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The mathematical analog of cutting away material to create a \ useful shape, envelopes find myriad applications where analytically \ determined, physically derived shapes are required. 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This example shows how powerful this \ technique is, where a very complex shape can be expressed in just a few lines \ of code.\ \>", "Text", CellChangeTimes->{{3.5276496016766806`*^9, 3.527649661955187*^9}, { 3.5276497137004776`*^9, 3.527649753792548*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"Block", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"a", "=", "2"}], ",", RowBox[{"b", "=", "1"}], ",", RowBox[{"c", "=", "4"}], ",", RowBox[{"d", "=", "1"}], ",", RowBox[{"e", "=", "0.2"}], ",", "s1", ",", "s2"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"ConveyorFunction", "=", RowBox[{"Function", "[", RowBox[{ RowBox[{"{", RowBox[{"z", ",", "\[Phi]"}], "}"}], ",", RowBox[{"Evaluate", "[", RowBox[{"h", "[", RowBox[{"z", ",", "\[Phi]"}], "]"}], "]"}]}], "]"}]}]}], "\[IndentingNewLine]", "]"}], ";"}]], "Input", CellChangeTimes->{{3.5268511666668*^9, 3.526851170584024*^9}, { 3.526852393455968*^9, 3.526852402862506*^9}, 3.527873429906596*^9, { 3.5280607882413635`*^9, 3.5280608105026026`*^9}, {3.528060873308313*^9, 3.5280609311376143`*^9}}] }, Open ]], Cell[CellGroupData[{ Cell["Gear Surfaces", "Subsection", CellChangeTimes->{{3.5239704608843274`*^9, 3.5239704693878136`*^9}}], Cell[TextData[{ "For these examples, we will be using a simple gear, a ", StyleBox["spur gear", FontSlant->"Italic"], ", to generate the surfaces for a type of right angle drive called a ", StyleBox["face gear", FontSlant->"Italic"], ". In the first example, we consider the simple case. In the second case, \ we consider one example among more exotic variations, which allow us to \ operate a different angles, have stronger teeth, or a less noisy meshing." }], "Text", CellChangeTimes->{{3.5273703731315565`*^9, 3.527370569771804*^9}, { 3.5274633990260487`*^9, 3.5274634050320587`*^9}}], Cell[CellGroupData[{ Cell["Explicit", "Subsubsection", CellChangeTimes->{{3.523970566827387*^9, 3.523970569643548*^9}}], Cell[TextData[{ "The generating surface will be an involute curve, extended in the \ z-direction. The function is nested, with parameters ", Cell[BoxData[ FormBox[ SubscriptBox["r", "b"], TraditionalForm]], FormatType->"TraditionalForm"], " and ", Cell[BoxData[ FormBox["\[Epsilon]", TraditionalForm]], FormatType->"TraditionalForm"], " as arguments to make the solution more generic. 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