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In mechanics, the degree of freedom (DOF) of a mechanical system is the number of independent parameters that define its configuration. It is the number of parameters that determine the state of a physical system and is important to the analysis of systems of bodies in mechanical engineering, aeronautical engineering, robotics, and structural engineering. The position of a single car (engine) moving along a track has one degree of freedom because the position of the car is defined by the distance along the track. A train of rigid cars connected by hinges to an engine still has only one degree of freedom because the positions of the cars behind the engine are constrained by the shape of the track. An automobile with highly stiff suspension can be considered to be a rigid body traveling on a plane (a flat, two-dimensional space). This body has three independent degrees of freedom consisting of two components of translation and one angle of rotation. Skidding or drifting is a good example of an automobile's three independent degrees of freedom. The position and orientation of a rigid body in space is defined by three components of translation and three components of rotation, which means that it has six degrees of freedom. The Exact constraint mechanical design method manages the degrees of freedom to neither underconstrain nor overconstrain a device.〔http://ocw.mit.edu/courses/mechanical-engineering/2-76-multi-scale-system-design-fall-2004/readings/reading_l3.pdf〕 ==Motions and dimensions== The position of an ''n''-dimensional rigid body is defined by the rigid transformation, () = (), where ''d'' is an ''n''-dimensional translation and ''A'' is an ''n'' × ''n'' rotation matrix, which has ''n'' translational degrees of freedom and ''n''(''n'' − 1)/2 rotational degrees of freedom. The number of rotational degrees of freedom comes from the dimension of the rotation group SO(n). A non-rigid or deformable body may be thought of as a collection of many minute particles (infinite number of DOFs), this is often approximated by a finite DOF system. When motion involving large displacements is the main objective of study (e.g. for analyzing the motion of satellites), a deformable body may be approximated as a rigid body (or even a particle) in order to simplify the analysis. The degree of freedom of a system can be viewed as the minimum number of coordinates required to specify a configuration. Applying this definition, we have: #For a single particle in a plane two coordinates define its location so it has two degrees of freedom; #A single particle in space requires three coordinates so it has three degrees of freedom; #Two particles in space have a combined six degrees of freedom; #If two particles in space are constrained to maintain a constant distance from each other, such as in the case of a diatomic molecule, then the six coordinates must satisfy a single constraint equation defined by the distance formula. This reduces the degree of freedom of the system to five, because the distance formula can be used to solve for the remaining coordinate once the other five are specified. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Degrees of freedom (mechanics)」の詳細全文を読む スポンサード リンク
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