Aiming at the problem that the jerk value is discontinuous in the traditional S-curve model, which affects the accuracy and service life of the equipment, a new trajectory planning and multi-axis synchronization algorithm are proposed. Firstly, an infinitely differentiable 15-segment jerk model is constructed based on the piecewise trigonometric function, then the time-optimal point-to-point trajectory satisfying the kinematic constraints is interpolated, and finally, the parametric expression of point-to-point multi-axis synchronization algorithm with minimum velocity is derived. The method is simple to calculate and can obtain analytical solutions, and at the same time, it can ensure that the generated curve is smooth. The simulation show that the proposed method can generate continuous smooth trajectories while increasing the total planning time by less than 5% compared with the conventional S-curve. Therefore, the correctness and effectiveness of the proposed method are verified.