Analysis and verification of terminal position error of leg parallel mechanism of quadruped robot

In order to reasonably determine the manufacturing tolerance range of 2-DOF planar parallel mechanism parts on quadruped robot, the error sensitivity analysis of the leg parallel mechanism and the position precision estimation in the working space were proposed in this paper. The leg mechanism of the quadruped robot analyzed in the paper was composed of a 2-DOF planar parallel mechanism and a RPR mechanism in series. The planar parallel mechanism realized the forward direction of leg lifting and stepping, and the RPR mechanism realized the lateral pendulum movement of leg mechanism, and the coordinate movement of the 2 mechanisms realized the spatial movement of leg mechanism. The advantage of the leg structure was that the planar parallel mechanism could enlarge the stroke of the end position to achieve rapid leg lifting and stride, and the RPR mechanism could achieve lateral swing decoupling motion. In the manufacturing process of the leg mechanism, due to the relatively simple structure of RPR mechanism and the coupling and complexity of parallel mechanism, the manufacturing of 2-DOF planar parallel mechanism was emphatically analyzed. Firstly, the composition of the leg mechanism was introduced, the position equation of 2-DOF planar parallel mechanism was established, an error model of 2-DOF planar parallel mechanism was established by using the full differential theory, the mapping relation of each error source to the end position error was obtained. Secondly, the position error sensitivity model and evaluation index of the mechanism were established. The histogram of each geometric error source on the end position precision under the significance of generalization was drawn according the sensitivity evaluation index, and the influence degree of each error source on the end position precision was revealed. The result showed that the angle error sources had a great influence on the position precision of leg mechanism, the angle error between the rod BC and the X axis was the most sensitive, other angle errors were more sensitive, while the influence of other manufacturing error sources was relatively small. Then, according to the 3σ principle and sensitivity evaluation index, the allowable manufacturing tolerances of the parts of each error source were determined. Finally, according to the allowable manufacturing tolerance range, the actual parts were designed and processed. The manufacturing error values of each part were measured by using the three coordinate measuring instrument, and the actual manufacturing errors of each part were obtained. According to the error transfer model and the sensitivity evaluation index, the distribution of the end position precise in the workspace was estimated. At the same time, the representative 6 pose points in the working space of the experimental prototype were measured with the three coordinate measuring instrument, and the end precision estimation was verified by some examples. The result of precision estimation showed that the error value of the lower part of the working space was within the range of 0.18-0.3 mm, and the precision was higher; the error value of the upper part of the working space was within the range of 0.4-1 mm, and the precision was poor; and the precision of the upper part of the working space was worse, and the error of the left upper and top part was up to 1 mm. Therefore, when performing more precise tasks, the trajectory of the foot contacting to ground could be planned in the lower part of the workspace to improve the foot positioning precision. The experiments results showed that the maximum error absolute value between the actual position precision value and the theoretical position precision estimation was 0.003 8 mm, and the minimum error absolute value was 0.001 5 mm, which verifies the correctness of the error transfer model and the position precision estimation, and the validity of the method to determine the manufacturing tolerance of components. The results laid a foundation for the kinematics calibration, error compensation and trajectory planning of the leg mechanism of the quadruped robot. © 2019, Editorial Department of the Transactions of the Chinese Society of Agricultural Engineering. All right reserved.