Abstract: For industrial robot nonuniform rational B-spline (NURBS) trajectory planning in Cartesian space, we use the sinusoidal acceleration curve speed control and the composite Simpson quadrature formula to calculate the track length of the NURBS curved line. We perform the industrial robot feed rate control for the NURBS curve with constraints of maximum contour error and maximum acceleration. In addition, we use Adams differential equations for NURBS interpolation, and control the acceleration and the jerk of the position and the orientation of the curve during the interpolating process. By several hyper-sphere rotation quaternion descriptions of the robot trajectory attitude and spherical linear interpolation, we provide an efficient solution for trajectory planning. Simulation and verification of a six-joint handling robot control system platform are performed. By detection and comparison of the free curved trajectory interpolation step, real-time chord error, and relative deviation, the feasibility and effectiveness of the algorithm is confirmed.