Derivation of screw systems for displacing plane elements

This paper sysmetically derives the screw systems for displacing three plane elements, a plane, a unidirectional plane, and a plane-line, by using the linear representation of the screw triangle. The novel three-system for displacing a unidirectional plane is derived from the four-system for displacing a plane by adding a geometrical constraint to the plane. The two-system for displacing a plane-line is obtained by adding another constraint to the undirectional plane.