Research On Path Planning Of Five-axis Linkage Of C-shaped Gantry Parallel Machine Tool

In this paper,a five-axis machine tool consisting of a Three-Translational C-shaped gantry parallel machine tool and a 2-DOF rotary table is studied.The machine kinematics is studied.The tool compensation algorithm,interpolation algorithm and velocity control algorithm which are closely related to path planning are also deeply studied.The main work of this paper is as follows:Firstly,kinematics is studied.According to the kinematic relationship of machine tool and the principle of coordinate transformation,the forward and backward equations of position are derived.Based on the inverse position equation,the velocity and acceleration relationship between the moving platform and the driving mechanism is deduced.Through the speed simulation analysis with MATLAB,the dead-point position of the moving platform and the changing trend of the maximum speed in the workspace are obtained,and the judging conditions of the movement of the redundant slider are determined.According to dead-point position,workspace,stiffness of machine tool and size of the workpiece,different methods to determine the installation position of rotary table are given.Secondly,the algorithm of tool radius compensation is studied.Based on the principle of 2D tool radius compensation,the cutter radius compensation algorithm for side milling is deduced by using the principle of space matrix transformation and projection.The algorithm of face milling radius compensation is closely related to the type of tool.The algorithms of end mill,ball end mill and end mill with corner rounding are studied.The simulation results show that the tool radius compensation algorithm can realize the space tool radius compensation.Then,according to the structural characteristics and motion relationship of machine tools,a two-step interpolation algorithm is proposed.The tool orientation interpolation algorithm is used in Cartesian space,and the cubic B-spline interpolation curve interpolation is used in joint space.The results of MATLAB simulation shows that the two-step interpolation algorithm not only effectively reduces the non-linear error,but also improves the smoothness of machine motion.Finally,the velocity control algorithm and arc transition algorithm which are suitable for the two-step interpolation algorithm are proposed.The advantages and disadvantages of acceleration and deceleration control algorithms are analyzed,and the S-curve speed control algorithm is improved.The improved speed control algorithm is combined with arc transition transfer algorithm,which not only realizes the continuity of speed and acceleration,but also improves the flexibility of the system and the processing accuracy.