When and how machine dynamics emerged from practical engineering issues is historically studied. The ever-increasing speed and power of steam engines in the mid-19th century energized the engineers to develop new techniques of balancing wheels, particularly those of steam locomotives, to obtain running stability at high speed. Vibration of slender shaftings placed along the ceiling of factories was another urgent problem to be solved. The concept of flexural critical speed of a rotating shaft was thereby introduced, resulting in the birth of a new disciplinary field known as "machine dynamics".