Perigal was an eccentric who had strongly-held unorthodox views regarding the rotation of the Moon. He used a geometric chuck, the most sophisticated piece of machinery available to ornamental turners, to create complex curves, and was the first to classify the results mathematically.

This material shows the relatively simple results of rolling circles around other circles to produce epicycloids. Perigal ordered his results carefully. Three sheets are of bicircloids, one is of centric bicircloids, one is of orthoidal bicircloids and one is of cuspidate bicircloids.