Box = {{0, 0}, {0, 1}, {-1, 1}, {-1, 0}, {0, 
            0}};
Ito = {{-1/2, 0}, {-1/2, 1}};
Ro[
          t_] := {{Cos[t], -Sin[t]}, {Sin[t], 
            Cos[t]}};
Lev[t_] := 
      Which[Tan[t] < 
          0.5, {{-1, 1/4 - Tan[t]/2}, {0, 
            1/4 + Tan[t]/2}}, 
0.5 ≤ 
          Tan[t] ≤ 
          1.5,  {{-2/(1 + 2  Tan[t]), 0}, {0, 
            1/4 + Tan[t]/2}}, 
1.5 < 
          Tan[t], {{-1/4 - 1/(2  Tan[t]), 
            0}, {-1/4 + 1/(2  Tan[t]), 
            1}}]
Do[Show[
        Graphics[{Line[Box . Ro[t]], Line[Ito . Ro[t]], 
            Line[Lev[t] . Ro[t]]}], AspectRatio -> Automatic, 
        Axes -> None, PlotRange -> {{-1, 1}, {0, 1.5}}], {t, 0, 
        Pi/2 - 0.01, Pi/36}]