Formalized description manipulative systems of industrial robots (MS IR) also called functional model (FM) MS IR is suggested. FM MS IR based in usage of quaternion theory and its advantages.
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For the first time the approach to the forming of the functional models of IR Gr based on the elements of the theory of quaternions has been reviewed. The representation of rotational and linear movements of Gr's jaws has been formed. Using the common mathematical apparatus (the theory of quaternions) for forming descriptions of IR's manipulate system and Gr, makes it possible to create an integrated IR's functional model that will be used in the future to solve a number of functional tasks of TI for AS of RMAT developed in Zhytomyr State Technological University, Ukraine.
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