By D. Sc., Ph. D. Miomir Vukobratović, Ph. D. Veljko Potkonjak (auth.)

This ebook is a logical continuation of quantity 1 of the sequence entitled "Scientific basics of Robotics" which provides the entire uncomplicated equipment for automatic development of dynamics of manipulation ro bots in addition to the basic innovations of computer-aided layout in their mechanics. Vol. 1 of the sequence additionally includes the most useful re sults from the elastodynamics of manipulation robots, having in brain a necessity for forming a working laptop or computer method which permits effective tests 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 element of stories of manipulation robots, the authors have made a type of a topic-based choice by way of leaving unconsidered a few facets of stories of robots, corresponding to elasticity, and discussing others, extra im portant of their opinion, to such an volume as suffices to cause them to virtually acceptable. The authors have determined 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 proven utilizing the strategy defined in Vol. 1 of the Series.

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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. Further, let wi be the angular velocity and Ei the angular acceleration of the same segment.

A) "Specificity" of (i-l)-th segment on the upper end (b) "Specificity" of i-th segment on the lower end / / Fig. 7. Definition of the generalized coordinate in the case of "specificity" The definition of generalized coordinate in the case of "specificity" is shown in Fig. 7. The existence of "specificity" has to be given to the algorithm via special indicators. If Sj is a linear joint, then the corresponding generalized coordinate 30 q. e. q. = I~I J J J (Fig. 5). Coordinate systems and transition matrices.

But if the same manipulator comes into position of Fig. f. f. f. is lost. The gripper really Fig. 13. Two-body mechanism cannot rotate around the axis "c". 44 So this manipulator has a true singularity in position (b). f) (b) (a) Fig. 14. f. f. (of the whole manipulator and of its gripper). f. f. to solve the task geometrically. This is due to the fact that for such manipulators the tasks are usually imposed on the gripper. f. If we consider a manipulator with n>6 (a redundant manipulator), then the discussion is rather complicated.