Kinematics analysis of six-bar parallel mechanism and its applications in synchrotron radiation beamline

Six-bar parallel mechanism is now widely applied in synchrotron radiation beamline, while the six-dimensional adjustment is difficult and inefficient for lack of theoretical direction. This paper introduces a special six-bar parallel mechanism. By means of coordinate transformations, the inverse kinematics of six-bar parallel mechanism is studied, and the precise equations for six bars' lengths are obtained. Based on the inverse kinematics, forward kinematics of six-bar parallel mechanism is obtained with trust region method working for nonlinear optimization. The corresponding MATLAB program is also designed. The results show that trust region method is an effective way to solve forward kinematics, and the program is stable, reliable and rapid. This method has small errors with linear precision of 10−12 mm and rotational precision of 10−15 deg. Using differential snail adjustment, monochromator chamber's attitude can reach a linear resolution of 5 μm and a rotational resolution of 3″, which entirely satisfies the practical requirements.