Manipulate[
ParametricPlot3D[{(2 + Cos[t]) Cos[t], (2 + Cos[t]) Sin[t],
Sin[t]}, {t, 0, tRange}, {s, 0, sRange},
PlotRange -> {{-3, 3}, {-3, 3}, {-1, 1}}],
{{tRange, Pi, "tRange"}, 0.1, 2 Pi, .1, Appearance -> "Labeled"},
{{sRange, Pi, "sRange"}, 0.1, 2 Pi, .1, Appearance -> "Labeled"}]