An Algorithm for Kinematic Calibration of 3-DOF Delta Parallel Robot Based on Variations Calculation of Forward Kinematics Using Stereo Vision

Since forward kinematics in parallel robots has more difficulty and often does not lead to an analytical solution, in most studies, inverse kinematics has been preferred for parallel robot calibration. In this study, a technique was presented that does not need to completely solve direct kinematics. With the help of the forward kinematics, variation of the end effector with respect to the deviation of the kinematics parameters has been calculated. Then, by linearizing the equations, the possibility to use the linear least squares has been provided. The presented model like Zero-Reference model and Product of Exponential Formula, only uses one fixed reference frame and unlike D-H model does not have singularity problems. In the simulation, it was shown that the algorithm with a small number of selected poses and with high speed in a fraction of a second by a few iterations reaches an answer in the range of nanometers. Also, by using stereo vision, the presented theory was experimentally examined and shown that the proposed algorithm can reach the accuracy of the measuring instrument, similar to the simulation results.