length measurements are developed. It is shown that for a full position measurement, the solution for the calibration can be obtained analytically. However, since a ball-bar is less expensive and sufficiently accurate for calibration, the kinematic calibration experiment on the prototype machine is performed by using a ball-bar. The effectiveness of the kinematic calibration method with a ball-bar is verified through the well- known circular test.