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<HTML><HEAD><TITLE>new</TITLE><META content="text/html; charset=gb2312" http-equiv=Content-Type><LINK href="text.css" rel=stylesheet type=text/css><META content="Microsoft FrontPage 4.0" name=GENERATOR></HEAD><body leftmargin="15"><center><b><br>3 虚位移 虚功</b></center> <table border="0" cellpadding="0" cellspacing="0" width="560"> <tr> <td width="20"><b><font color="#0000FF">一、</font></b></td> <td width="560"><b><font color="#0000FF">虚位移</font></b></td> </tr> <tr> <td width="20"></td> <td width="560">定义：在给定位置上，质点或质点系在<font color="#0000FF">约束所容许的条件下</font><font color="#008000">可能发生的</font><font color="#FF00FF">任何</font><font color="#800000">无限小</font>位移,称为质点或质点系的<b>虚位移。</b></td> </tr> <tr> <td width="20"></td> <td width="560"> <table border="0" cellpadding="0" cellspacing="0" width="100%"> <tr> <td width="50%"><b>虚位移的数学意义</b>——广义坐标的变分<br> <b>虚位移有两种情形</b>：<br> <b>质点的虚位移</b>——线位移<br> <b>刚体的虚位移</b>——角位移<br> </td> <td width="50%" bgcolor="#0000FF"> <table border="0" cellspacing="1" width="100%"> <tr> <td width="100%" bgcolor="#FFFFFF">理解虚位移有4个要点：<br> ①为约束所容许，即不能破坏系统的约束<br> ②可能发生的，即假想的，与时间无关<br> ③所有的，可不止一种；<br> ④无限小，不改变系统位置。</td> </tr> </table> </td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="560"><b>例子：</b></td> </tr> <tr> <td width="20"></td> <td width="560"> <table border="0" cellspacing="0" width="100%" cellpadding="0"> <tr> <td width="50%"><img border="0" src="pic2/3071_39.GIF" width="278" height="160"></td> <td width="50%" rowspan="2"> <p align="center"><img border="0" src="pic2/3071_310.GIF" width="271" height="196"></td> </tr> <tr> <td width="50%"><img border="0" src="pic2/3071_311.GIF" width="345" height="99"></td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="560"> <table border="0" cellpadding="0" cellspacing="0" width="100%"> <tr> <td width="50%"> <p align="center">虚<br> 位<br> 移<br> 与<br> 实<br> 位<br> 移<br> 的<br> 比<br> 较<br> </td> <td width="50%"><img border="0" src="pic2/3071_312.GIF" width="503" height="240"></td> </tr> </table> </td> </tr> <tr> <td width="20"><b><font color="#0000FF">二、</font></b></td> <td width="560"><b><font color="#0000FF">虚位移的求法——实际是求虚位移的关系</font></b></td> </tr> <tr> <td width="20"></td> <td width="560"><font color="#0000FF">1. 几何法（运动分析法）</font></td> </tr> <tr> <td width="20"></td> <td width="560"> <table border="0" cellpadding="0" cellspacing="0" width="102%"> <tr> <td width="53%">假想系统运动，找该位置下各速度（角速度）的关系，即各虚位移的关系。通常将各有关虚位移用广义坐标的虚位移表示。</td> <td width="49%" rowspan="4"><img border="0" src="pic2/3071_313.GIF" width="271" height="196"></td> </tr> <tr> <td width="53%">例：曲柄连杆机构</td> </tr> <tr> <td width="53%">选φ为广义坐标。</td> </tr> <tr> <td width="53%"> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td>OA杆：</td> <td><img border="0" src="pic2/3071_314.GIF" width="113" height="29"></td> </tr> <tr> <td>AB瞬心在I：</td> <td><img border="0" src="pic2/3071_315.GIF" width="135" height="50"></td> </tr> <tr> <td>所以：</td> <td><img border="0" src="pic2/3071_316.GIF" width="217" height="50"></td> </tr> </table> </td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="560"><font color="#0000FF">2. 解析法（变分法）</font></td> </tr> <tr> <td width="20"></td> <td width="560"> <table border="0" cellpadding="0" cellspacing="0" width="100%"> <tr> <td width="28%">第 i 点：</td> <td width="72%"><img border="0" src="pic2/3071_317.GIF" width="269" height="27"></td> </tr> <tr> <td width="28%">虚位移：</td> <td width="72%"><img border="0" src="pic2/3071_318.GIF" width="252" height="58"></td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="560">通常选直角坐标系，直接写各点直角坐标的变分，且不在图中画出虚位移：</td> </tr> <tr> <td width="20"></td> <td width="560"> <table border="0" cellpadding="0" cellspacing="0" width="100%"> <tr> <td width="50%"><b>例</b>：曲柄连杆机构</td> <td width="50%" rowspan="3"><img border="0" src="pic2/3071_319.GIF" width="235" height="108"></td> </tr> <tr> <td width="50%">选φ为广义坐标，考虑几何关系：</td> </tr> <tr> <td width="50%"><img border="0" src="pic2/3071_320.GIF" width="200" height="28"></td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="560"><img border="0" src="pic2/3071_321.GIF" width="337" height="29"> <img border="0" src="pic2/3071_322.GIF" width="114" height="26"></td> </tr> <tr> <td width="20"></td> <td width="560"><img border="0" src="pic2/3071_323.GIF" width="228" height="27"></td> </tr> <tr> <td width="20"></td> <td width="560"><img border="0" src="pic2/3071_324.GIF" width="180" height="50"> <img border="0" src="pic2/3071_325.GIF" width="156" height="28"></td> </tr> <tr> <td width="20"></td> <td width="560"><img border="0" src="pic2/3071_326.GIF" width="477" height="29"></td> </tr> <tr> <td width="20"></td> <td width="560">注：通常两种方法各有侧重，有些问题用几何法容易，有些问题有解析法容易。