Tractriz: an approach from the perspective of Trail Geometry

Abstract

This academic work presents discussions about the Tractriz, a particular case of the pursuit curves set. The Tractriz is the curve that results from the movement of a block being pulled by a constant lenght rope. This rope, firstly positioned vertically, when shifts its opposite ends of the block, horizontally, the path described by the block will be the Tractriz pursuit curve. The curve described by this block path can be observed in many daily situations, such as a simple walk with a dog, or even a car track, having applications such as trumpets fabrication. In order to increase the discussions about the pursuit curves, especially Tractriz, we present here the obtaining of the characteristic equation of this curve and its behavior verification through an experimental activity performed with a bicycle. In face of that, we discussed a possible pursuit curve variation described by the rear wheel of a bicycle, based on the variation of handlebar’s angle of rotation, as well as possible aplications for parking systems and its representation in natural phenomena.