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In this book some worked out kinematical and kinetic examples can be studied. These examples can be useful not only for practicing constructor mechanical engineers but also for mechanical engineer students. Applied methods are relatively easy to use. In first chapter some kinematical examples in the field of synthesis of planar mechanisms can be seen. By presentation of a few examples concerning four-bar and slider-crank mechanisms this chapter covers path generation synthesis and function generation synthesis. In second chapter there are a couple of application of numerical method presented by examples of single degree-of-freedom nonlinear mechanical vibration and multi degree-of-freedom linear torsional vibration of beams. In case of construction of oscillating systems the most important parameters are their natural frequencies. Because of phenomena of resonance the avoidance of them is definitely needed. The last subchapter is about the critical shaft speed to be taken into consideration for the constructors.