In this work, a rigid-body motion is defined by using the Sannia frame at the striction point of a ruled surface. The relation between the Frenet-Serret motion based on a regular curve and the Sannia motion is given. A Frenet-Serret motion can be seen as a Sannia motion generated by the tangent developable ruled surface to the given curve. However, the converse is not true. An example is presented to show that a Sannia motion is not a Frenet-Serret motion in general. The fixed frame and moving frame velocity twists of the Sannia motions are found and it is noted that the directions of the velocity twists align with the Darboux vector of the Sannia frame. Finally, the Sannia frame motions are completely characterised as the rigid-body motions whose body-frame velocity twist lies in a \(\overline {IB^0}\) 4-system of screws.