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</span><span style="text-indent: 21pt; font-family: 宋体;">常常会遇到两个或若干个立体相交的问题</span><span lang="EN-US" style="text-indent: 21pt;">(</span><span style="text-indent: 21pt; font-family: 宋体;">在画法几何中</span><span lang="EN-US" style="text-indent: 21pt;">, </span><span style="text-indent: 21pt; font-family: 宋体;">我们称之为相贯</span><span lang="EN-US" style="text-indent: 21pt;">), </span><span style="text-indent: 21pt; font-family: 宋体;">比如在机械生产</span><span style="text-indent: 21pt;"> </span><span style="text-indent: 21pt; font-family: 宋体;">化工设备</span><span style="text-indent: 21pt;"> </span><span style="text-indent: 21pt; font-family: 宋体;">运输管道</span><span style="text-indent: 21pt;"> </span><span style="text-indent: 21pt; font-family: 宋体;">钢结构构件的连接中</span><span lang="EN-US" style="text-indent: 21pt;">, </span><span style="text-indent: 21pt; font-family: 宋体;">通常会遇到一些平面与曲面立体之间的截交以及曲面立体曲面立体之间的相贯问题</span><span lang="EN-US" style="text-indent: 21pt;">. </span><span style="text-indent: 21pt; font-family: 宋体;">而通常我们只用作图法来求</span><span lang="EN-US" style="text-indent: 21pt;">, </span><span style="text-indent: 21pt; font-family: 宋体;">作图法虽然形象直观</span><span style="text-indent: 21pt;"> </span><span style="text-indent: 21pt; font-family: 宋体;">迅速</span><span lang="EN-US" style="text-indent: 21pt;">, </span><span style="text-indent: 21pt; font-family: 宋体;">但却由于受到作图操作和仪器工具的限制</span><span lang="EN-US" style="text-indent: 21pt;">, </span><span style="text-indent: 21pt; font-family: 宋体;">再加之作图过程繁顼</span><span style="text-indent: 21pt;"> </span><span style="text-indent: 21pt; font-family: 宋体;">图形绘制不准确</span><span lang="EN-US" style="text-indent: 21pt;">, </span><span style="text-indent: 21pt; font-family: 宋体;">往往给生产制作造成许多麻烦</span><span lang="EN-US" style="text-indent: 21pt;">, </span><span style="text-indent: 21pt; font-family: 宋体;">且精度更不能满足现代技术与计算机辅助设计和数控制造技术的要求</span><span lang="EN-US" style="text-indent: 21pt;">, </span><span style="text-indent: 21pt; font-family: 宋体;">因此这我们采用图解与计算相结合的方法</span><span lang="EN-US" style="text-indent: 21pt;">, </span><span style="text-indent: 21pt; font-family: 宋体;">通过投影图上的几何关系</span><span lang="EN-US" style="text-indent: 21pt;">, </span><span style="text-indent: 21pt; font-family: 宋体;">再利用解析方法</span><span lang="EN-US" style="text-indent: 21pt;">, </span><span style="text-indent: 21pt; font-family: 宋体;">建立相贯线上点的坐标方程或极坐标方程</span><span lang="EN-US" style="text-indent: 21pt;">. </span><span style="text-indent: 21pt; font-family: 宋体;">并根据所求的坐标方程或极坐标方程</span><span lang="EN-US" style="text-indent: 21pt;">, </span><span style="text-indent: 21pt; font-family: 宋体;">在</span><span lang="EN-US" style="text-indent: 21pt;"><a href="http://www.bethel-cnc.com/" target="_blank"><span lang="EN-US" style="font-family:宋体;mso-ascii-font-family:"Times New Roman"; mso-hansi-font-family:"Times New Roman"">数控机床</span></a></span><span style="text-indent: 21pt; font-family: 宋体;">上利用切割工具</span><span lang="EN-US" style="text-indent: 21pt;">, </span><span style="text-indent: 21pt; font-family: 宋体;">切割出我们所需的各种相贯曲线</span><span lang="EN-US" style="text-indent: 21pt;">. </span><span style="text-indent: 21pt; font-family: 宋体;">为此建立相贯线上的点的坐标方程或极坐标方程是非常重要的</span><span lang="EN-US" style="text-indent: 21pt;">.</span></p> <p class="MsoNormal" style="text-indent:21.0pt;mso-char-indent-count:2.0"><span lang="EN-US">1 </span><span style="mso-bidi-font-size: 10.5pt;font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">两圆柱体相贯</span><span lang="EN-US"><o:p></o:p></span></p> <p class="MsoNormal" style="text-indent:21.0pt;mso-char-indent-count:2.0"><span style="mso-bidi-font-size:10.5pt;font-family:宋体;mso-ascii-font-family:"Times New Roman"; mso-hansi-font-family:"Times New Roman"">如图</span><span lang="EN-US">1 </span><span style="mso-bidi-font-size: 10.5pt;font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">所示为轴线相交的两圆柱体相贯（正立投影）</span><span lang="EN-US"> , </span><span style="mso-bidi-font-size: 10.5pt;font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">现用作图与解析相结合的方法来求相贯线</span><span lang="EN-US">.