拨叉零件的机械加工工艺规程及铣两缺口平面工装夹具设计
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拨叉零件的机械加工工艺规程及铣两缺口平面工装夹具设计
零件
机械
加工
工艺
规程
缺口
平面
工装
夹具
设计
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拨叉零件的机械加工工艺规程及铣两缺口平面工装夹具设计,拨叉零件的机械加工工艺规程及铣两缺口平面工装夹具设计,零件,机械,加工,工艺,规程,缺口,平面,工装,夹具,设计
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XX大学机 械 加 工 工 序 卡产品型号零（部）件图号共8页产品名称零（部）件名称拔叉夹具第 1 页车 间工序号工序名称材料牌号1铸造铸钢毛坯种类毛坯外形尺寸每毛坯件数每台件数铸造拔叉夹具9317811设备名称设备型号设备编号同时加工件数1夹 具 编 号夹 具 名 称切 削 液工序工时准终单件序号工 步 内 容工 艺 装 备主轴转速(r/min)切削速度(m/min)进给量(mm/r)切削深度(mm)走刀次数时间定额机动辅助1按照零件图锻造合格的零件毛坯砂型铸造2检验毛坯卷尺编制（日期）审核（日期）会签（日期）标记处数更改文件号签字日期标记更改文件号签字日期XX大学机 械 加 工 工 序 卡产品型号零（部）件图号共11 页产品名称零（部）件名称拔叉夹具第 2 页车 间工序号工序名称材料牌号2热处理铸钢毛坯种类毛坯外形尺寸每毛坯件数每台件数铸造拔叉夹具9317811设备名称设备型号设备编号同时加工件数1夹 具 编 号夹 具 名 称切 削 液专用夹具工序工时准终单件序号工 步 内 容工 艺 装 备主轴转速(r/min)切削速度(m/min)进给量(mm/r)切削深度(mm)走刀次数时间定额机动辅助1正火编制（日期）审核（日期）会签（日期）标记处数更改文件号签字日期标记更改文件号签字日期XX大学机 械 加 工 工 序 卡产品型号零（部）件图号共11 页产品名称零（部）件名称拔叉夹具第 3 页车 间工序号工序名称材料牌号3铣铸钢毛坯种类毛坯外形尺寸每毛坯件数每台件数铸造拔叉夹具9317811设备名称设备型号设备编号同时加工件数1夹 具 编 号夹 具 名 称切 削 液分度卡盘工序工时准终单件序号工 步 内 容工 艺 装 备主轴转速(r/min)切削速度(m/min)进给量(mm/r)切削深度(mm)走刀次数时间定额机动辅助1粗铣25的端面并保证尺寸X5032；、齿数8的粗铣刀；千分尺；游标卡尺；4501490.14110.172 粗铣R57的端面并保证尺寸X5032；、齿数8的粗铣刀；千分尺；游标卡尺；4501490.14110.183精铣25的端面并保证尺寸X5032；高速钢三面刃圆盘铣刀（面铣刀）：，齿数为12；千分尺；游标卡尺；900343 0.080.110.254 精铣R57的端面并保证尺寸X5032；高速钢三面刃圆盘铣刀（面铣刀）：，齿数为12；千分尺；游标卡尺；9003430080.11028编制（日期）审核（日期）会签（日期）标记处数更改文件号签字日期标记更改文件号签字日期XX大学机 械 加 工 工 序 卡产品型号零（部）件图号共 11页产品名称零（部）件名称拔叉夹具第 4 页车 间工序号工序名称材料牌号4钻，扩，铰铸钢毛坯种类毛坯外形尺寸每毛坯件数每台件数铸造拔叉夹具93X17811设备名称设备型号设备编号同时加工件数1夹 具 编 号夹 具 名 称切 削 液专用夹具工序工时准终单件序号工 步 内 容工 艺 装 备主轴转速(r/min)切削速度(m/min)进给量(mm/r)切削深度(mm)走刀次数时间定额机动（min）辅助1钻25孔Z535；23mm标准高速钢麻花钻，磨出双锥和修磨横刃；游标卡尺；195140.4311.082扩25孔Z535；mm标准高速钢扩孔钻；游标卡尺；27521.30.5710.543铰25孔Z535；mm标准高速铰刀；游标卡尺；1007.81.610.52编制（日期）审核（日期）会签（日期）标记处数更改文件号签字日期标记更改文件号签字日期XX大学机 械 加 工 工 序 卡产品型号零（部）件图号共11 页产品名称零（部）件名称拔叉夹具第 5 页车 间工序号工序名称材料牌号5铣铸钢毛坯种类毛坯外形尺寸每毛坯件数每台件数铸造拔叉夹具9317811设备名称设备型号设备编号同时加工件数1夹 具 编 号夹 具 名 称切 削 液工序工时准终单件序号工 步 内 容工 艺 装 备主轴转速(r/min)切削速度(m/min)进给量(mm/r)切削深度(mm)走刀次数时间定额机动辅助1粗铣25的端面并保证尺寸X5032；、齿数5的粗铣刀；千分尺；游标卡尺；675211.80.14110.23 粗铣R57的端面并保证尺寸X5032；、齿数5的粗铣刀；千分尺；游标卡尺；675211.80.14110.25精铣25的端面并保证尺寸X5032；高速钢三面刃圆盘铣刀（面铣刀）：，齿数为8；千分尺；游标卡尺；600188.40.080.110.26 精铣R57的端面并保证尺寸X5032；高速钢三面刃圆盘铣刀（面铣刀）：，齿数为8；千分尺；游标卡尺；600188.40080.110.28编制（日期）审核（日期）会签（日期）标记处数更改文件号签字日期标记更改文件号签字日期XX大学机 械 加 工 工 序 卡产品型号零（部）件图号共 11页产品名称零（部）件名称拔叉夹具第 6 页车 间工序号工序名称材料牌号6铣铸钢毛坯种类毛坯外形尺寸每毛坯件数每台件数铸造拔叉夹具93X17911设备名称设备型号设备编号同时加工件数1夹 具 编 号夹 具 名 称切 削 液工序工时准终单件序号工 步 内 容工 艺 装 备主轴转速(r/min)切削速度(m/min)进给量(mm/r)切削深度(mm)走刀次数时间定额机动辅助1粗铣两缺口平面X5032；硬质合金可转位端铣刀（面铣刀）:YT15、齿数为5；千分尺；游标卡尺4751490.15220.522精铣两缺口平面X5032；硬质合金可转位端铣刀（面铣刀）:YT15、齿数为8；千分尺；游标卡尺600188.40.080.220.42编制（日期）审核（日期）会签（日期）标记处数更改文件号签字日期标记更改文件号签字日期XX大学机 械 加 工 工 序 卡产品型号零（部）件图号共11 页产品名称零（部）件名称拔叉夹具第 7 页车 间工序号工序名称材料牌号7钻铸钢毛坯种类毛坯外形尺寸每毛坯件数每台件数铸造拔叉夹具93X17911设备名称设备型号设备编号同时加工件数1夹 具 编 号夹 具 名 称切 削 液工序工时准终单件序号工 步 内 容工 艺 装 备主轴转速(r/min)切削速度(m/min)进给量(mm/r)切削深度(mm)走刀次数时间定额机动辅助1钻16的通孔Z535：高速钢麻花钻钻头，粗钻时do=4mm，后角o16，二重刃长度 ；游标卡尺；136024.30.2211.5编制（日期）审核（日期）会签（日期）标记处数更改文件号签字日期标记更改文件号签字日期XX大学机 械 加 工 工 序 卡产品型号零（部）件图号共11 页产品名称零（部）件名称拔叉夹具第 8 页车 间工序号工序名称材料牌号8钻铸钢毛坯种类毛坯外形尺寸每毛坯件数每台件数铸造拔叉夹具93X17911设备名称设备型号设备编号同时加工件数1夹 具 编 号夹 具 名 称切 削 液工序工时准终单件序号工 步 内 容工 艺 装 备主轴转速(r/min)切削速度(m/min)进给量(mm/r)切削深度(mm)走刀次数时间定额机动辅助1攻M8的螺纹到所要求的尺寸M18的丝锥；外圆车刀YT152211编制（日期）审核（日期）会签（日期）标记处数更改文件号签字日期标记更改文件号签字日期机械加工工艺过程卡片产品型号零件图号产品名称拨叉零件名称共1页第1页材 料 牌 号毛 坯 种 类毛坯外形尺寸每毛坯件数1每 台 件 数备 注工序号工 名序 称工 序 内 容车间工段设 备工 艺 装 备工 时准终单件1铸造按照零件图锻造合格的零件毛坯砂型铸造2检验毛坯检验毛坯卷尺3正火正火4铣粗铣25的端面并保证尺寸X5032X5032；齿数8的粗铣刀；千分尺；游标卡尺；铣粗铣R57的端面并保证尺寸X5032X5032；齿数8的粗铣刀；千分尺；游标卡尺；铣精铣25的端面并保证尺寸X5032X5032；高速钢三面刃圆盘铣刀（面铣刀）：，齿数为12；千分尺；游标卡尺；铣精铣R57的端面并保证尺寸X5032X5032；高速钢三面刃圆盘铣刀（面铣刀）：，齿数为12；千分尺；游标卡尺；5钻钻25孔Z535Z535；23mm标准高速钢麻花钻，磨出双锥和修磨横刃；游标卡尺；钻扩25孔Z535Z535；mm标准高速钢扩孔钻；游标卡尺；钻铰25孔Z535Z535；mm标准高速铰刀；游标卡尺；6铣粗铣25的端面并保证尺寸X5032X5032；、齿数5的粗铣刀；千分尺；游标卡尺；铣粗铣R57的端面并保证尺寸X5032X5032；、齿数5的粗铣刀；千分尺；游标卡尺；铣精铣25的端面并保证尺寸X5032X5032；高速钢三面刃圆盘铣刀（面铣刀）：，齿数为8；千分尺；游标卡尺；铣精铣R57的端面并保证尺寸X5032X5032；高速钢三面刃圆盘铣刀（面铣刀）：，齿数为8；千分尺；游标卡尺；7铣粗铣两缺口平面X5032X5032；硬质合金可转位端铣刀（面铣刀）:YT15、齿数为5；千分尺；游标卡尺铣精铣两缺口平面X5032X5032；硬质合金可转位端铣刀（面铣刀）:YT15、齿数为8；千分尺；游标卡尺8钻钻16的通孔Z535Z535：高速钢麻花钻钻头，粗钻时do=4mm，后角o16，二重刃长度 ；游标卡尺；9攻攻M18的螺纹，深度为20Z535M18的丝锥；外圆车刀YT1510检验检查11入库入库设 计（日 期）校 对（日期）审 核（日期）标准化（日期）会 签（日期）标记处数更改文件号签 字日 期标记处数更改文件号签 字日 期设计说明书题目：拨叉零件的工艺规程及铣两缺口平面夹具设计 学 生： 学 号： 专 业： 班 级： 指导老师：题目: 拨叉工艺及夹具设计内容：1.