Kinematic Differential Geometry of a Line Trajectory in Spatial Movement

Abstract

This paper investigates the kinematic differential geometry of a line trajectory in spatial movement. Specifically, we provide a theoretical expression of inflection line congruence, which is the spatial equivalent of the inflection circle of planar kinematics. Additionally, we introduce new proofs for the Euler–Savary and Disteli formulae and thoroughly analyze their spatial equivalence.

Keywords

• E. Study map
• axodes
• line congruence
• Disteli formulae