<o:p></o:p></span></p> <p class="MsoNormal" style="text-indent:21.0pt;mso-char-indent-count:2.0"><span style="mso-bidi-font-size:10.5pt;font-family:宋体;mso-ascii-font-family:"Times New Roman"; mso-hansi-font-family:"Times New Roman"">设两圆柱的底面半径分别为</span><span lang="EN-US">r1 </span><span style="mso-bidi-font-size: 10.5pt;font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">与</span><span lang="EN-US">r2 (</span><span style="mso-bidi-font-size:10.5pt;font-family:宋体;mso-ascii-font-family: "Times New Roman";mso-hansi-font-family:"Times New Roman"">均已知</span><span lang="EN-US">),</span><span style="mso-bidi-font-size: 10.5pt;font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">两圆柱轴线的交点为</span><span lang="EN-US">o</span><span style="mso-bidi-font-size:10.5pt;font-family:宋体; mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"">它们之间的夹角为</span><span lang="EN-US"><!--[if gte vml 1]><v:shapetype id="_x0000_t75" coordsize="21600,21600" o:spt="75" o:preferrelative="t" path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f"> <v:stroke joinstyle="miter" /> <v:formulas> <v:f eqn="if lineDrawn pixelLineWidth 0" /> <v:f eqn="sum @0 1 0" /> <v:f eqn="sum 0 0 @1" /> <v:f eqn="prod @2 1 2" /> <v:f eqn="prod @3 21600 pixelWidth" /> <v:f eqn="prod @3 21600 pixelHeight" /> <v:f eqn="sum @0 0 1" /> <v:f eqn="prod @6 1 2" /> <v:f eqn="prod @7 21600 pixelWidth" /> <v:f eqn="sum @8 21600 0" /> <v:f eqn="prod @7 21600 pixelHeight" /> <v:f eqn="sum @10 21600 0" /> </v:formulas> <v:path o:extrusionok="f" gradientshapeok="t" o:connecttype="rect" /> <o:lock v:ext="edit" aspectratio="t" /> </v:shapetype><v:shape id="_x0000_i1025" type="#_x0000_t75" style='width:10.5pt; height:15pt'> <v:imagedata src="file:///E:\QQPCmgr\Temp\msohtml1\01\clip_image001.png" o:title="" /> </v:shape><![endif]--><!--[if !vml]--><img border="0" width="14" height="20" src="file:///E:/QQPCmgr/Temp/msohtml1/01/clip_image002.jpg" v:shapes="_x0000_i1025" alt="" /><!--[endif]--> (</span><span style="mso-bidi-font-size:10.5pt;font-family:宋体;mso-ascii-font-family: "Times New Roman";mso-hansi-font-family:"Times New Roman"">已知</span><span lang="EN-US">),</span><span style="mso-bidi-font-size: 10.5pt;font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">以</span><span lang="EN-US">o</span><span style="mso-bidi-font-size:10.5pt;font-family:宋体;mso-ascii-font-family:"Times New Roman"; mso-hansi-font-family:"Times New Roman"">为原点</span><span lang="EN-US">, </span><span style="mso-bidi-font-size: 10.5pt;font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">分别建立各自的三维坐标体系</span><span lang="EN-US">, y1 </span><span style="mso-bidi-font-size:10.5pt;font-family:宋体; mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"">轴垂直于</span><span lang="EN-US">x1 oz1 </span><span style="mso-bidi-font-size:10.5pt;font-family:宋体;mso-ascii-font-family:"Times New Roman"; mso-hansi-font-family:"Times New Roman"">平面</span><span lang="EN-US">y2 </span><span style="mso-bidi-font-size: 10.5pt;font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">轴垂直于</span><span lang="EN-US">x2 oz2 </span><span style="mso-bidi-font-size:10.5pt;font-family:宋体;mso-ascii-font-family: "Times New Roman";mso-hansi-font-family:"Times New Roman"">平面</span><span lang="EN-US">,</span><span style="mso-bidi-font-size: 10.5pt;font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">而</span><span lang="EN-US">x1 oz1 </span><span style="mso-bidi-font-size:10.5pt;font-family:宋体;mso-ascii-font-family: "Times New Roman";mso-hansi-font-family:"Times New Roman"">和</span><span lang="EN-US">x2 oz2 </span><span style="mso-bidi-font-size:10.5pt;font-family:宋体;mso-ascii-font-family:"Times New Roman"; mso-hansi-font-family:"Times New Roman"">正好在同一平面内</span><span lang="EN-US">, </span><span style="mso-bidi-font-size: 