产品零件图 1张 2.毛坯图 1张3. 夹具装配图 1张 5. 夹具零件图 2张 6. 课程设计说明书 1份目录摘 要4ABSTRCT5序言6一、零件的分析71.1零件的作用71.2零件的工艺分析8二、工艺规程设计82.1 确定毛坯的制造形式82.2 基面的选择92.3制定工艺路线102.4机械加工余量、工序尺寸及毛皮尺寸的确定102.5确立切削用量及基本工时12三、夹具设计24总 结28致 谢29参考文献3031摘 要本次设计内容涉及了机械制造工艺及机床夹具设计、金属切削机床、公差配合与测量等多方面的知识。拨叉加工工艺规程及其铣两缺口平面夹具设计是包括零件加工的工艺设计、工序设计以及专用夹具的设计三部分。在工艺设计中要首先对零件进行分析，了解零件的工艺再设计出毛坯的结构，并选择好零件的加工基准，设计出零件的工艺路线；接着对零件各个工步的工序进行尺寸计算，关键是决定出各个工序的工艺装备及切削用量；然后进行专用夹具的设计，选择设计出夹具的各个组成部件，如定位元件、夹紧元件、引导元件、夹具体与机床的连接部件以及其它部件；计算出夹具定位时产生的定位误差，分析夹具结构的合理性与不足之处，并在以后设计中注意改进。关键词：工艺、工序、切削用量、夹紧、定位、误差。ABSTRCTThis design content has involved the machine manufacture craft and the engine bed jig design, the metal-cutting machine tool, the common difference coordination and the survey and so on the various knowledge.The reduction gear box body components technological process and its the jig design is includes the components processing the technological design, the working procedure design as well as the unit clamp design three parts. Must first carry on the analysis in the technological design to the components, understood the components the craft redesigns the semi finished materials the structure, and chooses the good components the processing datum, designs the components the craft route; After that is carrying on the size computation to a components each labor step of working procedure, the key is decides each working procedure the craft equipment and the cutting specifications; Then carries on the unit clamp the design, the choice designs the jig each composition part, like locates the part, clamps the part, guides the part, to clamp concrete and the engine bed connection part as well as other parts; Position error which calculates the jig locates when produces, analyzes the jig structure the rationality and the deficiency, and will design in later pays attention to the improvement.Keywords: The craft, the working procedure, the cutting specifications, clamp, the localization, the error 序言机械制造工艺学课程设计使我们学完了大学的全部基础课、技术基础课以及大部分专业课之后进行的.这是我们在进行毕业设计之前对所学各课程的一次深入的综合性的总复习,也是一次理论联系实际的训练,因此,它在我们四年的大学生活中占有重要的地位。就我个人而言，我希望能通过这次课程设计对自己未来将从事的工作进行一次适应性训练，从中锻炼自己分析问题、解决问题的能力，为今后参加祖国的“四化”建设打下一个良好的基础。由于能力所限，设计尚有许多不足之处，恳请各位老师给予指导。一、零件的分析1.1零件的作用题目所给的零件是一种车床的拨叉。它位于车床变速机构中，主要起换档，使主轴回转运动按照工作者的要求工作，获得所需的速度和扭矩的作用。零件上方的25孔与操纵机构相连，二下方的半圆缺口则是用于与所控制齿轮所在的轴接触。通过上方的力拨动下方的齿轮变速。1.2零件的工艺分析拨叉共有两处加工表面，其间有一定位置要求。分述如下：1.以25为中心的加工表面这一组加工表面包括：25的孔，以及其左右两个端面，孔内有一个16的孔与其贯通，两者夹角呈37其端面与大孔中心距离65，并攻有M18螺纹，深度20。2.以110缺口为中心的加工表面这一组加工表面包括：110的缺口，以及其左右两个端面。这两组表面有一定的位置度要求,即110缺口两平面对称度要求0.04，平行度要求0.05。其左、右两端面与B圆的垂直度要求0.06。由上面分析可知，加工时应先加工一组表面，再以这组加工后表面为基准加工另外一组。二、工艺规程设计2.1 确定毛坯的制造形式零件材料为精铸钢件。考虑零件在机床运行过程中所受冲击不大，零件不合适焊接和锻造，故选择铸件毛坯。零件毛坯图2.2 基面的选择基面选择是工艺规程设计中的重要工作之一。基面选择得正确与合理可以使加工质量得到保证，生产率得以提高。否则，加工工艺过程中会问题百出，更有甚者，还会造成零件的大批报废，是生产无法正常进行。（1）粗基准的选择。对于零件而言，尽可能选择不加工表面为粗基准。而对有若干个不加工表面的工件，则应以与加工表面要求相对位置精度较高的不加工表面作粗基准。根据这个基准选择原则，现选取外部不加工外轮廓表面作为粗基准，利用夹具支撑定位，并打压板固定，粗加工表面（2）精基准的选择。主要应该考虑基准重合的问题。当设计基准与工序基准不重合时，应该进行尺寸换算，精基准的选择，应该都以25的孔为中心。2.3制定工艺路线制定工艺路线得出发点,应当是使零件的几何形状、尺寸精度及位置精度等技术要求能得到合理的保证,在生产纲领已确定的情况下,可以考虑采用万能性机床配以专用工卡具,并尽量使工序集中来提高生产率。除此之外，还应当考虑经济效果，以便使生产成本尽量下降。1.加工工艺路线工序表3.3 最终加工工艺路线工序号工序内容工序一铸造（铸钢）工序二热处理（调质）工序三粗、精铣左端面工序四钻、扩、铰孔工序五粗、精铣右端面工序六粗、精铣两缺口平面工序七钻16的孔与25的孔相通工序八攻M18的螺纹，深度为20工序九检查工序十入库 工序一共是十步，效率比较高，实际铣削只有两次，而且刀具不用调整）。多次加工57、25孔，两缺口平面是精度要求所致。2.4机械加工余量、工序尺寸及毛皮尺寸的确定车床拨叉材料为精铸钢件，硬度150180HB，生产类型大批量，铸造毛坯。据以上原始资料及加工路线，分别确定各家工表面的机械加工余量、工序尺寸及毛坯尺寸如下：1. 外圆表面延轴线方向长度方向的加工余量及公差（25，57端面）。查机械制造工艺手册（以下称工艺手册）表2.22.5，取25，57端面长度余量均为5（均为双边加工）铣削加工余量为：粗铣 4.5mm精铣 0.5mm精铣后尺寸与零件图尺寸相同，且保证各个尺寸精度。2. 内孔参照参考文献3表2.22、2.225、2.313和参考文献5表18，可以查得：孔：钻孔的精度等级：，表面粗糙度，尺寸偏差是扩孔的精度等级：，表面粗糙度，尺寸偏差是铰孔的精度等级：，表面粗糙度，尺寸偏差是根据工序要求，小头孔分为钻、扩、铰三个工序，各工序余量如下：钻孔参照参考文献机械加工工艺手册表2.3-47，表2.3-48。确定工序尺寸及加工余量为：加工该组孔的工艺是：钻扩铰钻孔： 23 扩孔： 2Z=1.7mm （Z为单边余量）铰孔： （Z为单边余量）镗半圆孔加工该组孔的工艺是：粗镗精镗粗镗： R57孔，参照参考文献3表2.3-48,其余量值为4.2mm；精镗： R57孔，参照参考文献3表2.3-48,其余量值为0.7mm；铸件毛坯的基本尺寸分别为：114半圆孔毛坯基本尺寸为：114+4.2+0.7=118.9mm根据参考文献3表2.2-2可得锻件加工该孔经济精度为IT9。 R57孔毛坯名义尺寸为：114-4.2-0.7=118.9mm；2.5确立切削用量及基本工时工序一，二 属于如处理工艺工序三 以40外圆为粗基准，粗，精铣R57半圆孔,25孔下端面。（1）粗铣孔上下平面1. 加工条件工件材料：铸钢 ,b =0.16GPa HB=150180,铸造。加工要求：粗铣25孔上下端面。机床：X5032立式铣床。刀具：刀具：硬质合金三面刃圆盘铣刀（面铣刀），材料：， ，齿数，此为粗齿铣刀。因其单边余量：Z=1mm所以铣削深度：=1mm,故据切削用量简明手册（后简称切削手册）取刀具直径do=80mm。选择刀具前角o5后角o8，副后角o=8，刀齿斜角s=10,主刃Kr=60,过渡刃Kr=30,副刃Kr=5过渡刃宽b=1mm。