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</span><span style="line-height: 11pt; text-indent: 0pt; font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">2.6</span><span style="line-height: 11pt; text-indent: 0pt; font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">奇异位形分析</span></p> <p class="NewStyle21" style="margin-left: 0pt; text-indent: 18pt; line-height: 23.3pt;"><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">奇异使得机构在整个运行过程中的一些特殊位形处，出现一些特殊的现象，例如, 机构处于死点不能继续运动、失去稳定性、自由度发生变化；特殊位形下还会出现受力 情况变坏，甚至会对机构造成破坏。但奇异也有好的一面，例如，家喻户晓的脚踏式缝 纫机，为了顺利通过踏板四连杆机构的死点位置，在缝纫机启动前需要用手转动缝纫机 上的手轮。</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;"><o:p></o:p></span></p> <p class="NewStyle21" style="margin-left: 0pt; text-indent: 18pt; line-height: 23.3pt;"><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">奇异位形是并联机构研宄中较为复杂的问题，奇异位形分为边界奇异、局部奇异和 结构奇异三种形式。当速度雅可比矩阵行列式等于零时，机构处于边界奇异位形状态， 边界奇异位形又分为内边界奇异位形和外边界奇异位形。当速度雅可比矩阵行列式趋于 无穷大时，机构处于局部奇异位形状态，局部奇异位形是并联机器人特有的奇异位形， 处于该位形时并联机器人有一个不可控的局部自由度。当速度雅可比矩阵行列式趋于零 比零时，机构处于结构奇异位形状态，结构奇异位形也是并联机构特有的性质，只有满 足特殊参数时才会产生结构奇异位形。</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;"><o:p></o:p></span></p> <p class="NewStyle21" style="margin-left: 0pt; text-indent: 18pt; line-height: 23.3pt;"><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">奇异是机构不可避免的现象，不同的机构有不同的奇异位形，所以，每种机构在设 计期间都要进行奇异位形分析。机器人的奇异点出现在可达工作空间的内外边界，由于 并联机器人的结构特点使得并联机器人的工作空间小于同等尺寸的串联机器人，再加上 机器人的奇异位形，使得并联机器人的工作空间变得更小。所以，为了对</span><span class="17" style="font-family: Georgia; letter-spacing: 0pt; font-size: 10.5pt;">Delta</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">机器人 机构的型综合和轨迹规划进行深入的研宄，需要对</span><span class="17" style="font-family: Georgia; letter-spacing: 0pt; font-size: 10.5pt;">Delta</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">机器人进行奇异位形分析，为 了使得奇异分析更加简洁，采用图</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">2-6</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">中平面</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">5</span><span class="17" style="font-family: Georgia; letter-spacing: 0pt; font-size: 10.5pt;">R</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">机器人模型对样机进行串联奇异和并 联奇异分析。</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;"><o:p></o:p></span></p> <p class="MsoNormal"><span style="font-family: MingLiU; letter-spacing: 0pt; font-size: 1pt;"> </span></p> <p class="MsoNormal"><span style="font-family: MingLiU; letter-spacing: 0pt; font-size: 1pt;"> </span></p> <p class="MsoNormal"><span style="font-family: MingLiU; letter-spacing: 0pt; font-size: 1pt;"> </span></p> <p class="NewStyle21" style="margin-left: 0pt; text-indent: 18pt; line-height: 23.75pt;"><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">串联奇异一般出现在机器人可达工作空间边界上，当平面</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">5</span><span class="17" style="font-family: Georgia; letter-spacing: 0pt; font-size: 10.5pt;">R</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">并联机器人位于串联 奇异位形时，末端执行器在可达工作空间边界法线方向上失去自由度，</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">5</span><span class="17" style="font-family: Georgia; letter-spacing: 0pt; font-size: 10.5pt;">R</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">并联机器人 共有四种串联奇异位形，如图</span><span class="18" style="font-family: 宋体; letter-spacing: 0.5pt; font-size: 10pt;">2-11</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">所示，图中末端执行器分别失去了 </span><span class="19" style="font-family: Georgia; letter-spacing: 0pt; font-size: 9.5pt;">A</span><span class="18" style="font-family: 宋体; letter-spacing: 0.5pt; font-size: 10pt;">'、</span><span class="18" style="font-family: 宋体; letter-spacing: 0.5pt; font-size: 10pt;">忠</span><span class="19" style="font-family: Georgia; letter-spacing: 0pt; font-size: 9.5pt;">P</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">方向的 </span><span class="15" style="font-family: 宋体; letter-spacing: -1pt; font-size: 11pt;">自由度。其中，图</span><span class="15" style="font-family: 宋体; letter-spacing: -1pt; font-size: 11pt;">（</span><span class="17" style="font-family: Georgia; letter-spacing: 0pt; font-size: 10.5pt;">a</span><span class="15" style="font-family: 宋体; letter-spacing: -1pt; font-size: 11pt;">)、（</span><span class="17" style="font-family: Georgia; letter-spacing: 0pt; font-size: 10.5pt;">b</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">)</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">分别为第一、二支链分别完全展开的串联奇异位形，图</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">（</span><span class="17" style="font-family: Georgia; letter-spacing: 0pt; font-size: 10.5pt;">c</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">)、 (</span><span class="17" style="font-family: Georgia; letter-spacing: 0pt; font-size: 10.5pt;">d</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">)</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">分别为第一、二支链分别完全收缩的串联奇异位形</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt; vertical-align: super;">[65]</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">。</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;"><o:p></o:p></span></p> <p class="NewStyle21" style="margin-left: 0pt; text-indent: 18pt; line-height: 25.9pt;"><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">当平面</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">5</span><span class="17" style="font-family: Georgia; letter-spacing: 0pt; font-size: 10.5pt;">R</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">并联机器人位于并联奇异位形时，机构的从动臂与</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">5</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt; vertical-align: sub;">2</span><span class="17" style="font-family: Georgia; letter-spacing: 0pt; font-size: 10.5pt;">P</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">共线，机构 的奇异位形如图</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">2-12</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">所示。