To improve the arc trajectory precision of puma560 end-effector passing the non-collinear three points and reduce the calculation amount of real-time interpolation, In this paper, the quaternion is used to describe the end attitude of the manipulator, and the five-segment S-curve normalization operator is applied to the spherical interpolation of the quaternion, it make the orientation change smoothly, and the speed does not change suddenly. At the same time, it proposes to apply the five-segment s-curve in the manipulator Cartesian space interpolation algorithm to achieve a smooth transition to velocity and acceleration, avoiding the vibration of the manipulator effectively. In this paper, we use Matlab as a simulation platform to analyze the kinematics of manipulator, and to perform arc trajectory planning in the manipulator Cartesian space, and also perform simulation verification on the orientation trajectory. The simulation results show that the algorithm can guarantee the smooth transition to angular velocity and angular acceleration, avoid sudden change of the orientation of the manipulator, and verify the effect of the trajectory planning visually. It provides an efficient and feasible trajectory planning method.