Mechanism to Generate a Hyperbolic Paraboloid

move in direction x

move in direction y

This Demonstration illustrates a mechanical device that constrains a point to move on the surface of a hyperbolic paraboloid.

A point on the surface of a hyperbolic paraboloid is equidistant to two skew perpendicular lines

l

and

m

(shown as bars) that are at a distance of 1/4 from the center. The red cylinders represent telescoping bars attached at right angles to

l

and

m

with bearings that can slide or rotate on

l

and

m

. The ends of the telescopic bars meet in a blue point that moves over the surface.