2）每齿进给量：根据参考文献3表2.475，取 铣削速度：参照参考文献5表3034，取V=1.35mm/s机床主轴转速： 式（4.1）式中 V铣削速度； d刀具直径。代入式（4.1）得=按照参考文献3表3.174 n=450r/min实际铣削速度：V=2.36mm/s进给量：=0.14x8x450/60=8.4mm/s工作台每分进给量： = =8.4mm/s=504r/min ：根据参考文献3表281,切削工时被切削层长度：由毛坯尺寸可知， 刀具切入长度： 式（4.2）刀具切出长度：取走刀次数为1机动时间： 所以粗铣左右两端面总的时间是0.34min（2）精铣孔上下平面加工条件工件材料：铸钢 ,b =0.16GPa HB=150180,铸造。 机床： X6140卧式铣床根据参考文献5表3031刀具：高速钢三面刃圆盘铣刀（面铣刀）：， ，齿数12，此为细齿铣刀。精铣该平面的单边余量：Z=0.2mm铣削深度：=0.1mm每齿进给量：根据参考文献5表3031，取铣削速度：参照参考文献5表3031，取机床主轴转速：由式（4.1）得，按照参考文献3表3.131 n=900r/min 实际铣削速度：V=5.72mm/s进给量：=0.08x12x900/60=144mm/s工作台每分进给量： = =14.4mm/s=864r/min被切削层长度：由毛坯尺寸可知 刀具切入长度：精铣时刀具切出长度：取走刀次数为1机动时间： 以20孔上端面为精基准，钻、扩、铰、精铰20孔，保证垂直度误差不超过0.05mm,孔的精度达到IT7。工序四：加工孔到要求尺寸 以20孔上端面为精基准，钻、扩、铰、精铰20孔，保证垂直度误差不超过0.05mm,孔的精度达到IT7。工件材料为铸钢，硬度180HBS。孔的直径为25mm，公差为H7，表面粗糙度。加工机床为Z535立式钻床，加工工序为钻、扩、铰，加工刀具分别为：钻孔23mm标准高速钢麻花钻，磨出双锥和修磨横刃；扩孔mm标准高速钢扩孔钻；铰孔mm标准高速铰刀。选择各工序切削用量。（1）确定钻削用量1）确定进给量 根据参考文献5表28-10可查出，由于孔深度比，故。查Z535立式钻床说明书，取。 根据表28-8，钻头强度所允许是进给量。由于机床进给机构允许的轴向力（由机床说明书查出），根据参考文献5表28-9，允许的进给量。 由于所选进给量远小于及，故所选可用。2）确定切削速度、轴向力F、转矩T及切削功率 根据表28-15，由插入法得 ， ， 由于实际加工条件与上表所给条件不完全相同，故应对所的结论进行修正。由参考文献5表283，故查Z535机床说明书，取。实际切削速度为 由表28-5，故 3）校验机床功率 切削功率为 机床有效功率故选择的钻削用量可用。即，相应地，切削工时 被切削层长度：刀具切入长度： 刀具切出长度： 取走刀次数为1机动时间：（2）确定扩孔切削用量1）确定进给量 根据参考文献5表2831，。根据Z535机床说明书，取=0.57mm/r。2）确定切削速度及 根据参考文献5表2833，取。修正系数： ，故 查机床说明书，取。实际切削速度为 切削工时被切削层长度：刀具切入长度，有：刀具切出长度： 取走刀次数为1机动时间：（3）确定铰孔切削用量1）确定进给量 根据参考文献5表2836，按该表注4，进给量取小植。查Z535说明书，取。2）确定切削速度及 由参考文献5表2839，取。由参考文献5表283，得修正系数 ， 故查Z535说明书，取，实际铰孔速度 切削工时被切削层长度：刀具切入长度， 式（4.3）由式（4.3）得刀具切出长度： 取走刀次数为1机动时间：该工序的加工机动时间的总和是： 4）各工序实际切削用量 根据以上计算，各工序切削用量如下：钻孔：，扩孔：，铰孔：， 工序五 以25孔为精基准，粗、精铣R57，孔上端面 （1）粗铣两端面机床：X5032立式铣床刀具：硬质合金可转位端铣刀（面铣刀），材料：， ，齿数，此为粗齿铣刀。因其单边余量：Z=1mm所以铣削深度：=1mm每齿进给量：根据参考文献3表2.473，取=0.14 铣削速度：参照参考文献3表2.481，取v=2.12m/s机床主轴转速：由式（4.1）得=675r/min按照参考文献3表3.174 n=675r/min 实际铣削速度：v=3.53M/S 进给量：=0.14x5x675/60=7.9mm/s 工作台每分进给量：=7.9mm/s=473r/min ：根据参考文献3表2.481,切削工时被切削层长度：由毛坯尺寸可知， 刀具切入长度： 式（4.4）刀具切出长度：取走刀次数为1机动时间：由于是粗铣两个两侧面，所以粗铣的时间为0.448min（2）精铣两端面机床：X5032立式铣床刀具：硬质合金可转位端铣刀（面铣刀），材料：， ，齿数8，此为细齿铣刀。精铣该平面的单边余量：Z=0.2mm铣削深度：=0.1mm每齿进给量：根据参考文献3表2.473，=0.08取铣削速度：参照参考文献3表2.481，取机床主轴转速：由式（4.1）得，按照参考文献3表3.131 实际铣削速度：进给量：=0.08x8x600/60=6.4mm/s工作台每分进给量： =384r/min被切削层长度：由毛坯尺寸可知 刀具切入长度：精铣时刀具切出长度：取走刀次数为1机动时间：工序六 粗、精铣两缺口平面 （1）粗铣两端面机床：X5032立式铣床刀具：硬质合金可转位端铣刀（面铣刀），材料：， ，齿数，此为粗齿铣刀。因其单边余量：Z=1mm所以铣削深度：=1mm每齿进给量：根据参考文献3表2.473，取=0.14 铣削速度：参照参考文献3表2.481，取v=2.47m/s机床主轴转速：由式（4.1）得，按照参考文献3表3.174 实际铣削速度： 进给量： 工作台每分进给量： ：根据参考文献3表2.481,切削工时被切削层长度：由毛坯尺寸可知l=30mm， 刀具切入长度：=17mm 刀具切出长度：取走刀次数为1机动时间：t=0.21min所以粗加工两缺口侧面的时间为0.42min （2）精铣两侧面 机床：X5032立式铣床 刀具：硬质合金可转位端铣刀（面铣刀），材料：， ，齿数8，此为细齿铣刀。精铣该平面的单边余量：Z=02mm铣削深度：=0.1mm每齿进给量：根据参考文献3表2.473，取铣削速度：参照参考文献3表2.481，取机床主轴转速：由式（4.1）得，按照参考文献3表3.131 实际铣削速度：进给量：工作台每分进给量： 被切削层长度：由毛坯尺寸可知 刀具切入长度：精铣时刀具切出长度：取走刀次数为1机动时间：所以精铣的总时间为0.52min工序七 以25孔及其两端面为精基准，钻一个16孔 机床：z535立式钻床 1. 选择钻头 选择高速钢麻花钻钻头，粗钻时do=4mm，后角o16，二重刃长度 2.选择切削用量 （1）决定进给量查切 按钻头强度选择 按机床强度选择最终决定选择机床已有的进给量 经校验校验成功。 （2）钻头磨钝标准及寿命后刀面最大磨损限度（查切）为0.50.8mm，寿命（3）切削速度查切 修正系数 故。查切机床实际转速为故实际的切削速度（4）校验扭矩功率 故满足条件，校验成立。.计算工时螺纹钻削由于没有手册可查，故以钻削切削用量及其他钻螺纹工序估算。祥见工艺卡片。工序八 攻丝 在16孔上攻M18的螺纹孔 深度为20mm.工序九 检查其余几步数据见工艺卡片。三、夹具设计 夹具的设计是为了提高劳动生产效率，保证加工质量、降低劳动强度。在加工零件曲柄时， 需要设计专用夹具。机床夹具是在机械加工中使用的一种工艺装备， 它的主要功能是实现对被加工工件的定位和夹紧。通过定位，使被加工工件在 夹具中占有同一个正确的加工位置，通过夹紧，克服加工中存在的各种作用力， 使这一正确的位置得到保证，从而使加工过程得以顺利进行。机床夹具的组成 1、定位装置：其作用是使工件在夹具中占据正确的位置。 2、夹紧装置：其作用是将工件压紧夹牢，保证工件在加工过程中受到外力（切削力等）作用是不离开已经占据的正确位置。 3、对刀或导向装置：其作用是确定刀具相对定位元件的正确位置。 4、连接元件：其作用是确定夹具在机床上的正确位置。 5、夹具体：夹具体是机床夹具的基础件，通过它将夹具的所有元件连接成一个整体 。 6、其他元件或装置：是指夹具中因特殊需要而设置的元件或装置。根据加工需要，有些夹具上设置分度装置、靠模装置；为能方便、准确定位，常设置预定位装置；对于大型夹具，常设置吊装元件等。以上各组成部分中，定位元件、夹紧装置和夹具体是机床夹具的基础组成部分。工件的装夹方法 工件装夹的方法有两种： 1.将工件直接装夹在机床的工作台或花盘上。 2.将工件装夹在夹具上。 采用第一种方法装夹的效率低，一般要求先按图纸要求在工件的表面上线，划出加工表面的尺寸和位置，装夹时，用划针或面分表找正后再夹紧。一般用于单件或小批量生产。批量较大时，都采用夹具装夹工件。采用夹具装夹工件有如下优点： 1.保证加工精度，稳定加工质量； 2.缩短辅助时间，提高劳动生产率； 3.扩大机床的使用范围，实现“一机多能”； 4.改善工人的劳动条件，降低生产成本。根据课程设计任务书的要求，设计铣110缺口的夹具，110缺口两平面对称度要求0.04，平行度要求0.05。表面粗糙度6.3，其左、右两端面与B圆的垂直度要求0.06。见下图： 如前所述，零件的定位全部都以25的孔为中心。加工缺口之前，应该先将定位孔加工到位。将零件的左端面放置在工作台上，因为底部不在一个平面，所以将右边用垫块垫高。垫块通过螺栓与底板相连接。工件通过定位杆进行定位，定位杆与底板用螺栓联接，为了防止螺纹误差导致中心度偏差，设计了一个定位沉孔，提高定心精度。定位杆的顶部，加工出一段螺纹，对夹具设计，要求能快速定位装夹，为了实现拨动顶尖座的快速拆、装，在顶部，设计一个开口垫。开口销的上部是一个特殊螺母，该螺母的最大外圆，必须小于拨动顶尖座的内孔，这样，螺母扭松，可以将开口垫直接拿出，然后零件可以穿过螺母，迅速从上取出。在夹具的右边，设置了两个对刀块，便于加工时刀具对刀使用，整体装配效果如下：总 结设计即将结束了，时间虽然短暂但是它对我们来说受益菲浅的，通过这次的设计使我们不再是只知道书本上的空理论，不再是纸上谈兵，而是将理论和实践相结合进行实实在在的设计，使我们不但巩固了理论知识而且掌握了设计的步骤和要领，使我们更好的利用图书馆的资料，更好的更熟练的利用我们手中的各种设计手册和AUTOCAD等制图软件，为我们踏入设计打下了好的基础。