Trochoids: Marking the Point away from Circle

1. Parametrization, $r \mathcal{T}_\lambda$: \[ \underline{r}(t) = \begin{pmatrix} r(t+\lambda \sin{t})\\r(1-\lambda \cos{t}) \end{pmatrix} = r\left( t\underline{\mathbf{i}} + \underline{\mathbf{j}} + \lambda \underline{\mathbf{q}}(t) \right), ~t \in \mathbb{R} \]
2. Cycloid, iff: $\lambda=\pm 1$.