Preface
This book deals with the problems related to planning motion laws and tra-
jectories for the actuation system of automatic machines, in particular for
those based on electric drives, and robots. The problem of planning suitable
trajectories is relevant not only for the proper use of these machines, in order
to avoid undesired effects such as vibrations or even damages on the mechan-
ical structure, but also in some phases of their design and in the choice and
sizing of the actuators. This is particularly true now that the concept of “elec-
tronic cams” has replaced, in the design of automatic machines, the classical
approach based on “mechanical cams”.
The choice of a particular trajectory has direct and relevant implications
on several aspects of the design and use of an automatic machine, like the
dimensioning of the actuators and of the reduction gears, the vibrations and
efforts generated on the machine and on the load, the tracking errors during
the motion execution.
For these reasons, in order to understand and appreciate the peculiarities
of the different techniques available for trajectory planning, besides the math-
ematical aspects of their implementation also a detailed analysis in the time
and frequency domains, a comparison of their main properties under different
points of view, and general considerations related to their practical use are
reported.
For these reasons, we believe that the contents of this book can be of
interest, besides for students of Electrical and Mechanical Engineering courses,
also for engineers and technicians involved in the design and use of electric
drives for automatic machines.
We would like to thank all the persons and colleagues which have con-
tributed to this book. In particular, we would like to thank Claudio Bonivento,
for the initial suggestions and motivations, and Alberto Tonielli for the dis-
cussions on electric drives and their use. The colleagues and friends Roberto
Zanasi, Cesare Fantuzzi, and Alessandro De Luca have contributed not only
with several constructive comments, but also with the development of some
of the algorithms presented in this book.
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