project.nb

函数再现机构设计 试设计一曲柄摇杆机构

(************** Content-type: application/mathematica **************
                     CreatedBy='Mathematica 5.2'

                    Mathematica-Compatible Notebook

This notebook can be used with any Mathematica-compatible
application, such as Mathematica, MathReader or Publicon. The data
for the notebook starts with the line containing stars above.

To get the notebook into a Mathematica-compatible application, do
one of the following:

* Save the data starting with the line of stars above into a file
  with a name ending in .nb, then open the file inside the
  application;

* Copy the data starting with the line of stars above to the
  clipboard, then use the Paste menu command inside the application.

Data for notebooks contains only printable 7-bit ASCII and can be
sent directly in email or through ftp in text mode.  Newlines can be
CR, LF or CRLF (Unix, Macintosh or MS-DOS style).

NOTE: If you modify the data for this notebook not in a Mathematica-
compatible application, you must delete the line below containing
the word CacheID, otherwise Mathematica-compatible applications may
try to use invalid cache data.

For more information on notebooks and Mathematica-compatible 
applications, contact Wolfram Research:
  web: http://www.wolfram.com
  email: [e-mail]
  phone: [phone] (U.S.)

Notebook reader applications are available free of charge from 
Wolfram Research.
*******************************************************************)

(*CacheID: 232*)


(*NotebookFileLineBreakTest
NotebookFileLineBreakTest*)
(*NotebookOptionsPosition[     20020,        517]*)
(*NotebookOutlinePosition[     20666,        539]*)
(*  CellTagsIndexPosition[     20622,        535]*)
(*WindowFrame->Normal*)



Notebook[{
Cell[BoxData[{
    \(\($PrePrint = 
        If[MatrixQ[#1] || VectorQ[#1], 
            MatrixForm[#1], #1] &;\)\[IndentingNewLine]\), "\
\[IndentingNewLine]", 
    \(\[Beta]\_0[X_] := 
      ArcTan[X\[LeftDoubleBracket]1\[RightDoubleBracket]*
          Sin[X\[LeftDoubleBracket]4\[RightDoubleBracket]]/\((1 - 
                X\[LeftDoubleBracket]1\[RightDoubleBracket]*
                  Cos[X\[LeftDoubleBracket]4\[RightDoubleBracket]])\)]\), "\
\[IndentingNewLine]", 
    \(\[Delta]\_0[X_] := 
      ArcCos[\((\((X\[LeftDoubleBracket]1\[RightDoubleBracket])\)^2 - \((X\
\[LeftDoubleBracket]2\[RightDoubleBracket])\)^2 + \((X\[LeftDoubleBracket]3\
\[RightDoubleBracket])\)^2 + 1 - 
              2*X\[LeftDoubleBracket]1\[RightDoubleBracket]*
                Cos[X\[LeftDoubleBracket]4\[RightDoubleBracket]])\)/\((2*
              X\[LeftDoubleBracket]3\[RightDoubleBracket]*
              Sqrt[\((X\[LeftDoubleBracket]1\[RightDoubleBracket])\)^2 + 1 - 
                  2*X\[LeftDoubleBracket]1\[RightDoubleBracket]*
                    Cos[X\[LeftDoubleBracket]4\[RightDoubleBracket]]])\)]\
\[IndentingNewLine] (*\:6211\:4eec\:6bcf\:96943\:5ea6\:53d6\:4e00\:70b9, \
\:5171\:8ba160\:4e2a\:70b9*) \), "\[IndentingNewLine]", 
    \(\[Beta]\_m[X_] := 
      ArcTan[X\[LeftDoubleBracket]1\[RightDoubleBracket]*
          Sin[X\[LeftDoubleBracket]4\[RightDoubleBracket] + 
                i*\[Pi]/60]/\((1 - 
                X\[LeftDoubleBracket]1\[RightDoubleBracket]*
                  Cos[X\[LeftDoubleBracket]4\[RightDoubleBracket] + 
                      i*\[Pi]/60])\)]\), "\[IndentingNewLine]", 
    \(\[Delta]\_m[X_] := 
      ArcCos[\((\((X\[LeftDoubleBracket]1\[RightDoubleBracket])\)^2 - \((X\
\[LeftDoubleBracket]2\[RightDoubleBracket])\)^2 + \((X\[LeftDoubleBracket]3\
\[RightDoubleBracket])\)^2 + 1 - 
              2*X\[LeftDoubleBracket]1\[RightDoubleBracket]*
                Cos[X\[LeftDoubleBracket]4\[RightDoubleBracket] + 
                    i*\[Pi]/60])\)/\((2*
              X\[LeftDoubleBracket]3\[RightDoubleBracket]*
              Sqrt[\((X\[LeftDoubleBracket]1\[RightDoubleBracket])\)^2 + 1 - 
                  2*X\[LeftDoubleBracket]1\[RightDoubleBracket]*
                    Cos[X\[LeftDoubleBracket]4\[RightDoubleBracket] + 
                        i*\[Pi]/
                            60]])\)]\[IndentingNewLine]\[IndentingNewLine] \
(*\:673a\:6784\:7684\:8f93\:51fa\:89d2\:5ea6\:4e3a\[CurlyPhi] = \[Beta]\_0 + \
\[Delta]\_0 - \[Beta]\_m - \[Delta]\_m*) \), "\[IndentingNewLine]", 
    \(f[X_] := \[Beta]\_0[X] + \[Delta]\_0[X] - \[Beta]\_m[X] - \[Delta]\_m[
          X]\[IndentingNewLine]\[IndentingNewLine] (*\(f\_m\) \:4e3a\:7ed9\
\:5b9a\:7684\:76ee\:6807\:51fd\:6570*) \[IndentingNewLine]\), "\
\[IndentingNewLine]", 
    \(\(f\_m = \[Pi]*
          Sin[i*\[Pi]/60]/
            6;\)\[IndentingNewLine] \
(*fobj\:4e3a\:518d\:73b0\:51fd\:6570\:548c\:76ee\:6807\:51fd\:6570\:4e4b\:95f4\
\:7684\:504f\:5dee*) \), "\[IndentingNewLine]", 
    \(fobj[
        X_] := \[Sum]\+\(i = 0\)\%60\((f[X] - 
              f\_m)\)^2\), "\[IndentingNewLine]", 
    \(\(dvX = {l1, l2, l3, \[Theta]0};\)\), "\[IndentingNewLine]", 
    \(\)}], "Input"],