一般容易作运动学分析的问题宜选用几何法。</td> </tr> <tr> <td width="20"><b><font color="#0000FF">三、</font></b></td> <td width="560"><b><font color="#0000FF">虚功</font></b></td> </tr> <tr> <td width="20"></td> <td width="560">力在虚位移上所做的功称为<b>虚功</b>。</td> </tr> <tr> <td width="20"></td> <td width="560"> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td>力： </td> <td><img border="0" src="pic2/3071_327.GIF" width="350" height="31"></td> </tr> <tr> <td> <p align="center">或</td> <td><img border="0" src="pic2/3071_328.GIF" width="134" height="31"></td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="560"> <table border="0" cellpadding="0" cellspacing="0" width="100%"> <tr> <td width="50%"> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td><img border="0" src="pic2/3071_329.GIF" width="61" height="31"></td> <td>指力</td> <td><img border="0" src="pic2/3071_330.GIF" width="22" height="26"></td> <td>对轴或瞬心P之矩，</td> </tr> </table> </td> <td width="50%" rowspan="6"><img border="0" src="pic2/3071_331.GIF" width="251" height="199"></td> </tr> <tr> <td width="50%">特别对刚体此式常用</td> </tr> <tr> <td width="50%"> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td>力偶： </td> <td><img border="0" src="pic2/3071_332.GIF" width="93" height="28"></td> </tr> </table> </td> </tr> <tr> <td width="50%"><b>例</b> 曲柄连杆机构，求各主动力之虚功。</td> </tr> <tr> <td width="50%"><b>解1</b>：<font color="#800000">几何法</font></td> </tr> <tr> <td width="50%"> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td>力偶M： </td> <td><img border="0" src="pic2/3071_333.GIF" width="100" height="26"></td> </tr> </table> </td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="560"> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td>力F： </td> <td><img border="0" src="pic2/3071_334.GIF" width="106" height="26"></td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="560"> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td>力G： </td> <td>直接求C点虚位移不易，故不用下式求虚功： </td> <td><img border="0" src="pic2/3071_335.GIF" width="105" height="29"></td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="560"> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td>而用G对瞬心的力矩求： </td> <td><img border="0" src="pic2/3071_336.GIF" width="249" height="45"></td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="560"> <table border="0" cellpadding="0" cellspacing="0" width="100%"> <tr> <td width="50%"><b>解2：</b><font color="#800000">变分法</font></td> <td width="50%" rowspan="5"><img border="0" src="pic2/3071_337.GIF" width="235" height="109"></td> </tr> <tr> <td width="50%">建立图示坐标系。选φ为广义坐标。</td> </tr> <tr> <td width="50%"> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td>力偶M： </td> <td><img border="0" src="pic2/3071_338.GIF" width="100" height="26"></td> </tr> </table> </td> </tr> <tr> <td width="50%">力F：</td> </tr> <tr> <td width="50%"><img border="0" src="pic2/3071_339.GIF" width="114" height="26"></td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="560"><img border="0" src="pic2/3071_340.GIF" width="228" height="27"></td> </tr> <tr> <td width="20"></td> <td width="560"><img border="0" src="pic2/3071_341.GIF" width="180" height="50"> <img border="0" src="pic2/3071_342.GIF" width="156" height="28"></td> </tr> <tr> <td width="20"></td> <td width="560"><img border="0" src="pic2/3071_343.GIF" width="477" height="29"></td> </tr> <tr> <td width="20"></td> <td width="560"><img border="0" src="pic2/3071_344.GIF" width="366" height="32"></td> </tr> <tr> <td width="20"></td> <td width="560"> <table border="0" cellpadding="0" cellspacing="0" width="228"> <tr> <td width="64">力G：</td> <td width="160"><img border="0" src="pic2/3071_345.GIF" width="160" height="49"></td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="560"><img border="0" src="pic2/3071_346.GIF" width="391" height="50"></td> </tr> <tr> <td width="20"></td> <td width="560"><img border="0" src="pic2/3071_347.GIF" width="292" height="46"></td> </tr> <tr> <td width="20"></td> <td width="560"></td> </tr> <tr> <td width="20"></td> <td width="560"></td> </tr> <tr> <td width="580" colspan="2"> <p align="center"> <a href="3071_2.htm"><font color="#FF6666">[ 上一节 ]</font></a> <a 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