设计使我们认识到了只努力的学好书本上的知识是不够的，还应该更好的做到理论和实践的结合。因此同学们非常感谢老师给我们的辛勤指导，使我们学到了好多，也非常珍惜学院给我们的这次设计的机会，它将是我们毕业设计完成的更出色的关键一步。致 谢这次设计使我收益不小，为我今后的学习和工作打下了坚实和良好的基础。但是，查阅资料尤其是在查阅切削用量手册时，数据存在大量的重复和重叠，由于经验不足，在选取数据上存在一些问题，不过我的指导老师每次都很有耐心地帮我提出宝贵的意见，在我遇到难题时给我指明了方向，最终我很顺利的完成了毕业设计。这次设计成绩的取得，与指导老师的细心指导是分不开的。在此，我衷心感谢我的指导老师，特别是每次都放下她的休息时间，耐心地帮助我解决技术上的一些难题，她严肃的科学态度，严谨的治学精神，精益求精的工作作风，深深地感染和激励着我。从课题的选择到项目的最终完成，她都始终给予我细心的指导和不懈的支持。多少个日日夜夜，她不仅在学业上给我以精心指导，同时还在思想、生活上给我以无微不至的关怀，除了敬佩指导老师的专业水平外，她的治学严谨和科学研究的精神也是我永远学习的榜样，并将积极影响我今后的学习和工作。在此谨向指导老师致以诚挚的谢意和崇高的敬意。参考文献1 徐嘉元，曾家驹主编机械制造工艺学北京：机械工业出版社1997.82 艾兴，肖诗纲切削用量简明手册北京：机械工业出版社19943 赵家齐：机械制造工艺学课程设计指导书北京：机械工业出版社4 李益民主编：机械制造工艺设计简明手册北京：机械工业出版社，2005年7月第一版5 吴拓主编现代机床夹具设计哈尔滨：化学工业出版社 2009.3 6 孙巳德主编机床夹具图册北京：机械工业出版社1985.6 7 孟少安主编机械加工工艺手册北京：机械工业出版社1991.98 孟少农主编机械加工工艺手册北京：机械工业出版社1991.99 宋昭祥主编机械制造基础北京：机械工业出版社1998.1010 李名望主编，机床夹具设计实例教程，北京：化学工业出版社2009.911 陆剑中，孙家宁主编金属切削原理与刀具北京：机械工业出版 2005.112 孙绍文主编最新机械制图实用手册图例天津：科学技术出版社 1989.313 赵家齐主编机械制造工艺学课程设计指导书北京：机械出业出版社 2000.1014 杨叔子主编机械加工工艺师手册北京：机械工业出版社 2002.115 陈于萍，周兆元主编互换性与测量技术基础北京：机械工业出版社 2005.1016 朱耀祥，浦林祥主编现代夹具设计手册北京：机械工业出版社 2010.217 陈宏钧主编典型零件机械加工生产实例北京：机械工业出版社 2005.1Robotics and Computer-Integrated Manufacturing 21 (2005) 368378Locating completeness evaluation and revision in fixture planH. Song?, Y. RongCAM Lab, Department of Mechanical Engineering, Worcester Polytechnic Institute, 100 Institute Rd, Worcester, MA 01609, USAReceived 14 September 2004; received in revised form 9 November 2004; accepted 10 November 2004AbstractGeometry constraint is one of the most important considerations in fixture design. Analytical formulation of deterministiclocation has been well developed. However, how to analyze and revise a non-deterministic locating scheme during the process ofactual fixture design practice has not been thoroughly studied. In this paper, a methodology to characterize fixturing systemsgeometry constraint status with focus on under-constraint is proposed. An under-constraint status, if it exists, can be recognizedwith given locating scheme. All un-constrained motions of a workpiece in an under-constraint status can be automatically identified.This assists the designer to improve deficit locating scheme and provides guidelines for revision to eventually achieve deterministiclocating.r 2005 Elsevier Ltd. All rights reserved.Keywords: Fixture design; Geometry constraint; Deterministic locating; Under-constrained; Over-constrained1. IntroductionA fixture is a mechanism used in manufacturing operations to hold a workpiece firmly in position. Being a crucialstep in process planning for machining parts, fixture design needs to ensure the positional accuracy and dimensionalaccuracy of a workpiece. In general, 3-2-1 principle is the most widely used guiding principle for developing a locationscheme. V-block and pin-hole locating principles are also commonly used.A location scheme for a machining fixture must satisfy a number of requirements. The most basic requirement is thatit must provide deterministic location for the workpiece 1. This notion states that a locator scheme producesdeterministic location when the workpiece cannot move without losing contact with at least one locator. This has beenone of the most fundamental guidelines for fixture design and studied by many researchers. Concerning geometryconstraint status, a workpiece under any locating scheme falls into one of the following three categories:1. Well-constrained (deterministic): The workpiece is mated at a unique position when six locators are made to contactthe workpiece surface.2. Under-constrained: The six degrees of freedom of workpiece are not fully constrained.3. Over-constrained: The six degrees of freedom of workpiece are constrained by more than six locators.In 1985, Asada and By 1 proposed full rank Jacobian matrix of constraint equations as a criterion and formed thebasis of analytical investigations for deterministic locating that followed. Chou et al. 2 formulated the deterministiclocating problem using screw theory in 1989. It is concluded that the locating wrenches matrix needs to be full rank toachieve deterministic location. This method has been adopted by numerous studies as well. Wang et al. 3 consideredARTICLE IN