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For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. ***********************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 55446, 1195]*) (*NotebookOutlinePosition[ 56345, 1224]*) (* CellTagsIndexPosition[ 56301, 1220]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell["POV Data for Planar 4R Chain", "Title"], Cell[BoxData[ \(Quit[]\)], "Input"], Cell[CellGroupData[{ Cell["Input Position and Linkage Data", "Section"], Cell[CellGroupData[{ Cell[BoxData[ \(data1 = << "\"\)], "Input"], Cell[BoxData[ \({{0, 0, 0}, {22, \(-6\), 11}, {68, \(-17\), 13}}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(npos = Length[data1]\)], "Input"], Cell[BoxData[ \(3\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \({pO, \ pA, \ pB, pC} = << "\"\)], "Input"], Cell[BoxData[ \({{\(-15\), 0}, {\(-12.23340699382514`\), \(-2.8571956875574873`\)}, \ {\(-11.962204093248042`\), \(-7.981967927707509`\)}, {5, 1}}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \({Th, Ph, \ Ps, \ Ze} = << "\"\)], "Input"], Cell[BoxData[ \({{5.431719529019564`, 1.8464638793758672`, 2.9434846012813454`}, {5.566767035357889`, 3.252809813260752`, 2.9586405472726653`}, {3.5786245470207056`, 3.1898391867676175`, 3.200283330362072`}, {1.1366767101771609`, 1.9094345058690017`, 2.701841818191939`}}\)], "Output"] }, Open ]], Cell[BoxData[ \(LinkLength[a_, b_] := N[Sqrt[Dot[b - a, b - a]]]\)], "Input"], Cell[BoxData[ \(JointAngle[b_, c_] := N[ArcTan[Dot[b, c], Det[{b, c}]]]\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(a = LinkLength[pO, \ pA]\)], "Input"], Cell[BoxData[ \(3.9771351572221874`\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(b = LinkLength[pC, pB]\)], "Input"], Cell[BoxData[ \(19.19354359036827`\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(g = LinkLength[pC, pO]\)], "Input"], Cell[BoxData[ \(20.024984394500787`\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(h = LinkLength[pB, pA]\)], "Input"], Cell[BoxData[ \(5.131943250533243`\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(BaseTh = JointAngle[{1, 0}, pC - pO]\)], "Input"], Cell[BoxData[ \(0.049958395721942765`\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(rem = {{1, 0, 0}, {0, 1, 0}}\)], "Input"], Cell[BoxData[ \({{1, 0, 0}, {0, 1, 0}}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["Functions for 4x4 transformations", "Subsection"], Cell[BoxData[ \(Disp[t_, d_] := {{Cos[t], \(-Sin[t]\), 0, d[\([1]\)]}, \ {Sin[t], Cos[t], 0, d[\([2]\)]}, {0, 0, 1, 0}, \ {0, 0, 0, 1}}\)], "Input"], Cell[BoxData[ \(Zdisp[t_] := Disp[t, {0, 0}]\)], "Input"], Cell[BoxData[ \(Xdisp[t_] := Disp[0, {t, 0}]\)], "Input"], Cell[BoxData[ \(Ydisp[t_] := Disp[0, {0, t}]\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(DtoR = N[Pi/180]\)], "Input"], Cell[BoxData[ \(0.017453292519943295`\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(RtoD = N[180/Pi]\)], "Input"], Cell[BoxData[ \(57.29577951308232`\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(test = MatrixForm[Disp[DtoR*30, {1, 2}]]\)], "Input"], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"0.8660254037844387`", \(-0.5`\), "0", "1"}, {"0.5`", "0.8660254037844387`", "0", "2"}, {"0", "0", "1", "0"}, {"0", "0", "0", "1"} }], "\[NoBreak]", ")"}], (MatrixForm[ #]&)]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(position = Table[Disp[ DtoR*data1[\([i, 1]\)], {data1[\([i, 2]\)], data1[\([i, 3]\)]}], {i, npos}]\)], "Input"], Cell[BoxData[ \({{{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}}, {{0.9271838545667874`, \(-0.374606593415912`\), 0, \(-6\)}, {0.374606593415912`, 0.9271838545667874`, 0, 11}, {0, 0, 1, 0}, {0, 0, 0, 1}}, {{0.37460659341591196`, \(-0.9271838545667874`\), 0, \(-17\)}, {0.9271838545667874`, 0.37460659341591196`, 0, 13}, {0, 0, 1, 0}, {0, 0, 0, 1}}}\)], "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Kinematics Equations for RR chain", "Subsection"], Cell[BoxData[ \(RReqn[t_, a_, p_] := Zdisp[t] . 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