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 all the easy equipment for automatic building of dynamics of manipulation ro bots in addition to the fundamental thoughts 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 strategy 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 experiences of manipulation robots, the authors have made one of those a topic-based choice by means of leaving unconsidered a few facets of reviews of robots, equivalent to elasticity, and discussing others, extra im portant of their opinion, to such an quantity as suffices to cause them to essentially 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 possibly, satisfacto rily good, be proven utilizing the tactic defined in Vol. 1 of the Series.
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Matrices: ~ is a 3xn matrix, the columns of which are the coefficients of the generalized accelerations in the expression for~. 1 (in the i-th itera- tion) , 8 is a 3x1 matrix, containing the free term of the same expression. Now the acceleration ~. can be written in the matrix form 1 W. 25 ) G. 26 ) 36 Further, let us define the following matrices: f is a 3 x n matrix, the columns of which are, in the i-th iteration, the coefficients of the generalized accelerations in the expression for ~ '"E i , is a 3x1 matrix, containing the free term of the same expression.
A vertical z-axis is suitable but is not obligatory. -f. in the sequel) Cartesian coordinate system 0ixiYizi is defined. g. Ci of the segment and the axes are oriented along the inertial principal axes. -f. axes is also suitable but is not obligatory. l to designate a vector corresponding to the i-th segment or i-th joint and which is expressed via three projections ai 7 onto the axes of the external coordinate system. designates the same vector but expressed by projections onto axes of the i-th body-fixed 7 system.
2) where P is the n-dimensional vector of driving forces and torques in mechanism joints. As previously stated the nxn inertial matrix W depends on q and the n x l matrix U depends on the state q, q. By the term formation of dynamic model we mean the calculation of the matrices W and U. Hence, we now derive the procedure for numerical computation of W, U for the known mechanism state q, q and the configuration consid- ered. Mechanism configuration. This method considers the mechanism of open chain type consisting of n arbitrary rigid bodies (Fig.