Cell[BoxData[
    \(\(\( (*g1~
        g9\:4e3a\:6c42fobj\:6700\:5c0f\:503c\:7684\:7ea6\:675f\:6761\:4ef6\
*) \)\(\[IndentingNewLine]\)\(g1[X_] := \(-1\) + 
        X\[LeftDoubleBracket]1\[RightDoubleBracket] + 
        X\[LeftDoubleBracket]2\[RightDoubleBracket] - 
        X\[LeftDoubleBracket]3\[RightDoubleBracket]\n
    g2[X_] := \(-1\) + X\[LeftDoubleBracket]1\[RightDoubleBracket] - 
        X\[LeftDoubleBracket]2\[RightDoubleBracket] + 
        X\[LeftDoubleBracket]3\[RightDoubleBracket]\n
    g3[X_] := 
      1 + X\[LeftDoubleBracket]1\[RightDoubleBracket] - 
        X\[LeftDoubleBracket]2\[RightDoubleBracket] - 
        X\[LeftDoubleBracket]3\[RightDoubleBracket]\[IndentingNewLine]
    g4[X_] := \(-2\)*X\[LeftDoubleBracket]2\[RightDoubleBracket]*
          X\[LeftDoubleBracket]3\[RightDoubleBracket]*
          Cos[40*\[Pi]/
                180] + \((X\[LeftDoubleBracket]2\[RightDoubleBracket])\)^2 + \
\((X\[LeftDoubleBracket]3\[RightDoubleBracket])\)^2 - \((1 - 
              X\[LeftDoubleBracket]1\[RightDoubleBracket])\)^2\
\[IndentingNewLine]
    g5[X_] := 
      2*X\[LeftDoubleBracket]2\[RightDoubleBracket]*
          X\[LeftDoubleBracket]3\[RightDoubleBracket]*
          Cos[140*\[Pi]/
                180] - \((X\[LeftDoubleBracket]2\[RightDoubleBracket])\)^2 - \
\((X\[LeftDoubleBracket]3\[RightDoubleBracket])\)^2 + \((1 + 
              X\[LeftDoubleBracket]1\[RightDoubleBracket])\)^2\
\[IndentingNewLine]
    g6[X_] := \(-X\[LeftDoubleBracket]4\[RightDoubleBracket]\)\
\[IndentingNewLine]
    g7[X_] := \(-X\[LeftDoubleBracket]1\[RightDoubleBracket]\) + 
        0.1\[IndentingNewLine]
    g8[X_] := \(-X\[LeftDoubleBracket]2\[RightDoubleBracket]\) + 
        0.1\[IndentingNewLine]
    g9[X_] := \(-X\[LeftDoubleBracket]3\[RightDoubleBracket]\) + 
        0.1\[IndentingNewLine]
    \)\)\)], "Input"],

