The refraction problem, well-known in calculus and physics, continues to reveal new insights. This paper presents a geometric solution in which the trammel of Archimedes plays the prominent role. When properly configured, the trammel generates an ellipse and its family of normal lines. One normal line in particular intersects the boundary separating the media, the intersection point being the solution. The trammel, implemented as a rolling circle mechanism, can be constructed physically and/or programmed as a computer animation.