Kinematic calibration of a 2 DOF parallel mechanism based on nonlinear programming

The explicit kinematic solutions of a 2 DOF parallel mechanism are derived by the forward kinematic analysis. An efficient method is presented to calibrate the mechanism here. Instead of measuring all or partial position and orientation of the end effector, the kinematic parameters of the mechanism are calibrated by measuring a serial of displacements of its end effector, moving from one point to another in its workspace. A universal tool microscope rather than extra sensors is used to measure those displacements. With the help of Matlab optimization toolbox, the optimal kinematic parameters are obtained by solving a nonlinear programming problem, which minimizes the measuring errors of the end effector. Experiment is performed to show the validity of the calibration method and to find out the optimal kinematic parameters. The experiment result shows the average deviation of those distances is closed to zero, and the measuring accuracy of the mechanism is improved by 42.2 % after calibration.