PRESS/locate/rcim0736-5845/$-see front matter r 2005 Elsevier Ltd. All rights reserved.doi:10.1016/j.rcim.2004.11.012?Corresponding author. Tel.: +15088316092; fax: +15088316412.E-mail address: hsong (H. Song).locatorworkpiece contact area effects instead of applying point contact. They introduced a contact matrix andpointed out that two contact bodies should not have equal but opposite curvature at contacting point. Carlson 4suggested that a linear approximation may not be sufficient for some applications such as non-prismatic surfaces ornon-small relative errors. He proposed a second-order Taylor expansion which also takes locator error interaction intoaccount. Marin and Ferreira 5 applied Chous formulation on 3-2-1 location and formulated several easy-to-followplanning rules. Despite the numerous analytical studies on deterministic location, less attention was paid to analyzenon-deterministic location.In the Asada and Bys formulation, they assumed frictionless and point contact between fixturing elements andworkpiece. The desired location is q*, at which a workpiece is to be positioned and piecewisely differentiable surfacefunction is gi(as shown in Fig. 1).The surface function is defined as giq? 0: To be deterministic, there should be a unique solution for the followingequation set for all locators.giq 0;i 1;2;.;n,(1)where n is the number of locators and q x0;y0;z0;y0;f0;c0? represents the position and orientation of theworkpiece.Only considering the vicinity of desired location q?; where q q? Dq; Asada and By showed thatgiq giq? hiDq,(2)where hiis the Jacobian matrix of geometry functions, as shown by the matrix in Eq. (3). The deterministic locatingrequirement can be satisfied if the Jacobian matrix has full rank, which makes the Eq. (2) to have only one solutionq q?:rankqg1qx0qg1qy0qg1qz0qg1qy0qg1qf0qg1qc0:qgiqx0qgiqy0qgiqz0qgiqy0qgiqf0qgiqc0:qgnqx0qgnqy0qgnqz0qgnqy0qgnqf0qgnqc026666666664377777777758:9=; 6.(3)Upon given a 3-2-1 locating scheme, the rank of a Jacobian matrix for constraint equations tells the constraint statusas shown in Table 1. If the rank is less than six, the workpiece is under-constrained, i.e., there exists at least one freemotion of the workpiece that is not constrained by locators. If the matrix has full rank but the locating scheme hasmore than six locators, the workpiece is over-constrained, which indicates there exists at least one locator such that itcan be removed without affecting the geometry constrain status of the workpiece.For locating a model other than 3-2-1, datum frame can be established to extract equivalent locating points. Hu 6has developed a systematic approach for this purpose. Hence, this criterion can be applied to all locating schemes.ARTICLE IN PRESSX Y Z O X Y Z O (x0,y0,z0) gi UCS WCS Workpiece Fig. 1. Fixturing system model.H. Song, Y. Rong / Robotics and Computer-Integrated Manufacturing 21 (2005) 368378369Kang et al. 7 followed these methods and implemented them to develop a geometry constraint analysis module intheir automated computer-aided fixture design verification system. Their CAFDV system can calculate the Jacobianmatrix and its rank to determine locating completeness. It can also analyze the workpiece displacement and sensitivityto locating error.Xiong et al. 8 presented an approach to check the rank of locating matrix WL(see Appendix). They also intro-duced left/right generalized inverse of the locating matrix to analyze the geometric errors of workpiece. It hasbeen shown that the position and orientation errors DX of the workpiece and the position errors Dr of locators arerelated as follows:Well-constrained :DX WLDr,(4)Over-constrained :DX WTLWL?1WTLDr,(5)Under-constrained :DX WTLWLWTL?1Dr I6?6? WTLWLWTL?1WLl,(6)where l is an arbitrary vector.They further introduced several indexes derived from those matrixes to evaluate locator configurations, followed byoptimization through constrained nonlinear programming. Their analytical study, however, does not concern therevision of non-deterministic locating. Currently, there is no systematic study on how to deal with a fixture design thatfailed to provide deterministic location.2. Locating completeness evaluationIf deterministic location is not achieved by designed fixturing system, it is as important