Two types of problems associated with load carrying capacity of robot manipulators are studied. The first type of problem involves determining the maximum load carrying capacity of a robot manipulator given a dynamic robot trajectory. The second problem involves synthesizing point-to-point dynamic robot motions with optimum load carrying capacities. In this Part I of the paper, the first type problem and the formulation of the second type problem are presented. A computational procedure for obtaining numerical solutions to the second type problem together with the application of the results to advanced trajectory synthesis and classification of multi-degree-of-freedom robot manipulators are given in the companion Part II of the paper.

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