p1 = ParametricPlot3D[{(3 + Cos[v]) Sin[u], (3 + Cos[v]) Cos[u],
    Sin[v]}, {u, 0, 2 Pi}, {v, 0, 2 Pi},
   PlotStyle -> Opacity[.5], Mesh -> None];

ClearAll[p2, p3]
p2[tmax_] := ParametricPlot3D[{Cos[Sqrt[2] t] (3 + Cos[t]),
    Sin[Sqrt[2] t] (3 + Cos[t]), Sin[t]}, {t, 0, tmax}, PlotStyle -> Thick];
p3[tmax_] := ParametricPlot3D[{Cos[Sqrt[2] t] (2 + Cos[t]),
     Sin[Sqrt[2] t] (2 + Cos[t]), 8 + Sin[t]}, {t, 0, tmax}] /.
   Line -> ({CapForm[None], FaceForm[Green, White], Tube[#, .25]} &);

Manipulate[Show[p1, p2[tmax], p3[tmax], PlotRange -> All], {tmax, 1, 50}]