By Anisim Fedorovich Bermant
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Extra info for A course of mathematical analysis, Part I (International series of monographs on pure and applied mathematics;vol.44)
Applied Control of Manipulation Robots: Analysis, Synthesis and Exercises, Springer-Verlag, 1989. 12 including figures was taken over from ref. . 1 General About Computer-Oriented Procedures for Forming of Mathematical Models of Robot Dynamics Active spatial mechanisms are multivariable mechanical systems of exceptionally complex and variable structure. Their main features include, a large number of links (segments) and degrees of freedom of their relative motions as well as frequent alterations in their kinematic chain configurations.
And l will be termed as the total reaction force at the i-th jOint. In determining the overall reaction the external forces F~ and moments}iu (j=i,i+1, ... ,n) are reduced to the cenJ J tre of the i-th jOint. Reactions of drives of all subsequent jOints need not be taken into account since each drive acts upon two adjacent links with forces and moments of equal magnitude but opposite direction which are thus annulled in the summation process. The overall reactions can therefore be written as : \' +u L F.
43 Active mechani~m An active mechanism represents a system comprising: a) a mechanical part that can be modelled by an appropriate kinematic chain, and b) a set of driving units (actuators) which produce driving torques (forces) . To form the mathematical model of an active mechanism dynamics, it is necessary to: 1) identify the parameters of kinematic chain and actuators, 2) form the dynamic model of mechanism, and 3) form the models of actuators. The dynamic model of an open active mechanism represents a set of n nonlinear differential equations which describe system motion in the space of joint coordinates under the action of driving forces.
A course of mathematical analysis, Part I (International series of monographs on pure and applied mathematics;vol.44) by Anisim Fedorovich Bermant