Manipulators are equipped with several joints and it is possible to operate along any given trajectories. This flexibility is essential advantages and valuable studies are conducted for trajectory planning to effectively control manipulators. However, manipulators belong to a class of complex nonlinear dynamic systems and the application of trajectory planning leads to substantial difficulties. Therefore, various methods are proposed to solve optimal problems by adding or neglecting adequate

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... straints. However, they do not seem to offer generalized trajectory formation methods. This paper discusses trajectory planning of point-to-point operations under condition that only an initial and a final states are given. Performance criterion is defined by consumed energy dissipated in operations and motor torque limit is considered. Mathematical formulation to calculate optimal trajectories is proposed and simulation is conducted for a 2 degrees of freedom manipulator. Amount of energy dissipation is discussed in relation with optimal and various operating time for typical manipulator movements. Besides, merit of trajectory planning based on a minimum-energy criterion and operating time is stated. Finally, characteristics of energy consumption in human arm movements is discussed and formulated trajectories are verified that they show similar features with human arm trajectories in relatively fast movements.