When motion involving large displacements is the main objective of study (e.g. The number of rotational degrees of freedom comes from the dimension of the rotation group SO(n).Ī 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. 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 exact constraint mechanical design method manages the degrees of freedom to neither underconstrain nor overconstrain a device. 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. Skidding or drifting is a good example of an automobile's three independent degrees of freedom. This body has three independent degrees of freedom consisting of two components of translation and one angle of rotation. 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.Īn automobile with highly stiff suspension can be considered to be a rigid body traveling on a plane (a flat, two-dimensional space). The position of a single railcar (engine) moving along a track has one degree of freedom because the position of the car is defined by the distance along the track. 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. In physics, the degree of freedom (DOF) of a mechanical system is the number of independent parameters that define its configuration. For other fields, see Degrees of freedom.
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