for designers to knowwhat the constraint status is and how to improve the design. If the fixturing system is over-constrained, informa-tion about the unnecessary locators is desired. While under-constrained occurs, the knowledge about all the un-constrained motions of a workpiece may guide designers to select additional locators and/or revise the locatingscheme more efficiently. A general strategy to characterize geometry constraint status of a locating scheme is describedin Fig. 2.In this paper, the rank of locating matrix is exerted to evaluate geometry constraint status (see Appendixfor derivation of locating matrix). The deterministic locating requires six locators that provide full rank locatingmatrix WL:As shown in Fig. 3, for given locator number n; locating normal vector ai;bi;ci? and locating position xi;yi;zi? foreach locator, i 1;2;.;n; the n ? 6 locating matrix can be determined as follows:WLa1b1c1c1y1? b1z1a1z1? c1x1b1x1? a1y1:aibiciciyi? biziaizi? cixibixi? aiyi:anbncncnyn? bnznanzn? cnxnbnxn? anyn2666666437777775.(7)When rankWL 6 and n 6; the workpiece is well-constrained.When rankWL 6 and n46; the workpiece is over-constrained. This means there are n ? 6 unnecessary locatorsin the locating scheme. The workpiece will be well-constrained without the presence of those n ? 6 locators. Themathematical representation for this status is that there are n ? 6 row vectors in locating matrix that can be expressedas linear combinations of the other six row vectors. The locators corresponding to that six row vectors consist oneARTICLE IN PRESSTable 1RankNumber of locatorsStatuso 6Under-constrained 6 6Well-constrained 646Over-constrainedH. Song, Y. Rong / Robotics and Computer-Integrated Manufacturing 21 (2005) 368378370locating scheme that provides deterministic location. The developed algorithm uses the following approach todetermine the unnecessary locators:1. Find all the combination of n ? 6 locators.2. For each combination, remove that n ? 6 locators from locating scheme.3. Recalculate the rank of locating matrix for the left six locators.4. If the rank remains unchanged, the removed n ? 6 locators are responsible for over-constrained status.This method may yield multi-solutions and require designer to determine which set of unnecessary locators shouldbe removed for the best locating performance.When rankWLo6; the workpiece is under-constrained.3. Algorithm development and implementationThe algorithm to be developed here will dedicate to provide information on un-constrained motions of theworkpiece in under-constrained status. Suppose there are n locators, the relationship between a workpieces position/ARTICLE IN PRESSFig. 2. Geometry constraint status characterization.X Z Y (a1,b1,c1) 2,b2,c2) (x1,y1,z1) (x2,y2,z2) (ai,bi,ci) (xi,yi,zi) (aFig. 3. A simplified locating scheme.H. Song, Y. Rong / Robotics and Computer-Integrated Manufacturing 21 (2005) 368378371orientation errors and locator errors can be expressed as follows:DX DxDyDzaxayaz2666666666437777777775w11:w1i:w1nw21:w2i:w2nw31:w3i:w3nw41:w4i:w4nw51:w5i:w5nw61:w6i:w6n2666666666437777777775?Dr1:Dri:Drn2666666437777775,(8)where Dx;Dy;Dz;ax;ay;azare displacement along x, y, z axis and rotation about x, y, z axis, respectively. Driisgeometric error of the ith locator. wijis defined by right generalized inverse of the locating matrix Wr WTLWLWTL?15.To identify all the un-constrained motions of the workpiece, V dxi;dyi;dzi;daxi;dayi;dazi? is introduced such thatV DX 0.(9)Since rankDXo6; there must exist non-zero V that satisfies Eq. (9). Each non-zero solution of V represents an un-constrained motion. Each term of V represents a component of that motion. For example, 0;0;0;3;0;0? says that therotation about x-axis is not constrained. 0;1;1;0;0;0? means that the workpiece can move along the direction given byvector 0;1;1?: There could be infinite solutions. The solution space, however, can be constructed by 6 ? rankWLbasic solutions. Following analysis is dedicated to find out the basic solutions.From Eqs. (8) and (9)VX dxDx dyDy dzDz daxDax dayDay dazDaz dxXni1w1iDri dyXni1w2iDri dzXni1w3iDri daxXni1w4iDri dayXni1w5iDri dazXni1w6iDriXni1Vw1i;w2i;w3i;w4i;w5i;w6i?TDri 0.10Eq. (10) holds for 8Driif and only if Eq. (11) is true for 8i1pipn:Vw1i;w2i;w3i;w4i;w5i;w6i?T 0.