10.5pt;font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">所以</span><span lang="EN-US">y1 </span><span style="mso-bidi-font-size:10.5pt;font-family:宋体;mso-ascii-font-family: "Times New Roman";mso-hansi-font-family:"Times New Roman"">与</span><span lang="EN-US">y2 </span><span style="mso-bidi-font-size: 10.5pt;font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">为同一条轴</span><span lang="EN-US">,</span><span style="mso-bidi-font-size:10.5pt;font-family:宋体;mso-ascii-font-family:"Times New Roman"; mso-hansi-font-family:"Times New Roman"">其坐标我们均计为</span><span lang="EN-US">y, </span><span style="mso-bidi-font-size: 10.5pt;font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">由图</span><span lang="EN-US"> 1 </span><span style="mso-bidi-font-size:10.5pt;font-family:宋体;mso-ascii-font-family: "Times New Roman";mso-hansi-font-family:"Times New Roman"">的几何关系可得下面解析式</span><span lang="EN-US">:<o:p></o:p></span></p> <p class="MsoNormal" style="text-indent:21.0pt;mso-char-indent-count:2.0"><img src="/upload/images/201406/14033650815373.jpg" alt="" /></p> <p class="MsoNormal" style="text-indent:21.0pt;mso-char-indent-count:2.0"><span style="mso-bidi-font-size:10.5pt;font-family:宋体;mso-ascii-font-family:"Times New Roman"; mso-hansi-font-family:"Times New Roman"">在制作该相贯线时</span><span lang="EN-US">, </span><span style="mso-bidi-font-size: 10.5pt;font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">可将圆柱面展开成板</span><span lang="EN-US">, </span><span style="mso-bidi-font-size:10.5pt;font-family:宋体; mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"">横坐标为</span><span lang="EN-US"> , </span><span style="mso-bidi-font-size: 10.5pt;font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">纵坐标为</span><span lang="EN-US"> , </span><span style="mso-bidi-font-size:10.5pt;font-family:宋体;mso-ascii-font-family: "Times New Roman";mso-hansi-font-family:"Times New Roman"">在数控机床</span><span lang="EN-US">[5]</span><span style="mso-bidi-font-size: 10.5pt;font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">上用数控线切割机按坐标便可加工出所需曲线</span><span lang="EN-US">.<o:p></o:p></span><img src="/upload/images/201406/1403365091268.jpg" alt="" /></p> <p class="MsoNormal" style="text-indent:21.0pt;mso-char-indent-count:2.0"> </p> <p class="MsoNormal" style="text-indent:21.0pt;mso-char-indent-count:2.0"><span lang="EN-US">2 </span><span style="mso-bidi-font-size: 10.5pt;font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">圆柱体与圆锥体相贯</span><span lang="EN-US"><o:p></o:p></span></p> <p class="MsoNormal" style="text-indent:21.0pt;mso-char-indent-count:2.0"><span style="mso-bidi-font-size:10.5pt;font-family:宋体;mso-ascii-font-family:"Times New Roman"; mso-hansi-font-family:"Times New Roman"">如图</span><span lang="EN-US"> 2 </span><span style="mso-bidi-font-size: 10.5pt;font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">所示为轴线相交的圆柱体与圆锥体的相贯</span><span lang="EN-US">[1 2], </span><span style="mso-bidi-font-size:10.5pt;font-family:宋体; mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"">圆锥顶角为</span><img src="/upload/images/201406/14033651882693.jpg" alt="" /></p> <p class="MsoNormal" style="text-indent:21.0pt;mso-char-indent-count:2.0"><span lang="EN-US">, </span><span style="mso-bidi-font-size:10.5pt;font-family:宋体;mso-ascii-font-family: "Times New Roman";mso-hansi-font-family:"Times New Roman"">圆柱体的中心轴线与</span><span lang="EN-US">x </span><span style="mso-bidi-font-size: 10.5pt;font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">轴的夹角为</span><img src="/upload/images/201406/14033651992741.jpg" alt="" /></p> <p class="MsoNormal" style="text-indent:21.0pt;mso-char-indent-count:2.0"><span lang="EN-US">, </span><span style="mso-bidi-font-size:10.5pt;font-family:宋体;mso-ascii-font-family: "Times New Roman";mso-hansi-font-family:"Times New Roman"">且其中心轴线与圆锥中心轴线相交</span> <span style="mso-bidi-font-size:10.5pt; font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">坐标如图</span><span lang="EN-US"> 2 </span><span