Temple H. Fay is the origin of the aesthetically pleasing plane curve shaped like a butterfly; she
is a mathematician that loved to draw plane curves, and got intrigued into drawing them with the
aid of a computer with the use of different polar equations [1]. A gear is a simple machine that
controls the magnitude of a force, meshing their teeth forms a mechanism called a gear train; it is
usually utilized in transferring energy throughout a system. A gear train is utilized in this project
to draw a butterfly curve. This report is divided into the following sections: (1) vector kinematic
equations that follow a trace point, (2) a description of the experimental apparatus and
procedures used to verify the design, (3) the generated curve from MATLAB, and SolidWorks,
(4) the interpretation of the results produced, and (5) a conclusion which discusses the overall
project and results.