其中，图</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">（</span><span class="17" style="font-family: Georgia; letter-spacing: 0pt; font-size: 10.5pt;">a</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">)</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">为</span><span class="17" style="font-family: Georgia; letter-spacing: 0pt; font-size: 10.5pt;">S</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">'</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">、尽</span><span class="17" style="font-family: Georgia; letter-spacing: 0pt; font-size: 10.5pt;">Z</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt; vertical-align: super;">3</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">重合并共线时的并联奇异位形， 图</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">（</span><span class="17" style="font-family: Georgia; letter-spacing: 0pt; font-size: 10.5pt;">b</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">)</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">为</span><span class="17" style="font-family: Georgia; letter-spacing: 0pt; font-size: 10.5pt;">S</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">'、</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">展开并共线时的并联奇异位形</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt; vertical-align: super;">[65]</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">。</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;"><o:p></o:p></span></p> <p class="MsoNormal"><span style="font-family: MingLiU; letter-spacing: 0pt; font-size: 1pt;"> </span></p> <p class="NewStyle21" style="margin-left: 0pt; text-indent: 18pt; line-height: 25.9pt;"><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">在图</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">2-12</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">中，由于為孕,4</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt; vertical-align: sub;">2</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">5</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt; vertical-align: sub;">2</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">几何结构限制点孕，</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt; vertical-align: super;">5</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt; vertical-align: sub;">2</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">不能完全重合，图</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">（</span><span class="17" style="font-family: Georgia; letter-spacing: 0pt; font-size: 10.5pt;">a</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">)</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">中的并 联奇异位形不会出现。由于机械结构中尽/</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt; vertical-align: super;">5</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;"> + 5</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt; vertical-align: sub;">2</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">/</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt; vertical-align: super;">?</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">>4</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt; vertical-align: sub;">1</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">5</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt; vertical-align: sub;">1</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">+為晃+^木，杆件5</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt; vertical-align: sub;">1</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">/</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt; vertical-align: super;">}</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">、沒</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt; vertical-align: sub;">2</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">尸不 能展开并共线，图</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">（</span><span class="17" style="font-family: Georgia; letter-spacing: 0pt; font-size: 10.5pt;">b</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">)</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">中的并联奇异位形不会出现。</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;"><o:p></o:p></span></p> <p class="NewStyle22" style="margin-left: 0pt; text-indent: 0pt; line-height: 11pt;"><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">2.7</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;"> </span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">本章小结</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;"><o:p></o:p></span></p> <p class="NewStyle21" style="margin-left: 0pt; text-indent: 18pt; line-height: 23.3pt;"><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">本章主要对平面两自由度高速并联工业机器人</span><span class="17" style="font-family: Georgia; letter-spacing: 0pt; font-size: 10.5pt;">Delta</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">进行了机构学、运动学和动力 学分析，对所设计的机器人的机构进行了阐述，指出了机器人特色，对其进行了运动学 逆解和运动学正解分析，得到了相应的位移、速度、加速度表达式，利用拉格朗日方法 对机器人进行了简化的动力学分析，得到了简化的动力学表达式。最后，对机器人进行 了工作空间分析和奇异位形分析，从理论上得到了机器人的工作空间和奇异位形。</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;"><o:p></o:p></span></p> <p class="NewStyle21" style="margin-left: 0pt; text-indent: 18pt; line-height: 23.3pt;"><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">论文将从第三章开始对机器人的轨迹规划方法进行深入的研宄，使用不同方法进行 相应的轨迹规划和优化，以期待得到优良的机器人运动控制拟合曲线。</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;"><br clear="all" 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