Issue Plotting Torus Link

Here's I think a generalization of what Ulrich gave to an arbitrary $(p, q)$ torus (if I read Wikipedia right):

plotPQTorus[{p_, q_}, a : _?NumericQ : 1, d : _?NumericQ : 4, 
  ops : OptionsPattern[]] :=
 Block[{t},
  ParametricPlot3D[
    Evaluate@
     Table[
      RotationMatrix[
        i*2 \[Pi]/q, {0, 0, 1}].{(a*Sin[q*t] + d)*
         Sin[p*t], (a*Sin[q*t] + d)*Cos[p*t], a*Cos[q*t]},
      {i, 0, If[Divisible[q, p], p - 1, 0]}
      ],
    {t, 0, 2*Pi},
    PlotRange -> All,
    ops
    ] /. Line[pts_, rest___] :> Tube[pts, 0.2, rest]
  ]

Here are a few plots:

Table[plotPQTorus[{p, Fibonacci[q]}, Boxed -> False, 
   Axes -> None], {p, 1, 4}, {q, 2, 6, 2}] // Grid

Note that relatively prime things are single connected loops (as Wikipedia suggests they should be)

The second torus is created by a rotation of $\pi/4$ (around {0, 0, 1}):

R = RotationMatrix[Pi/4, {0, 0, 1}];
torus = {(a*Sin[q*t] + d)*Sin[p*t], (a*Sin[q*t] + d)*Cos[p*t], a*Cos[q*t]};
ParametricPlot3D[{torus, R.torus} // Evaluate, {t, 0, 2*Pi}, PlotStyle -> {Orange, Blue}, PlotRange -> All] 

The (1,4) torus knot is known to KnotData[], so we can use that to build the (2,8) knot:

knot14 = First[KnotData[{"TorusKnot", {1, 4}}, "ImageData"]];

Graphics3D[MapThread[Insert[##, {2, 1}] &,
                     {{knot14, MapAt[RotationTransform[π/4, {0, 0, 1}], knot14, {1}]}, 
                      Directive[Specularity[1, 10], #] & /@ {Blue, Red}}], 
           Boxed -> False, Lighting -> "Neutral", ViewPoint -> {0, 0, ∞}]