The procedure of modeling and the complete general form mathematical model of manipulators with six degrees of freedom in cooperative work are presented in the paper, together with the solution of undefiniteness problem with respect to force distribution. For the first time, a system of active spatial six-degree-of-freedom mechanisms elastically interconnected with the object (dynamic environment) is modeled. The reason for the emergence of the undefiniteness problem with respect to force is explained and the procedure for solving this problem given. Unlike the approaches given in the available literature, the undefiniteness problem with respect to force is solved in accordance with physical phenomena. The modeling procedure is illustrated by a simplified example.

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