Aiming at the problems of grab failure and manipulator damage, this paper proposes a dynamic gangue trajectory planning method for the manipulator synchronous tracking under multi-constraint conditions. The main reason for the impact load is that there is a speed difference between the end of the manipulator and the target when the manipulator grabs the target. In this method, the mathematical model of seven-segment manipulator trajectory planning is constructed first. The mathematical model of synchronous tracking of dynamic targets based on a time-minimum manipulator is constructed by taking the robot’s acceleration, speed, and synchronization as constraints. The model transforms the multi-constraint-solving problem into a single-objective-solving problem. Finally, the particle swarm optimization algorithm is used to solve the model. The calculation results are put into the trajectory planning model of the manipulator to obtain the synchronous tracking trajectory of the manipulator. Simulation and experiments show that each joint of the robot’s arm can synchronously track dynamic targets within the constraint range. This method can ensure the synchronization of the position, speed, and acceleration of the moving target and the target after tracking. The average position error is 2.1 mm, and the average speed error is 7.4 mm/s. The robot has a high tracking accuracy, which further improves the robot’s grasping stability and success rate.