To improve the running accuracy of the end-actuator of a flexible manipulator in the desired trajectory and reduce the vibrations caused by the motion of the manipulator in a confined space, this study proposed a trajectory planning strategy based on the particle swarm optimization algorithm and genetic algorithm to effectively suppress vibrations. In the study, the slender actuator was abstracted as a flexible beam with concentrated terminal mass attachment, and the dynamics of the flexible beam were simplified using the Cartesian modeling method. The interpolation parameters of the end-actuator trajectory planning were adjusted by the optimization algorithm, considering the end-actuator vibrations during the task execution and the residual vibrations at the end of the task, and an optimization model was built to minimize the amplitude of vibrations. The simulation results show that the optimized trajectory significantly reduces the vibration amplitude of the end-actuator throughout the motion process. To ensure that the manipulator can accurately execute the trajectory, a multi-body kinematic model of the manipulator system was established, and the optimal joint motion trajectory was obtained by solving the problem under the singularity space and obstacle constraint conditions. In the experiment, the joint motion commands were executed by the manipulator, and the actual motion of the flexible end-actuator was monitored by the binocular vision system to verify the effectiveness of the dynamics-based trajectory planning in vibration suppression.