In Euclidean geometry, a translation is a geometric transformation that moves every point of a figure or space by the same distance in a given direction. It can also be interpreted as the addition of a constant vector at each point, or as a displacement of the origin of the coordinate system.
In Physics, translation is defined as the act of motion of a material body subject to an action such as to cause a displacement on a straight path. The translation is a special case of rotation around an instant center of rotation infinitely distant, located in the direction perpendicular to that of translation. In other words, it is as if a body is moving on a circular trajectory with an infinite radius.
Known the motion of the center of mass, the positions of all points are also known because the distances are fixed. The translation is described by three degrees of freedom, which correspond to the coordinates of the center of mass. In other words, the translational motion of a rigid body has three degrees of freedom described by the three coordinates of the position vector of the center of mass.