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

ISBN-10: 3642818544

ISBN-13: 9783642818547

ISBN-10: 3642818560

ISBN-13: 9783642818561

This monograph represents the 1st booklet of the sequence entitled "SCI­ ENTIFIC basics OF ROBOTICS". the purpose of this monograph is to ap­ proach the dynamics of energetic mechanisms from the point of view of its program to the synthesis of advanced movement and computer-aided de­ signal of manipulation mechanisms with a few optimum performances. The fast improvement of a brand new type of mechanisms, that could be often called lively mechanisms, contributed to their software in numerous environments (from underwater to cosmic) . due to a few particular fea­ tures, those mechanisms require very cautious description, either in a mechanical experience (kinematic and dynamic) and within the synthesis of algo­ rithms for specified monitoring of the above movement below insufficiently outlined working stipulations. Having additionally in brain the necessity for a really speedy (even real-time) calculation of method dynamics and for getting rid of, in precept, the mistakes made while forming mathematical types "by hand" this monograph will essentially current equipment for automated for­ mUlation of dynamic equations of movement of energetic spatial mechanisms. except those computer-oriented tools, point out can be made up of all these tools that have preceded the computer-oriented approaches, predominantly constructed for various difficulties of inflexible physique dynamics. If we want to systematically identify the origins of the medical self-discipline, which may be known as robotic dynamics, we needs to keep in mind a few teams and participants, who, via fixing real difficulties within the synthe­ sis and keep an eye on of synthetic movement, have contributed to a gentle formation of this discipline.

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Additional info for Dynamics of Manipulation Robots: Theory and Application

Example text

I Fig. 11. Fictitious interruption of the chain in the joint Si_l Now let Si-l be a rotational joint. Then MRi 1 ei _ l . 8) o. 9) are obtained by repeating the procedure for all £ rotational joints. 9) are obtained. 1) by using block matrix formalism. The coordinate system and transition matrices. Let us introduce the coordinate systems. First, there is an external non-moving Cartesian system Oxyz. A vertical z-axis is suitable, but is not obligatory.

Is the mass of i-th segment and J. is the 1. 1. -f. system. The initial state of the mechanism must also be prescribed. So the initial generalized coordinates and the initial generalized velocities are also input data: Depending on the type of dynamical problem there are also the input data: k = O,l, ... ,k end , if a direct problem of dynamics is to be solved, or P(tk ) , k = O,l, ... ,k end , in the case of the inverse problem of dynamics. If a mixed problem is considered, some accelerations and some drives are prescribed.

Fig. 6. Determination of the transition matrix Introducing h. = ~. } are obtained. , we also obtain the. }. ~ ~ ~ Let A~ be the transition matrix corresponding to qi o. 8) Now matrix notation will be introduced. Let e i be the 3xl matrix corresponding to the vector ~i. Analogous matrix notation will be used for all other vectors in the text. ~ bd = Ai i a. ~ b i ] [e i a. 10) o By computing the matrix Ai' the process of "assembling" the joint is 38 completed. The columns of the matrix A~ represent the unit vectors of 1.

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Dynamics of Manipulation Robots: Theory and Application by D. Sc., Ph. D. Miomir Vukobratović, Ph. D. Veljko Potkonjak (auth.)

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