The inherent characteristics of the (nonlinear) dynamics of robot manipulators are studied. The study is based on a new method, referred to as the trajectory pattern method. The inverse dynamics models of the manipulator are divided into classes of inverse dynamics models, each corresponding to a different trajectory pattern. For each trajectory pattern, the structure of the resulting inverse dynamics model is fixed and is used to study the characteristics of the dynamics of the manipulator by examining the harmonic content of the required actuation torques (forces) and the relative significance of each harmonic. The harmonic content of the actuating torques is shown to be a function of the path length in the joint coordinate space and the harmonic content of the selected trajectory pattern, but is independent of the number of degrees-of-freedom of the manipulator. The relative contribution of each harmonic is a function of the path length, direction of motion, the position of the path of motion within the workspace of the manipulator, and the magnitude of the fundamental frequency. The study provides a systematic approach to path and trajectory planning from the vibration control point of view. As an example, the characteristics of the dynamics of a spatial 3R manipulator is studied for motions with two different path lengths, starting from a specified point and extending in different directions.

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