A free joint, sometimes called a 6-DOF joint or motion sensor, is shown in the diagram below with two reference frames at either end of the connection: on body 1, and on body 2. The free joint places no restrictions on the relative motion of the two frames, but simply provides a means for measuring the relative translations and rotations. The translation of the end frame, relative to the start frame, is represented by the vector, r , which is resolved into its three components in the frame. The rotation of relative to , is represented by three Euler angles.