渐开线方程

a--渐开线基圆半径β--渐开线发生角，初值（0）、步长（t=0.02）(看你需要的曲线精度了，步长越小越精确）xy 015150.0115.00074998 4.99995E-06150.0215.0029997 3.99984E-05150.0315.006748480.000134988150.0415.01199520.000319949150.0515.018738280.000624844150.0615.02697570.001079611150.0715.036704990.00171416150.0815.047923230.002558362150.0915.060627040.003642048150.115.07481260.004995002150.1115.090475670.006646951150.1215.107611510.008627565150.1315.126214980.010*********.1415.146280480.013693128150.1515.167801970.016837062150.1615.190772950.020*********.1715.215186490.024********.1815.241035240.029*********.1915.268311380.034171355150.215.297006660.0398********.2115.327112410.046101116150.2215.35861950.052982763150.2315.391518380.06051379150.2415.425799080.068722687150.2515.461451170.0776********.2615.498463820.0872********.2715.536825760.0976*******.2815.57652530.108901888150.2915.617550310.120922518150.315.659888270.133788899150.3115.703526210.147528447150.3215.748450760.162168402涡旋线是一种渐开线/阿基米德螺线，在实际应用中一般选圆的渐开线，因为它比较容品中还需对该渐开线修正。

下面介绍下在CAD中如何划精确曲线（方程曲线）（以圆的渐开线为例）： 源 x=a*(cos(β)+βsin(β)) y=a*(sin(β)-βcos(β)) 其中:a--渐开线基圆半径，已知项 β--渐开输入a、β、x、y、(x,y)，给a赋值 3，定β项的初值（0）、步长（t=0.02）(看你需要的曲线精度了，入为初值。

按EXCEL函数在x、y栏中输入方程公式,在(x,y)栏中按此输入 =C3&","&D3 解释：C3为x栏，行至第二行，在β栏改为输入EXCEL函数 =B3+0.02 解释：上行该栏加步长。

拷贝该行至第三——N行。

中，先顶原点位置，点“多段线”或“样条曲线”，在下面输入栏中“指定第一点或[对象]：”单击，望抛砖引玉！150.3315.794648140.177735825 150.3415.842104150.194257588 150.3515.890804180.211760369 150.3615.940733210.230270651 150.3715.991875830.249814711 150.3816.044216210.270418618 150.3916.097738130.292108227 150.416.152424960.314909171 150.4116.208259710.338846859 150.4216.265224960.363946472 150.4316.323302920.390232951 150.4416.382475420.417730999 150.4516.442723890.446465071 150.4616.50402940.476459372 150.4716.566372630.507737849 150.4816.629733910.540324189 150.4916.694093160.574241812 150.516.759429970.609513865 150.5116.825723550.64616322 150.5216.892952770.684212466 150.5316.961096120.723683907 150.5417.030131750.764599556 150.5517.100037470.806981127 150.5617.170790730.850850036 150.5717.242368640.896227393 150.5817.3147480.943133998 150.5917.387905240.991590334 150.617.46181648 1.041616567 150.6117.53645753 1.093232538 150.6217.61180384 1.146457761 150.6317.68783059 1.201311416 150.6417.76451261 1.257812345 150.6517.84182443 1.31597905 150.6617.91974031 1.375829688 150.6717.99823416 1.437382063 150.6818.07727963 1.500653629 150.6918.15685006 1.565661478 150.718.23691853 1.632422342 150.7118.3174578 1.700952586 150.7218.39844039 1.771268205 150.7318.47983854 1.843384819 150.7418.5616242 1.917317673 150.7518.64376908 1.993081626 150.7618.72624464 2.070691154 150.7718.80902205 2.150160345 150.7818.89207227 2.231502893 150.7918.97536601 2.314732096150.819.05887373 2.399860851 150.8119.14256566 2.486901655 150.8219.22641181 2.575866596 150.8319.31038197 2.666767354 150.8419.3944457 2.759615194 150.8519.47857235 2.854420967 150.8619.56273108 2.951195104 150.8719.64689084 3.049947614 150.8819.73102036 3.15068808 150.8919.81508823 3.253425658 150.919.8990628 3.358169073 150.9119.98291229 3.464926615 150.9220.06660471 3.573706139 150.9320.15010791 3.68451506 150.9420.23338959 3.797360353 150.9520.31641729 3.912248547 150.9620.39915837 4.029185725 150.9720.4815801 4.148177522 150.9820.56364955 4.26922912 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1.9821.2797241725.57857188 15 1.9921.1598907425.85114164 15221.0367202626.1238665 15 2.0120.910197726.39670684 15 2.0220.7803085126.66962276 15 2.0320.6470385826.94257407 15 2.0420.5103742927.21552033 15 2.0520.3703024627.48842079 15 2.0620.2268104327.76123448 15 2.0720.0798859928.03392014 15 2.0819.9295174328.30643629 15 2.0919.775693528.57874117 15 2.119.6184034828.85079279 15 2.1119.4576371229.12254895 15 2.1219.2933846929.39396719 15 2.1319.1256369329.66500484 15 2.1418.9543851129.935619 15 2.1518.7796210230.20576657 15 2.1618.6013369430.47540425 15 2.1718.4195256630.74448852 15 2.1818.2341805231.01297568 15 2.1918.0452953731.28082184 15 2.217.852*******.5479829315 2.2117.6568830231.81441469 15 2.2217.4573461632.08007271 15 2.2317.2542499532.34491241 15 2.2417.047590932.60888904 15 2.2516.8373660532.87195772 15 2.2616.6235729933.13407341 15 2.2716.4062098533.39519095 15 2.2816.1852753133.65526501 15 2.2915.960768633.91425019 15 2.315.732689534.17210092 15 2.3115.5010383534.42877154 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