By D. Sc., Ph. D. Miomir Vukobratović, Ph. D. Veljko Potkonjak (auth.)
This booklet is a logical continuation of quantity 1 of the sequence entitled "Scientific basics of Robotics" which provides the entire simple equipment for automatic building of dynamics of manipulation ro bots in addition to the basic suggestions 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 process 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 a type of a topic-based choice by way of leaving unconsidered a few points of reports of robots, corresponding 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 proven utilizing the strategy defined in Vol. 1 of the Series.
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Fig. 20(c), (d) shows something analogous but for assembly tasks. 52 ( *) (a) oartial orientation part ia 1 ori enta ti 0 n (b) total orientation tota 1 ori enta ti on Fig. 20. The partial and the total orientation We now consider two examples which demonstrate that the orientation representation chosen (direction and angle) really follows from practical manipulation tasks. Fig. 21. presents a task of spraying powder along a prescribed trajectory. e. positioning) and along the trajectory the container should rotate around the direction (b) according to the prescribed law W(t).
Then we introduce -+* -+ -+* -+ a unit vector r ii perpendicular to e i (rii~ei) (Fig. 6b) and use it -+ instead of r ... ~~ -+* r .. 11 -+ e. __ -+ r.. ~~~t:~~~~ ~l~____~l~l__~ -+ r i -1 • i Ci S. 1 Fig. 6. (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.
Are not exponents but the upper indices. OAk designates the work of the gravity force of segment k. For this segment, using notation from Fig. 81}. 46) )-+, + r kk Then ------- ------ ..... / /" Fig. 2. 10. 48) 40 where the expression in square brackets represents the vector box product. 46). , and let us allow the linear coJ ordinate qj to have a virtual displacement oqj' keeping all other coordinates constant (Fig. 11). Over that displacement the work will be done by the driving force pF and the gravity forces of segments J j, j + 1, ...
Applied Dynamics and CAD of Manipulation Robots by D. Sc., Ph. D. Miomir Vukobratović, Ph. D. Veljko Potkonjak (auth.)