Roulettes

1. Warm-up Exercise

Record your results here.

2. The Spirograph

Record your experiments and results here.

3. Deriving Formulas

Enter your vector description for the center of the rolling wheel as a pair of parametric formulas:

xcenter[t_]:= ;
ycenter[t_]:= ;

Enter your vector description for the drawing point relative to the center of the rolling wheel.  If you first describe θ as a function of t, then you can use θ(t) in the formulas for xdraw and ydraw.

theta[t_]:= ;

xdraw[t_]:= ;
ydraw[t_]:= ;

Enter your parametric description of the moving point P as a function of t.  Use the "center" and "draw" functions you just defined.

x[t_]:= ;
y[t_]:= ;

Enter (or change) your values of a, b, c here, as well as the number n of complete rotations for the central angle t.  Then plot your curve.  To keep multiple pictures in the notebook, copy, paste, and edit these command lines.

a = 60;
b = 60;
c = 60;
n = 1;
ParametricPlot[{x[t], y[t]}, {t, 0, 2*n*Pi}, 
        AspectRatio -> 1];

4. Hypocycloids and Related Curves (Optional)

Enter your formulas (or copy and edit from Part 3), and do your calculations and plotting here.

5. Summary

Enter your responses to the summary questions here.