Degree of freedom, mechanical

The definitions and relationships of mass, stiffness, and damping in the preceding section assumed a single-degree of freedom. In other words, movement was limited to a single plane. Therefore, the formulas are applicable for all single degree of freedom mechanical systems. 

Fig. 19 Single-degree-of-freedom mechanical model of milling process...

The term mechanical unit relates to any units that contain parts placed in assemblies and, where applicable, allow movements between pairs of parts with a given degree of freedom. Mechanical units are required in all machines, instruments, cars, domestic appliances, home entertainment devices, etc. The modeling of mechanical units is applied in the engineering and production of most industrial products and production equipment as well as in devices for the manufacture of other products. For example, the same geometry is applied to describe curves in car bodies and in tools for making shoes. 

If the trajectories of all cracks are known beforehand (e.g., from symmetry considerations), the crack sizes take the part of generalized coordinates. When the number of cracks is bounded, the number of degrees of freedom will be bounded, too. Hence, we approach the problem of finite-degrees-of-freedom mechanical systems with unilateral constraints. Equations of continuum mechanics are to be used on the preparatory stage, when stress, strain, and displacement fields are evaluated for states Y.o and X ... 

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