Kinematics Analysis And Hinge Error Research Of The Fine Adjustment Platform Of The Large Radio Telescope

As a fine adjustment platform of the large radio telescope, the Stewart platform determines the pointing precision of the whole system, and the pointing accuracy directly affect the sensitivity of the large radio telescope, so the motion precision of the Stewart platform is extremely important in the whole system. Because the hinge manufacturing error will directly affect the location accuracy of the Stewart platform, and these errors are inevitable in the process of processing and manufacturing, it is particularly important to analyse and compensate these errors. The movement of the hinge must be understood before error analysis, so, kinematics analysis of the Stewart platform should be carried out first.To take one branched chain of the Stewart platform for instance, the hooke joint, the drive shaft and the ball joint are treated as two revolute pairs, a sliding pair and three revolute pairs respectively. The D-H coordinate systems are established on the hooke joint, the drive shaft and the ball joint orderly, then the D-H parameters and the pose transformation matrixes between adjacent D-H coordinate systems are obtained. Thus, the kinematics equation of each branched chain is received and the kinematics model is established.Inverse kinematics and direct kinematics arithmetic of the Stewart platform are determined, to make the platform move along a specified path and the track is divided into several pose points. Then the changes of each drive shaft and each joint variable are obtained by using MATLAB to do inverse kinematics simulation. The result of the simulation is accord with the actual situation, then the validity of inverse kinematics arithmetic is verified. Next, direct kinematics simulation is done. The pose parameters which are calculated by Newton-Raphson algorithm are compared with the theoretical pose parameters, then the distribution of the error between them is got. The result shows a high precision of direct kinematics, and the initial value of iteration has little effect on the accuracy of direct kinematics. Thus, the validity of direct kinematics arithmetic is verified.Considering offset error and angle error of the hinge, the actual transformation matrix is got by the using pose transformation matrix in an ideal condition. Then the error modelis built and the error analysis algorithm is determined. The actual pose of the platform is solved after giving the offset error, the angle error and the theoretical pose. By analysing the pose error of the platform in different circumstances, it can be concluded that the angle error has little effect on pose error and the offset error has large effect on position error while has little effect on orientation error.An error parameter identification algorithm is put forward base on the mechanical structure of the Stewart platform. Before error compensation, the position and orientation of typical points in the workspace of the Stewart platform can be measured by API T3. Then the distribution of the error between practical pose and theoretical pose is received, and the offset error of each branch chain can be calculated by the least square method. As the offset error can not be directly compensated, the offset error is converted to the control error of the drive shaft by projecting it in the direction of drive shaft, and an error compensation algorithm is received base on this idea. The software of MATLAB is used in error compensation programming, the pose error before and after compensation are compared, then concluding that the position accuracy of the platform is greatly improved and the orientation accuracy has also been significantly improved after compensating. Thus, the correctness of the error identification algorithm and the error compensation algorithm can be verified.