φ=Tan[1/3];
Clear[DrawPlus,MakeScene]
DrawPlus[p:{x_,y_},θ_]:=Module[{line},
line=Polygon[{{1,1},{3,1},{3,-1},{1,-1},{1,-3},{-1,-3},{-1,-1},{-3,-1},{-3,1},{-1,1},{-1,3},{1,3},{1,1}}];
line=GeometricTransformation[line,RotationMatrix[θ]];
GeometricTransformation[line,TranslationTransform[p]]
]
MakeScene[α_]:=Module[{p,q,θ=π α,gr},
p={1.,-3.}+(Sqrt[10]){Cos[θ-φ],-Sin[θ-φ]};
q={3.,1.} + (Sqrt[10]){Sin[θ-φ],Cos[θ-φ]};
gr=Flatten[Table[DrawPlus[i p +j q,If[EvenQ[i+j],0,-θ]],{i,-2,2},{j,-2,2}],1];
gr=GeometricTransformation[gr,RotationMatrix[θ/2]];
Graphics[{EdgeForm[Directive[Thick,Black]],Opacity[.5],RGBColor[0,0.4,1],gr},PlotRange->(20{{-1,1},{-1,1}}),ImageSize->300]
];

MakeScene[1/2]

Animate[MakeScene[β],{β,0,2,.00025}]

images=Table[MakeScene[β],{β,0,2,.01}];

Export["~/research/qr/hinges/anim.swf",Most[images]];