The robotic motion planning criteria has evolved from kinematics to dynamics in recent years. Many research achievements have been made in dynamic motion planning, but the externally applied loads are usually limited to the gravity force. Due to the increasing demand for generic tasks, the motion should be generated for various functions such as pulling, pushing, twisting, and bending. In this presentation, a comprehensive form of equations of motion, which includes the general external loads applied at any points of the system, is derived and implemented. An optimization-based algorithm is then developed to generate load-effective motions of redundant manipulators (single-loop and tree-structured chains) that guarantee the execution of the generic tasks under limited actuator capacities. It is shown that if the external loads are not incorporated in the motion planning formulation, then the generated motions do not always guarantee the execution of the task, especially when a large load is desired. By using our algorithm, the load-effective motions can be found that are executable for given external loads. The proposed method is also applicable in predicting realistic dynamic human motions. Some dual-arm human tasks are simulated to show different motions to sustain different amounts of external loads. Our formulation for general external loads will further advance the current motion planning methods for redundant manipulators.