style="mso-bidi-font-size:10.5pt;font-family:宋体;mso-ascii-font-family: "Times New Roman";mso-hansi-font-family:"Times New Roman"">所示</span><span lang="EN-US">, </span><span style="mso-bidi-font-size: 10.5pt;font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">则圆柱曲面方程</span><span lang="EN-US">[4]</span><span style="mso-bidi-font-size:10.5pt;font-family:宋体; mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"">为</span><span lang="EN-US">:<o:p></o:p></span></p> <p class="MsoNormal" style="text-indent:21.0pt;mso-char-indent-count:2.0"><img src="/upload/images/201406/1403365102055.jpg" alt="" /></p> <p class="MsoNormal" style="text-indent:21.0pt;mso-char-indent-count:2.0"><img src="/upload/images/201406/14033651159185.jpg" alt="" /></p> <p class="MsoNormal" align="left" style="text-indent: 21pt;"><span style="mso-bidi-font-size: 10.5pt;font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman";mso-bidi-font-family:宋体;mso-font-kerning:0pt">上式即为相贯线上任一点的极坐标方程</span> <span style="mso-bidi-font-size:10.5pt;font-family:宋体;mso-ascii-font-family:"Times New Roman"; mso-hansi-font-family:"Times New Roman";mso-bidi-font-family:宋体;mso-font-kerning: 0pt">在制作时将圆锥面展开成板</span> <span style="mso-bidi-font-size:10.5pt;font-family:宋体;mso-ascii-font-family: "Times New Roman";mso-hansi-font-family:"Times New Roman";mso-bidi-font-family: 宋体;mso-font-kerning:0pt">用数控线切割机按该极坐标方程即可加工成形对于任何平面与立体截交以及立体与立体相贯</span> <span style="mso-bidi-font-size:10.5pt;font-family:宋体;mso-ascii-font-family:"Times New Roman"; mso-hansi-font-family:"Times New Roman";mso-bidi-font-family:宋体;mso-font-kerning: 0pt">都可求出其解析方程</span> <span style="mso-bidi-font-size:10.5pt;font-family:宋体;mso-ascii-font-family: "Times New Roman";mso-hansi-font-family:"Times New Roman";mso-bidi-font-family: 宋体;mso-font-kerning:0pt">使我们在</span><span lang="EN-US"><a href="http://www.bethel-cnc.com/" target="_blank"><span lang="EN-US" style="font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">数控机床</span></a></span><span style="mso-bidi-font-size:10.5pt;font-family:宋体;mso-ascii-font-family:"Times New Roman"; mso-hansi-font-family:"Times New Roman";mso-bidi-font-family:宋体;mso-font-kerning: 0pt">的生产中</span> <span style="mso-bidi-font-size:10.5pt;font-family:宋体;mso-ascii-font-family:"Times New Roman"; mso-hansi-font-family:"Times New Roman";mso-bidi-font-family:宋体;mso-font-kerning: 0pt">可以根据相贯线的曲线方程来控制切割工具的运动走向</span> <span style="mso-bidi-font-size:10.5pt; font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman";mso-bidi-font-family:宋体;mso-font-kerning:0pt">致使在机床上加工出我们所需的各种曲线</span> <span style="mso-bidi-font-size:10.5pt;font-family:宋体;mso-ascii-font-family:"Times New Roman"; mso-hansi-font-family:"Times New Roman";mso-bidi-font-family:宋体;mso-font-kerning: 0pt">且克服了由于作图而产生的误差</span> <span style="mso-bidi-font-size:10.5pt;font-family:宋体;mso-ascii-font-family: "Times New Roman";mso-hansi-font-family:"Times New Roman";mso-bidi-font-family: 宋体;mso-font-kerning:0pt">并能更好地满足日益发展的计算机辅助设计和制造技术的需要</span><span lang="EN-US" style="mso-bidi-font-size:10.5pt;font-family:宋体;mso-bidi-font-family:宋体; mso-font-kerning:0pt"><o:p></o:p></span></p> <p class="MsoNormal" align="center" style="margin-top:4.5pt;margin-right:0cm; margin-bottom:7.5pt;margin-left:0cm;text-align:center;line-height:13.5pt; mso-pagination:widow-orphan;mso-outline-level:1"><b><span style="mso-bidi-font-size: 10.5pt;font-family:宋体;mso-bidi-font-family:宋体;color:#666666;mso-font-kerning: 0pt">本文由<span lang="EN-US"> <a href="http://www.bethel-cnc.com/"><span lang="EN-US" style="color:#333333"><span lang="EN-US">伯特利数控</span></span></a></span>文章<span lang="EN-US"> </span>整理发表，文章来自网络仅参考学习，本站不承担任何法律责任。</span></b><span lang="EN-US" style="font-family: 微软雅黑;"><o:p></o:p></span></p> <p class="MsoNormal" align="center" style="text-align:center;text-indent:21.0pt; mso-char-indent-count:2.0;mso-pagination:widow-orphan"><span lang="EN-US" 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