Cell[BoxData[
    \(\(\( (*\:672c\:9898\:91c7\:7528 "\<\:589e\:5e7f\:62c9\:683c\:6717\:65e5\
\:4e58\:5b50\:6cd5\>" \:6c42\:89e3, 
      lamda\:4e3a\:62c9\:683c\:6717\:65e5\:4e58\:5b50, 
      penalty\:4e3a\:60e9\:7f5a\:56e0\:5b50*) \)\(\[IndentingNewLine]\)\(\
lamda = {lam1, lam2, lam3, lam4, lam5, lam6, lam7, lam8, 
          lam9};\)\)\)], "Input"],

Cell[BoxData[
    \(\(\( (*AugmentedLagrangian\:4e3a\:589e\:5e7f\:62c9\:683c\:6717\:65e5\
\:65b9\:7a0b*) \)\(\[IndentingNewLine]\)\(\(AugmentedLagrangian := 
      fobj[dvX] + 
        lamda[\([1]\)]\ *\ 
          Max[\ g1[dvX], \ \(-lamda[\([1]\)]\)/\((2*penalty)\)]\  + \ 
        penalty\ *\ 
          Max[\ g1[dvX], \ \(-lamda[\([1]\)]\)/\((2*penalty)\)]\^2 + 
        lamda[\([2]\)]\ *\ 
          Max[\ g2[dvX], \ \(-lamda[\([2]\)]\)/\((2*penalty)\)]\  + \ 
        penalty\ *\ 
          Max[\ g2[dvX], \ \(-lamda[\([2]\)]\)/\((2*penalty)\)]\^2 + 
        lamda[\([3]\)]\ *\ 
          Max[\ g3[dvX], \ \(-lamda[\([3]\)]\)/\((2*penalty)\)]\  + \ 
        penalty\ *\ 
          Max[\ g3[dvX], \ \(-lamda[\([3]\)]\)/\((2*penalty)\)]\^2 + 
        lamda[\([4]\)]\ *\ 
          Max[\ g4[dvX], \ \(-lamda[\([4]\)]\)/\((2*penalty)\)]\  + \ 
        penalty\ *\ 
          Max[\ g4[dvX], \ \(-lamda[\([4]\)]\)/\((2*penalty)\)]\^2 + 
        lamda[\([5]\)]\ *\ 
          Max[\ g5[dvX], \ \(-lamda[\([5]\)]\)/\((2*penalty)\)]\  + 
        penalty\ *\ 
          Max[\ g5[dvX], \ \(-lamda[\([5]\)]\)/\((2*penalty)\)]\^2 + 
        lamda[\([6]\)]\ *\ 
          Max[\ g6[dvX], \ \(-lamda[\([6]\)]\)/\((2*penalty)\)]\  + \ 
        penalty\ *\ 
          Max[\ g6[dvX], \ \(-lamda[\([6]\)]\)/\((2*penalty)\)]\^2 + 
        lamda[\([7]\)]\ *\ 
          Max[\ g7[dvX], \ \(-lamda[\([7]\)]\)/\((2*penalty)\)]\  + 
        penalty\ *\ 
          Max[\ g7[dvX], \ \(-lamda[\([7]\)]\)/\((2*penalty)\)]\^2 + 
        lamda[\([8]\)]\ *\ 
          Max[\ g8[dvX], \ \(-lamda[\([8]\)]\)/\((2*penalty)\)]\  + 
        penalty\ *\ 
          Max[\ g8[dvX], \ \(-lamda[\([8]\)]\)/\((2*penalty)\)]\^2 + 
        lamda[\([9]\)]\ *\ 
          Max[\ g9[dvX], \ \(-lamda[\([9]\)]\)/\((2*penalty)\)]\  + 
        penalty\ *\ 
          Max[\ g9[dvX], \ \(-lamda[\([9]\)]\)/\((2*penalty)\)]\^2\)\(\
\[IndentingNewLine]\)
    \)\)\)], "Input"],

