This paper unveils line-geometric foundations of finite displacement screw systems, with an emphasis on incompletely specified displacement of points. Linear line complexes are basic entities used in this research. Bisecting linear line complexes arising from finite displacements are proved to be subject to a reciprocal condition if a new definition of pitch of finite screws is defined. This definition was the one used to formulate finite screw systems. The relations among intersections of linear line complexes, screw systems, and varieties of lines are established in order to investigate finite screw systems. A novel treatment of point displacements allows us to visualize finite screw systems when they are formed by intersecting linear line complexes. This paper provides geometric insights into finite displacement screws and presents a new framework for the unification of finite and infinitesimal kinematics.

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