This monograph represents the first book of the series entitled "SCI-
ENTIFIC FUNDAMENTALS OF ROBOTICS". The aim of this monograph is to ap-
proach the dynamics of active mechanisms from the standpoint of its
application to the synthesis of complex motion and computer-aided de-
sign of manipulation mechanisms with some optimal performances. The
rapid development of a new class of mechanisms, which may be referred to
as active mechanisms, contributed to their application in various
environments (from underwater to cosmic) . Because of some specific fea-
tures, these mechanisms require very careful description, both in a
mechanical sense (kinematic and dynamic) and in the synthesis of algo-
rithms for precise tracking of the above motion under insufficiently
defined operating conditions. Having also in mind the need for a very
fast (even real-time) calculation of system dynamics and for
eliminating, in principle, the errors made when forming mathematical
models "by hand" this monograph will primarily present methods for
automatic for- mUlation of dynamic equations of motion of active spatial
mechanisms. Apart from these computer-oriented methods, mention will be
made of all those methods which have preceded the computer-oriented
procedures, predominantly developed for different problems of rigid body
dynamics. If we wish to systematically establish the origins of the
scientific discipline, which could be called robot dynamics, we must
recall some groups and individuals, who, by solving actual problems in
the synthe- sis and control of artificial motion, have contributed to a
gradual formation of this discipline.