A new geometrical approach to one-parameter spatial motion

The geometry and kinematics of one-parameter dual spherical motions is presented using Study's dual-line coordinates. The relations between invariants of the axodes are expressed in simple form with geometrical reasoning and explanation. In terms of this, the dual version of associated space curves is demonstrated for a ruled surface to be associated with the axodes of the motion. The relative motion between the axodes is used for deriving the geometry and kinematics of the paths instantaneously traced in the fixed space by a line associated with the moving axode. Especially, the distribution parameter and the inflection-line congruence are investigated. Furthermore, a new metric is developed and used to investigate the geometrical properties and kinematics of line trajectory as well as Disteli axis. Finally, as an application an example is put forward and explained in detail.