Kinematic generation of Darboux cyclides

TL;DR

This paper explores the geometric relationship between lines on quadrics and circles on Darboux cyclides within the Study quadric framework, revealing new insights into their interconnected structures.

Contribution

It establishes a novel relation between line families on quadrics and circle families on Darboux cyclides in the Study quadric.

Findings

Identifies a specific correspondence between lines on quadrics and circles on cyclides.

Provides a geometric framework linking different families of lines and circles.

Enhances understanding of the structure of Darboux cyclides and their relation to quadrics.

Abstract

We state a relation between two families of lines that cover a quadric surface in the Study quadric and two families of circles that cover a Darboux cyclide.