Basic Motion Profiles -- Analytic Expressions of Elementary Trajectories -- Composition of Elementary Trajectories -- Multipoint Trajectories -- Elaboration and Analysis of Trajectories -- Operations on Trajectories -- Trajectories and Actuators -- Dynamic Analysis of Trajectories -- Trajectories in the Operational Space -- Multidimensional Trajectories and Geometric Path Planning -- From Geometric Paths to Trajectories -- Appendices -- A Numerical Issues -- B B-spline, Nurbs and Bézier curves -- C Representation of the Orientation -- D Spectral Analysis and Fourier Transform -- Trajectory Planning -- Trajectory Planning.

This book deals with the problems related to planning motion laws and trajectories 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 mechanical 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 “electronic 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 mathematical 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.