Kinematic Calibration of a Three Degrees-of-Freedom Parallel Manipulator With a Laser Tracker

Kinematic calibration is commonly used to improve the accuracy of a parallel mechanism. This paper presents an effective method for calibrating an overconstrained three degrees-of-freedom parallel manipulator employing a direct kinematic model. An error-mapping function is formulated from the differential of its kinematic model which is established through vector chains with the geometrical errors. To simplify the measurement of the error, the positioning and orientation error of the moving platform is replaced by the positioning error of the tool center point, which can be measured by a laser tracker accurately. Three different objective functions F₁, F₂, and F_∞, respectively, representing 1-norm, 2-norm, and inf-norm of the error vector are used to identify the geometrical parameters of the manipulator. The results of computer simulation show that parameters after kinematic calibration through minimizing the objective function F₂ is highly accurate and efficient. A calibration experiment is carried out to verify the effectiveness of the method. The maximum residual of calibration points reduces greatly from 3.904 to 0.256 mm during parameter identification. The positioning errors of all points on and inside the space surrounded by the calibration points are smaller than 0.4 mm after error compensation.