Manipulate[
 ParametricPlot3D[{Cos[Sqrt[2] t] (3 + Cos[t]),
   Sin[Sqrt[2] t] (3 + Cos[t]), Sin[t]}, {t, 0, maxTime},
  ImageSize -> 300, PlotRange -> {{-4, 4}, {-4, 4}, {-1, 1}},
  PlotStyle -> Red]
 ,
 {{maxTime, 1, "time"}, 1, 50, 0.01, Appearance -> "Labeled"},
 TrackedSymbols :> {maxTime}
 ]