Fun With Cycloids

The curves we will be looking at in this lab are cycloids. So let's review. I'll assume that you already know a little about cycloids, but let's go over what you'll be seeing. The first type of cycloid we will be examining is the linear cycloid. (Remember a cycloid is the path swept out by a point on a circle rolling along a path. In this case the path is a line.) A linear cycloid can be defined parameterically as

x(t) = a*t - b*sin(t) y(t) = a - b*cos(t)

Question 1: Your first fun question.

What is the relationship between the absolute value of a, the absolute value of b, and the shape of the cycloid? Draw or describe each of the three different cycloid shapes.

Oh baby, it's a cardioid!

Now let's look at the cardioid. A cardioid is the cycloid swept out by a point on a circle rolling around another circle of equal radius. All cardioids have the same shape, the only potential differences are the orientation and size. The cardioid we will be looking at is r = 1 + cos(theta) This can be defined parameterically as

x(t) = (1 + cos(t))*cos(t) y(t) = (1 + cos(t))*sin(t)

Plot this curve and appreciate its beauty. If you do not you will be doomed to a life of misery and sorrow for this lost opportunity.

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