Cell[BoxData[
    \(\(\( (*\:8bbe\:7f6e\:62c9\:683c\:6717\:65e5\:4e58\:5b50, \:60e9\:7f5a\
\:56e0\:5b50\:548c\:672a\:77e5\:91cf\:7684\:521d\:503c, \:5e76\:8fdb\:884c\
\:7b2c\:4e00\:6b21\:8ba1\:7b97*) \)\(\[IndentingNewLine]\)\(L1 = 0.0; 
    L2 = 0.0; L3 = 0.0; L4 = 0.0; L5 = 0.0; L6 = 0.0; L7 = 0.0; L8 = 0.0; 
    L9 = 0.0; P = 0.0001;\n
    \(x0 = {0.2, 0.9, 0.7, 1};\)\)\)\)], "Input"],

Cell[BoxData[
    \(\(\(augmented := 
      AugmentedLagrangian\  /. \ {lam1 -> \ L1, \ lam2 -> L2, \ lam3 -> L3, \ 
          lam4 -> L4, \ lam5 -> L5, \ lam6 -> L6, \ lam7 -> L7, \ 
          lam8 -> L8, \ lam9 -> L9, \ penalty -> P}\)\(\[IndentingNewLine]\)
    \)\)], "Input"],

Cell[CellGroupData[{

Cell[BoxData[
    \(\(\( \
(*\:8c03\:7528UnconstrainedMin\:7a0b\:5e8f\:5305\:91cc\:7684SequentialSimplex\
\:51fd\:6570*) \)\(\[IndentingNewLine]\)\(<< "\<UnconstrainedMin.m\>"\
\[IndentingNewLine]
    Options[SequentialSimplex]\)\)\)], "Input"],

Cell[BoxData[
    TagBox[
      RowBox[{"(", "\[NoBreak]", 
        TagBox[GridBox[{
              {\(SolutionHistory \[Rule] False\)},
              {\(PlotHistory \[Rule] False\)},
              {\(Epsilon \[Rule] Automatic\)},
              {\(MaxIterations \[Rule] 50\)},
              {\(ReflectioN \[Rule] 1.`\)},
              {\(ExpansioN \[Rule] 2.`\)},
              {\(ContractioN \[Rule] 0.5`\)}
              },
            RowSpacings->1,
            ColumnAlignments->{Left}],
          Column], "\[NoBreak]", ")"}],
      Function[ BoxForm`e$, 
        MatrixForm[ BoxForm`e$]]]], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(\(\( \
(*\:4e0b\:9762\:4e09\:4e2a\:4e3aSequentialSimplex\:51fd\:6570\:91cc\:6240\
\:8981\:7528\:5230\:7684\:4e09\:4e2a\:6761\:4ef6*) \)\(\[IndentingNewLine]\)\(\
\(size = 0.05;\)\[IndentingNewLine]
    dvX\[IndentingNewLine]
    x0\)\)\)], "Input"],

Cell[BoxData[
    TagBox[
      RowBox[{"(", "\[NoBreak]", 
        TagBox[GridBox[{
              {"l1"},
              {"l2"},
              {"l3"},
              {"\[Theta]0"}
              },
            RowSpacings->1,
            ColumnAlignments->{Left}],
          Column], "\[NoBreak]", ")"}],
      Function[ BoxForm`e$, 
        MatrixForm[ BoxForm`e$]]]], "Output"],

Cell[BoxData[
    TagBox[
      RowBox[{"(", "\[NoBreak]", 
        TagBox[GridBox[{
              {"0.2`"},
              {"0.9`"},
              {"0.7`"},
              {"1"}
              },
            RowSpacings->1,
            ColumnAlignments->{Left}],
          Column], "\[NoBreak]", ")"}],
      Function[ BoxForm`e$, 
        MatrixForm[ BoxForm`e$]]]], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
    \(\(lastPt = 
        SequentialSimplex[augmented, dvX, x0, size, PlotHistory \[Rule] True, 
          MaxIterations \[Rule] 10, 
          Epsilon \[Rule] 1\/10\^2];\)\), "\[IndentingNewLine]", 
    \(x0 = \(Last[
          lastPt]\)\[LeftDoubleBracket]3\[RightDoubleBracket]\)}], "Input"],

Cell[BoxData[
    TagBox[
      RowBox[{"(", "\[NoBreak]",