In order to create a fundamentally new machine, impressive in simplicity and originality, it needs be oriented freely in the fundamental laws of physics and manageable in the classical methods of analysis and synthesis of mechanical systems. The main purpose of this book is to fill in the gaps of knowledge, partly lost in the practical work. In the first part of the book the methods of structural, kinematic and dynamic analysis of mechanisms and machine units are presented. Preference is given to the graphical methods of investigation as the most visible, flexible and high-precision (due to modern computer programs). The second part indicates the mechanisms’ synthesis methods from the preassigned output characteristics. At this point exactly the constructive and creative nature of engineering work becomes apparent. The third part draws attention to the vibrating units and, in particular, to the suppression of high-speed machine vibration. The main concepts from the theory of vibrations and balancing equipment are reported. A method of active vibration protection with energy recovery is elaborated.