By D. Sc., Ph. D. Miomir Vukobratović, Ph. D. Veljko Potkonjak (auth.)
This e-book is a logical continuation of quantity 1 of the sequence entitled "Scientific basics of Robotics" which offers the entire easy 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 functional 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 element of reviews 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, comparable to elasticity, and discussing others, extra im portant of their opinion, to such an quantity as suffices to lead them to virtually appropriate. 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 established utilizing the strategy defined in Vol. 1 of the Series.
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Extra resources for Applied Dynamics and CAD of Manipulation Robots
For the given direction (*) the direction (**) may be replaced by angle ~. Hence, the case (b) represents the total orientation. 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.
Rv is the position vector of the point v and m v is its mass. L designates the sum over all mate- v rial points. If the generalized coordinates are used to describe such a system then the function G becomes a quadratic form with respect to generalized accelerations. If there are n generalized coordinates then the dynamics of the system may be described by a system of equations (Appel's equations) : i=1, ... ,n Qi is a generalized force corresponding to the coordinate qi. 20) 35 Let us now apply this approach to the manipulation mechanism.
A. 2a) rq + ~. 2b) The matrices are calculated from the recursive expressions for velocities and accelerations of segments. 2a,b). g. and E is the angular acceleration of the gripper. The matrices n, e, r, ~ are cal- culated recursively during the formation of dynamic model. In each iteration they correspond to the new segment. At the end of model foDffing procedure these matrices correspond to the gripper. This is the reason that no indices are used with these matrices. The vectors wand E hold for the gripper and are expressed in the cor- responding body-fixed coordinate system.
Applied Dynamics and CAD of Manipulation Robots by D. Sc., Ph. D. Miomir Vukobratović, Ph. D. Veljko Potkonjak (auth.)