Kenneth E. Montgomery
For a wheel
rolling along a line (Figure 1), we let the point of tangency for the circle
and line be point T. The circle has center, C and radius
Open this GSP file to explore the cycloid of a circle,
rolling along the x-axis.
Figure 1: Cycloid of a wheel rolling along the x-axis
Derivation of Parametric
Equations for the Cycloid
Thus, we have
The parametric equations for the cycloid are therefore given by
We then plot these
parametric equations in Graphing Calculator 3.2 to obtain the graph in Figure
2, for four revolutions of the wheel.
Open this GCF file to explore the cycloid in Graphing Calculator.
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