# Parameter variation plot error

h = -5; k = 0;
ParametricPlot[{{(t - Sin[t] + h), (1 - Cos[t])}, {(Cos[t] -
1), (t - Sin[t]) + k} }, {t, 0, 2 Pi}, PlotLabel -> Cycloid_OT,
PlotStyle -> {Red, Thick}, GridLines -> Automatic]
ParametricPlot[
Evaluate@Table[{{(t - Sin[t] + h), (1 - Cos[t])}, {(Cos[t] -
1), (t - Sin[t]) + k} }, {h, -5, 5, 1}], {t, 0, 2 Pi},
PlotLabel -> Cycloid_OT, PlotStyle -> {Red, Thick},
GridLines -> Automatic]


The two cycloid curves parametrized below have slopes that multiply to $$-1$$.

$$[( t-\sin t),(1- \cos t)]$$ $$[\cos t , (t-\sin t)]$$

I am trying to generate a mesh of plots by varying $$h$$ and $$k$$.

But $$h$$ itself is in error.

The plot aims to show that not all intersections are orthogonal, by visible verification.

Thanks for errors correction.

EDIT1:

Plot of two families of cycloids suggested by kglr with plot $$Join$$ using half interval for (h,k) steps in the intervals $$(-2

• try Evaluate[Join@@Table[{{(t - Sin[t] + h), (1 - Cos[t])}, {(Cos[t] - 1), (t - Sin[t]) + k}}, {h, -5, 5, 1}]] in the first argument of ParametricPlot? – kglr Aug 2 at 5:22
• Thanks that works for $h$. Next please perturb the $k$ set for a full two parameter net. – Narasimham Aug 2 at 5:59
• how about ParametricPlot[ Evaluate[Join[Table[{(t - Sin[t] + h), (1 - Cos[t])}, {h, -5, 5}], Table[{(Cos[t] - 1), (t - Sin[t]) + k}, {k, -5, 5}]]], {t, 0, 2 Pi}, GridLines -> Automatic]? – kglr Aug 2 at 6:28
• The plot is ok now.. but shown result is not so encouraging. I had expected more orthogonal reticles. – Narasimham Aug 2 at 8:17