(11)Eq. (11) illustrates the dependency relationships among row vectors of Wr: In special cases, say, all w1jequal to zero,V has an obvious solution 1, 0, 0, 0, 0, 0, indicating displacement along the x-axis is not constrained. This is easy tounderstand because Dx 0 in this case, implying that the corresponding position error of the workpiece is notdependent of any locator errors. Hence, the associated motion is not constrained by locators. Moreover, a combinedmotion is not constrained if one of the elements in DX can be expressed as linear combination of other elements. Forinstance, 9w1ja0;w2ja0; w1j ?w2jfor 8j: In this scenario, the workpiece cannot move along x- or y-axis. However, itcan move along the diagonal line between x- and y-axis defined by vector 1, 1, 0.To find solutions for general cases, the following strategy was developed:1. Eliminate dependent row(s) from locating matrix. Let r rank WL; n number of locator. If ron; create a vectorin n ? r dimension space U u1:uj:un?rhi1pjpn ? r; 1pujpn: Select ujin the way that rankWL r still holds after setting all the terms of all the ujth row(s) equal to zero. Set r ? 6 modified locating matrixWLMa1b1c1c1y1? b1z1a1z1? c1x1b1x1? a1y1:aibiciciyi? biziaizi? cixibixi? aiyi:anbncncnyn? bnznanzn? cnxnbnxn? anyn2666666437777775r?6,where i 1;2;:;niauj:ARTICLE IN PRESSH. Song, Y. Rong / Robotics and Computer-Integrated Manufacturing 21 (2005) 3683783722. Compute the 6 ? n right generalized inverse of the modified locating matrixWr WTLMWLMWTLM?1w11:w1i:w1rw21:w2i:w2rw31:w3i:w3rw41:w4i:w4rw51:w5i:w5rw61:w6i:w6r26666666664377777777756?r3. Trim Wrdown to a r ? rfull rank matrix Wrm: r rankWLo6: Construct a 6 ? r dimension vector Q q1:qj:q6?rhi1pjp6 ? r; 1pqjpn: Select qjin the way that rankWr r still holds after setting all theterms of all the qjth row(s) equal to zero. Set r ? r modified inverse matrixWrmw11:w1i:w1r:wl1:wli:wlr:w61:w6i:w6r26666664377777756?6,where l 1;2;:;6 laqj:4. Normalize the free motion space. Suppose V V1;V2;V3;V4;V5;V6? is one of the basic solutions of Eq. (10) withall six terms undetermined. Select a term qkfrom vector Q1pkp6 ? r: SetVqk ?1;Vqj 0 j 1;2;:;6 ? r;jak;(5. Calculated undetermined terms of V: V is also a solution of Eq. (11). The r undetermined terms can be found asfollows.v1:vs:v62666666437777775wqk1:wqki:wqkr2666666437777775?w11:w1i:w1r:wl1:wli:wlr:w61:w6i:w6r2666666437777775?1,where s 1;2;:;6saqj;saqk;l 1;2;:;6 laqj:6. Repeat step 4 (select another term from Q) and step 5 until all 6 ? r basic solutions have been determined.Based on this algorithm, a C+ program was developed to identify the under-constrained status and un-constrained motions.Example 1. In a surface grinding operation, a workpiece is located on a fixture system as shown in Fig. 4. The normalvector and position of each locator are as follows:L1:0, 0, 10, 1, 3, 00,L2:0, 0, 10, 3, 3, 00,L3:0, 0, 10, 2, 1, 00,L4:0, 1, 00, 3, 0, 20,L5:0, 1, 00, 1, 0, 20.Consequently, the locating matrix is determined.WL0013?100013?300011?20010?203010?2012666666437777775.ARTICLE IN PRESSH. Song, Y. Rong / Robotics and Computer-Integrated Manufacturing 21 (2005) 368378373This locating system provides under-constrained positioning since rankWL 5o6: The program then calculatesthe right generalized inverse of the locating matrix.Wr000000:50:5?1?0:51:50:75?1:251:5000:250:25?0:5000:5?0:50000000:5?0:526666666643777777775.The first row is recognized as a dependent row because removal of this row does not affect rank of the matrix. Theother five rows are independent rows. A linear combination of the independent rows is found according therequirement in step 5 of the procedure for under-constrained status. The solution for this special case is obvious that allthe coefficients are zero. Hence, the un-constrained motion of workpiece can be determined as V ?1; 0; 0; 0; 0; 0?:This indicates that the workpiece can move along x direction. Based on this result, an additional locator should beemployed to constraint displacement of workpiece along x-axis.Example 2. Fig. 5 shows a knuckle with 3-2-1 locating system. The normal vector and position of each locator in thisinitial design are as follows:L1:0, 1, 00, 896, ?877, ?5150,L2:0, 1, 00, 1060, ?875, ?3780,L3:0, 1, 