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Cell[CellGroupData[{

Cell["Analyze the Spherical Linkage", "Section"],

Cell[CellGroupData[{

Cell["Compute the joint angles in the given configuraton", "Subsection"],

Cell[BoxData[
    \(UnitV[v_] := N[v/Sqrt[Dot[v, v]]]\)], "Input"],

Cell[BoxData[
    \(LinkAngle[a_, b_] := N[ArcCos[Dot[a, b]]]\)], "Input"],

Cell[CellGroupData[{

Cell[BoxData[
    \(RtoD = N[180/Pi]\)], "Input"],

Cell[BoxData[
    \(57.29577951308232`\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(alpha = RtoD*LinkAngle[sO, sA]\)], "Input"],

Cell[BoxData[
    \(29.999999999999986`\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(beta = RtoD*LinkAngle[sC, sB]\)], "Input"],

Cell[BoxData[
    \(70.`\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(gamma = RtoD*LinkAngle[sO, sC]\)], "Input"],

Cell[BoxData[
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}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
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Cell[BoxData[
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}, Open  ]],

Cell[BoxData[
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Cell[CellGroupData[{

Cell[BoxData[
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Cell[BoxData[
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}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(Ph = RtoD*JointAngle[sA, sA - sO, sB - sA]\)], "Input"],

Cell[BoxData[
    \(\(-15.697890241278879`\)\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(Ps = RtoD*JointAngle[sC, sC - sO, sB - sC]\)], "Input"],

Cell[BoxData[
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}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(Ze = RtoD*JointAngle[sB, sB - sC, \ sB - sA]\)], "Input"],

Cell[BoxData[
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}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell["Functions for Analysis", "Subsection"],

Cell[CellGroupData[{

Cell[BoxData[
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Cell[BoxData[
    \(0.017453292519943295`\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \({a, \ b, \ g, \ h} = DtoR*{alpha, \ beta, \ gamma, \ eta}\)], "Input"],

Cell[BoxData[
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      1.3596538019594986`}\)], "Output"]
}, Open  ]],

Cell[BoxData[
    \(Acoef[t_] := 
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Cell[BoxData[
    \(Bcoef[t_] := Sin[a]*Sin[b]*Sin[t]\)], "Input"],

Cell[BoxData[
    \(Ccoef[t_] := 
      Cos[h] - Cos[a]*Cos[b]*Cos[g] - \ 
        Cos[b]*Cos[t]*Sin[a]*Sin[g]\)], "Input"],

Cell[BoxData[
    \(Psi[t_, sgn_] := 
      ArcTan[Acoef[t], Bcoef[t]] + 
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