The manipulator with five degrees of freedom (5-DOF) cannot reach any pose, so it is easy to get no solution when the traditional pose description method is used to solve the inverse kinematics. In this paper, a 5-DOF manipulator consisting of four rotary joints and one prismatic joint, which is suitable for cleaning, spraying, welding and other operations, is taken as an example to establish a kinematic model and its inverse kinematic analysis is carried out. Then, an inverse kinematics solution method based on joint angle parameterization combined with the feasible direction of approach vector is proposed based on the end pose description of degree of freedom constraints. In this method, firstly, the motion space of the end executor is reduced from three dimensions to two dimensions through joint angle parameterization. Then, the feasible direction of the approach vector of the end executor at different target positions (distal, middle and proximal) is analyzed by geometric method, so as to avoid blind parameter setting and ensure the existence of inverse kinematics solutions. Thereafter, the optimal solution is selected according to the motion continuity and motion range of each joint. The simulation analysis results of path planning show that the actual path is very consistent with the planned path and the joint motion is stable, which proves the feasibility and accuracy of the proposed solution method. The 5-DOF manipulator studied in this paper is representative to some extent and the proposed solution method possesses the advantage of low computational complexity and simple solving process. Therefore, the solution idea can provide reference for the inverse kinematics solution of the manipulator with less degrees of freedom.

Fine particle shot peening is one of the key technologies for high-performance gear manufacturing. In the study of gear dynamics and gear precision manufacturing, one of the important research topics is accurately analyzing the influence of fine particle shot peening on the normal contact stiffness of gear. In this paper, the changes of micro morphology of gear teeth surface before and after the fine particle shot peening were compared and analyzed through characterizing the micro morphology of the fine particle shot peened gear surface. Based on the fractal theory, the normal contact stiffness model of the fine particle shot peened gear was established considering the elastic-elastoplastic-plastic deformation of a single asperity and asperity interaction. It conducted a simulation analysis on the variation law of the normal contact stiffness along with the normal load, the fractal dimension D, the fractal rough amplitude G and the parameter of material property. The influence of fine particle shot peening on the normal contact stiffness of the gear was analyzed by extracting the fractal parameters of fine particle shot peened gear surface with the power spectral density function method. The results show that fine particle shot peening leads to randomly distributed micron or even nanoscale pits on the gear surface, and the decrease of surface roughness. Also, the gear surface roughness increases with the increase of fine particle shot peening strength. The normal contact stiffness increases with the increase of normal load, material yield strength, and fractal dimension D, and decreases with the increase of fractal roughness amplitude G. Fine particle shot peening can change the gear normal contact stiffness by changing the micro morphology of gear surface, and then change the fractal dimension D and fractal roughness amplitude G. Compared with the gear without fine particle shot peening, the normal contact stiffness of fine particle shot peened gears is improved. With the increase of shot peening strength, the normal contact stiffness of gears decreases. The research results provide a theoretical basis for gear dynamics research and high-performance gear manufacturing.