00, 1010, ?959, ?6120,L4:0.9955, ?0.0349, 0.0880, 977, ?902, ?6240,L5:0.9955, ?0.0349, 0.0880, 977, ?866, ?6240,L6:0.088, 0.017, ?0.9960, 1034, ?864, ?3590.The locating matrix of this configuration isWL010515:000:8960010378:001:0600010612:001:01000:9955?0:03490:0880?101:2445?707:26640:86380:9955?0:03490:0880?98:0728?707:26640:82800:08800:0170?0:9960866:6257998:24660:093626666666643777777775,rankWL 5o6 reveals that the workpiece is under-constrained. It is found that one of the first five rows can beremoved without varying the rank of locating matrix. Suppose the first row, i.e., locator L1is removed from WL; theARTICLE IN PRESSXZYL3L4L5L2L1Fig. 4. Under-constrained locating scheme.H. Song, Y. Rong / Robotics and Computer-Integrated Manufacturing 21 (2005) 368378374modified locating matrix turns intoWLM010378:001:0600010612:001:01000:9955?0:03490:0880?101:2445?707:26640:86380:9955?0:03490:0880?98:0728?707:26640:82800:08800:0170?0:996866:6257998:24660:09362666666437777775.The right generalized inverse of the modified locating matrix isWr1:8768?1:8607?20:666521:37160:49953:0551?2:0551?32:444832:44480?1:09561:086212:0648?12:4764?0:2916?0:00440:00440:0061?0:006100:0025?0:00250:0065?0:00690:0007?0:00040:00040:0284?0:0284026666666643777777775.The program checked the dependent row and found every row is dependent on other five rows. Without losinggenerality, the first row is regarded as dependent row. The 5 ? 5 modified inverse matrix isWrm3:0551?2:0551?32:444832:44480?1:09561:086212:0648?12:4764?0:2916?0:00440:00440:0061?0:006100:0025?0:00250:0065?0:00690:0007?0:00040:00040:0284?0:028402666666437777775.The undetermined solution is V ?1; v2; v3; v4; v5; v6?:To calculate the five undetermined terms of V according to step 5,1:8768?1:8607?20:666521:37160:499526666666643777777775T?3:0551?2:0551?32:444832:44480?1:09561:086212:0648?12:4764?0:2916?0:00440:00440:0061?0:006100:0025?0:00250:0065?0:00690:0007?0:00040:00040:0284?0:0284026666666643777777775?1 0; ?1:713; ?0:0432; ?0:0706; 0:04?.Substituting this result into the undetermined solution yields V ?1;0; ?1:713; ?0:0432; ?0:0706; 0:04?ARTICLE IN PRESSFig. 5. Knuckle 610 (modified from real design).H. Song, Y. Rong / Robotics and Computer-Integrated Manufacturing 21 (2005) 368378375This vector represents a free motion defined by the combination of a displacement along ?1, 0, ?1.713 directioncombined and a rotation about ?0.0432, ?0.0706, 0.04. To revise this locating configuration, another locator shouldbe added to constrain this free motion of the workpiece, assuming locator L1was removed in step 1. The program canalso calculate the free motions of the workpiece if a locator other than L1was removed in step 1. This provides morerevision options for designer.4. SummaryDeterministic location is an important requirement for fixture locating scheme design. Analytical criterion fordeterministic status has been well established. To further study non-deterministic status, an algorithm for checking thegeometry constraint status has been developed. This algorithm can identify an under-constrained status and indicatethe un-constrained motions of workpiece. It can also recognize an over-constrained status and unnecessary locators.The output information can assist designer to analyze and improve an existing locating scheme.Appendix. Locating matrixConsider a general workpiece as shown in Fig. 6. Choose reference frame fWg fixed to the workpiece. Let fGg andfLig be the global frame and the ith locator frame fixed relative to it. We haveFiXw;Hw;rwi fiXli;Hli;rli,(12)where Xw2 3?1and Hw2 3?1(Xli2 3?1and Hli2 3?1) are the position and orientation of the workpiece(the ith locator) in the global frame fGg; rwi2 3?1(rli2 3?1) is the position of the ith contact point between theworkpiece and the ith locator in the workpiece frame fWg (the ith locator frame fLig).Assume that DXw2 3?1(DHw2 3?1) and Drwi2 3?1are the deviations of the position Xw2 3?1(orientationHw2 3?1) of the workpiece and the position of the ith contact point rwi2 3?1; respectively. Then we have the actualcontact on the workpiece,FiXw DXw;Hw DHw;rwi Drwi FiXw;Hw;rwi qFiqXwDXwqFiqHwDHwqFiqrwiDrwi,13where the second term in the right side of Eq. (13) is the positi
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