This paper discusses cycloids and their construction using the 19th century mechanical drawing instrument known as the Geometric Chuck. The first part of the paper is a brief history and description of the Geometric Chuck. The last part of the paper is devoted to a discussion the definition of cycloids and examples showing the results that various settings of the Geometric Chuck have on the cycloid patterns produced. This paper is an attempt, in part, to respond to the comment in the Savory book "As this book does not aim at giving a scientific account of the principles on which it works. It might be an exceedingly interesting subject for the scientific person, ...the scientific knowledge required to understand a three-part chuck would be so great that I doubt if there is the person existing who could describe the course of a line that would be produced ."