Kinematic-geometry of lines with special trajectories in spatial kinematics

This paper derives the expressions for kinematic-geometry of lines with special trajectories in spatial kinematics by means of the E. Study map. A particular assurance goes to the 2nd order movement characteristics for extracting a new proof of the Disteli formulae of the axodes. Meanwhile, a new height dual function is defined and utilized to investigate the geometrical properties of the Disteli-axis. Consequently, as an implementation, the spatial equivalent of the cubic of stationary curvature is established and researched. Finally, Disteli formulae of a line-trajectory are extracted and inspected in detail.