Workable Gears, Archimedian Solids and Planar Bipartite Graphs
Gary Gordon · American Mathematical Monthly · 1994
1. lNTRODUCTlON. My young daughters have a popular children's game which involves setting up a system of interlocking gears. Each of the plastic gears can be fastened to a plastic board in a variety of places. The gears come in three sizes and can be adorned with colorful plastic animals and other decorations. This toy can hold their attention for a long time (where 'long time' is defined as longer than five minutes). We will call an arrangement of the gears (which consists of a finite number of gears, some pairs of which interlock and some which don't) workable if whenever any one gear is turned, all the gears turn freely. Children usually discover that it is quite easy to construct an unworkable arrangement of the gears.