The Catenary as Roulette

Summary

The focus of a parabola rolling without sliding along a straight line traces a catenary. We give some historical notes on this classical kinematical construction, observe that it was rediscovered in a recent article, and give a simpler and more geometric alternative derivation.

Additional information

Notes on contributors

Javier Sánchez-Reyes

Javier Sánchez-Reyes ([email protected]) is a professor of graphics in engineering at the University of Castilla-La Mancha (Spain), where he has been on the faculty since 1999. He earned a Ph.D. in Mechanical Engineering from the Polytechnic University of Catalonia (Spain) (1988). Next he was a visiting scholar at the University of California, Berkeley (in Mechanical Engineering). His research focuses on computer-aided geometric design with particular emphasis on rational curves and surfaces.