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This work deals with the complex task of unscrewing and screwing a threaded cap with a dexterous anthropomorphic robotic hand. To that end, human motion profiles of nine test subjects were recorded using the CyberGlove II and the data were analyzed for unscrewing and screwing a bottle cap. Results showed that the periodic motions exhibited by the finger joints shared a common frequency for each subject, but differed in amplitude and phase. The unscrewing data appears highly similar to the mirror image of the screwing data. This implies that the screwing motions can be backdriven to produce the unscrewing motion and vice versa. A forward loop (FL) in time implies an increment in the time vector, which starts from zero and ends at some point resulting to unscrew the bottle cap. A reverse loop (RL) is produced by a decrement in time and results in screwing the bottle cap. From the gathered data, a set of sinusoidal trajectories were developed to approximate this motion for a robotic hand. Because the joint trajectories share the same frequency, a single sinusoidal input can be used in the path planning of the robot to achieve this task. The reference joint is given a sinusoidal input and the remaining joints are scaled in phase and amplitude with respect to this reference joint. This significantly reduces the computational cost and complexity of the task. Simulation results show that the developed sinusoidal trajectories show a close correlation with the motion profiles seen from human experiments. Using the developed sinusoidal trajectories, the robotic hand successfully unscrewed and screwed the bottle cap in all trials conducted.