Borromean rings

bez[pts_] := Module[{allpts, fs},
   allpts = Join[pts, pts];
   fs = (Interpolation[#, InterpolationOrder -> 3] &) /@
     Transpose[allpts];

   Flatten@Table[
     Tube[{
       Table[fs[[i]][j], {i, Length[fs]}],
       Table[fs[[i]][j + 0.1], {i, Length[fs]}]
       }, 0.02]
     , {j, 0.5 Length[pts], 1.5 Length[pts], 0.1}]
   ];
circ[x_, n_, e_] :=
  Table[{e Sin[2 Pi i /n] + x, Cos[2 Pi i/n], 0}, {i, n}];
circ2[x_, n_, r_] :=
 Table[{Sin[2 Pi i /n] + x, 0, r Cos[2 Pi i/n]}, {i, n}]
circ3[x_, n_, r1_, r2_, \[Alpha]_] :=
 Table[{x, r1 Cos [-2 Pi i /n + \[Alpha]],
   r2 Sin[-2 Pi i/n + \[Alpha]]}, {i, n}]
c2 = circ2[1.7, 12, 1];
loop = {
   {0.9, 0, -0.5},
   {0.6, -0.1, -0.5},
   {-0.6, -0.5, -0.1},
   {-0.9, -0.5, 0},
   {-0.6, -0.5, 0.1},
   {0.6, -0.1, 0.5},
   {0.9, 0, 0.5},
   {0.6, 0.1, 0.5},
   {-0.6, 0.5, 0.1},
   {-0.9, 0.5, 0},
   {-0.6, 0.5, -0.1},
   {0.6, 0.1, -0.5}
   };
frame[t_, i_] := (
   Graphics3D[
    Rotate[Rotate[
      {
       bez[
        If[t > 5, 6 - t, 1]
          (RotationTransform[
             Pi Min[t, 1], {0, 1, 0}, {-0.8 + Min[t^2, 1], 0, 0}] /@
            circ[-1.7, 12,
             1 + 0.5 Min[t, 1] - If[t > 2, 0.5 (Min[t, 3] - 2), 0]])
         + If[t > 5, t - 5, 0] Reverse[circ[-1.7, 12, 1]]
        ],
       bez[
        If[t > 5, 6 - t,
           1] (ScalingTransform[{1, 1,
                If[t > 3, 1 - 0.2 (Min[t, 4] - 3)^2, 1]}] /@

                   If[t < 2, c2,

               TranslationTransform[{2.2 (Min[t, 3] - 2), 0,
                  0}] /@ ((3 - Min[t, 3]) c2 +
                  (Min[t, 3] - 2) RotateLeft[
                    Join[circ2[1.7, 12, 0.9][[6 ;;]],
                    Map[(0.85 # + 0.15 {1.7, 0, 0}) &,
                    Reverse[
                    circ2[1.7, 12,
                    0.9 - If[t > 3, 0.2 (Min[t, 4] - 3),
                    0]][[7 ;; -2]]]]], 7])]
             If[t > 4, 5 - Min[t, 5], 1]
            +
            If[t > 4, Min[t, 5] - 4,
              0] TranslationTransform[{3, 0, 0}] /@
              RotateLeft[loop, 7])
         + If[t > 5, t - 5, 0] RotateLeft[loop, 7]
        ],

       bez[

        If[t > 5, 6 - t,
           1] RotationTransform[
            If[t > 4, -(Min[t, 5] - 4) Pi/2, 0], {0, 0, 1}, {3.7, 0,
             0}] /@

           TranslationTransform[{0, If[t > 3, 0.7 (Min[t, 4] - 3), 0],
               0}] /@

            If[t < 1, loop,
             loop If[t < 2, (2 - t), 0] +
              If[t < 2, (t - 1), 1] circ3[
                1.7 + If[t > 2, 2 (Min[t, 3] - 2), 0], 12,
                If[t > 2, 1.2 - (Min[t, 3] - 2)/5, 1.2],
                If[t > 2, 0.8 + (Min[t, 3] - 2)/20, 0.8], 5.1145]]
         + If[t > 5, t - 5, 0] RotateLeft[c2, 6]
        ]
       }
      , i Pi/2, {1, 0, 0}], i Pi, {0, 1, 0}]
    , Boxed -> False, ImageSize -> {500, 500}]);
frames = Join[
   Table[frame[t, 0], {t, 0, 6, 6/97}],
   Table[frame[t, 1], {t, 0, 6, 6/97}]];
Export["borr.gif", Join[frames]]