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