By D. Sc., Ph. D. Miomir Vukobratović, Ph. D. Veljko Potkonjak (auth.)
This publication is a logical continuation of quantity 1 of the sequence entitled "Scientific basics of Robotics" which offers the entire uncomplicated tools for automatic building of dynamics of manipulation ro bots in addition to the basic recommendations of computer-aided layout in their mechanics. Vol. 1 of the sequence additionally comprises the most sensible re sults from the elastodynamics of manipulation robots, having in brain a necessity for forming a working laptop or computer method which permits effective exams of elastic deformations of a manipulator tip or another of its charac teristic issues. Wishing so as to add a hugely applications-oriented measurement to the dynamic point of reviews of manipulation robots, the authors have made one of those a topic-based choice by means of leaving unconsidered a few points of stories of robots, equivalent to elasticity, and discussing others, extra im portant of their opinion, to such an quantity as suffices to cause them to virtually appropriate. The authors have made up our minds to not deal with intimately the matter of versatile manipulation robots for 2 purposes. the 1st effects from the atti tude that the permissible (desired) robotic elasticity may well, satisfacto rily good, be established utilizing the strategy defined in Vol. 1 of the Series.
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All the work about the formation of dynamic model is transferred to the computer. , the configuration represents input data. In addition, the model obtained has a suitable and compact matrix form. Such methods bring the theory closer to applications. -a. methods in the subsequent text) have been developed indepedently in Yugoslavia and USSR [1 - 6) and later on several methods have appeared [7 - 22). -a. methods play now the central role in the algorithms for the dynamic analysis. In this chapter we describe a computer algorithm for the complete dynamic analysis of manipulator motion.
E. the kinematic scheme. ). f. (=number of segments = number of joints), si' i=l, ... ~i' . i=l, ... ,n, determine the orientation of joint axis relative to the connected segments, *r ii , *r i ,i+l' .... i=l, ... , ** r ii or ** r i,i+l' in the case of "specificity" of i-th segment on the lower or upper end, mi , J i , i=l, ... -f. system. The mechanism state q, q is obtained by integration from the previous time instant and q is calculated from the external acceleration Xa. .... Kinematic relations.
G. are proper to each segment. -f. system. l , l'+1 + are constants. l has a constant position with respect to the i-th and (i-1)-th system. -f. system. That is ~. and e. are constants. Such _l l 31 * * * .. vectors r ii , r i ,i+l' e i , : i which determine the geometry of the i-th segment and the i-th joint have to be prescribed for each segment and joint. The transition matrices are obtianed recursively. In each iteration a new segment is added to the chain and the corresponding relative transition matrix is computed.