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英译原材料.pdf

安全带卷加速敏感器组件自动装配机设计【优秀】【带sw三维】【word+8张CAD图纸全套】【毕设】

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安全带卷加速敏感器组件自动装配机设计【优秀】【带sw三维】【word+8张CAD图纸全套】【毕设】.rar

前期 (自动装配设计).doc---(点击预览)

SW三维制图

1#机械手.SLDASM

1.SLDPRT

B型支承板.SLDPRT

二次装夹.SLDPRT

伸缩杆.SLDPRT

伸缩杆1.SLDPRT

六角螺钉.SLDPRT

夹具.SLDPRT

夹具装配体.SLDASM

安全带卷 (2).SLDPRT

安全带卷.SLDPRT

安全带卷1.SLDPRT

安全带卷2.SLDPRT

底座.SLDPRT

底座接管.SLDPRT

支承钉.SLDPRT

机1缸体前盖.SLDPRT

机1顶.SLDPRT

机械手-簧片.SLDPRT

机械手-簧片1.SLDPRT

机械手1.SLDASM

机械手2-1.SLDPRT

机械手2-1片.SLDPRT

机械手2-2.SLDPRT

机械手2-2片.SLDPRT

机械手2.SLDASM

机械手手爪.SLDPRT

气缸.SLDPRT

气缸1.SLDPRT

气缸1盖.SLDPRT

气缸1顶.SLDPRT

气缸后盖.SLDPRT

气缸底座.SLDPRT

片2.SLDPRT

盖1.SLDPRT

盖2.SLDPRT

管接管.SLDPRT

缸体前盖.SLDPRT

螺母.SLDPRT

螺钉1.SLDPRT

螺钉2.SLDPRT

螺钉3.SLDPRT

螺钉4.SLDPRT

螺钉5.SLDPRT

装配体.SLDASM

轴1.SLDPRT

轴2.SLDPRT

轴3.SLDPRT

轴4.SLDPRT

阶形螺钉.SLDPRT

顶1.SLDPRT

顶2.SLDPRT

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关键词：: 安全带卷加速敏感器组件自动装配装配机

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安全带卷加速敏感器组件自动装配机设计【优秀】【带sw三维】【word+8张CAD图纸全套】【毕业设计】

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SW三维制图

中期检查表.doc

任务书.doc

前期 (自动装配设计).doc

前期材料.doc

外文资料翻译.doc

夹具.dwg

实习调研报告.doc

开题报告.doc

机械手1.dwg

机械手2.dwg

正文.doc

英译原材料.pdf

选题.doc

零件1.dwg

零件2.dwg

零件3.dwg

零件4.dwg

零件5.dwg

任务书

1、本毕业设计（论文）课题应达到的目的：

通过课题研究，使学生掌握机械制造装备设计、分析的方法，并且熟悉使用一种CAD软件，着重培养学生综合应用专业知识和自动装配机器人设计技术知识的能力，以及独立解决和分析实际问题的能力。

2、本毕业设计（论文）课题任务的内容和要求（包括原始数据、技术要求、工作要求等）：

自动装配是当前应广泛的一种制造工艺，在生产生活中日益受到重视。本课题针对企业实际零件的制造需求和自动装配技术的应用现状，设计满足企业专门零件加工需要的自动装配机。主要针对专门零件，结合其装配工艺特点，设计满足企业实际工艺要求的专用自动装配机器人，为企业生产提供有效的手段和方法。

主要任务：

1）查阅相关文献资料15篇以上，并完成指定的不少于五千印刷符的英文资料翻译，掌握自动装配系统设计的一般方法，学会使用相关手册完成设计任务；

2）明确本题目的设计参数，技术条件，根据设计任务完成自动装配系统方案的拟定，绘制全套自动装配夹具和机器人的机械零件图、装配图；

3）完成毕业设计说明书。

毕业设计（论文）任务书

1、对本毕业设计（论文）课题成果的要求（包括毕业设计论文、

图表、实物样品等）：

1）机器人零件图一套；

2）自动装配夹具和机器人装配图一份；

3）毕业设计论文一份。

4、主要参考文献：

[1] 李陆山. 安全带卷收预紧装置[J]. 汽车运用. 2000,07:28-43

[2] 尚久浩主编.自动机械设计[M]. 中国轻工业出版社, 2003 ,02:18-25

[3] 融亦鸣等著.计算机辅助夹具设计[M]. 机械工业出版社, 2002,06:34-56

[4] Walter Frick. 需要定制的自动化系统[J]. 现代制造. 2008,28):

[5] 岁丰. 新型自动装配线[J]. 管理科学文摘. 1996,08:27-37

[6] 赵锡芳. 智能装配机器人机构的研究和发展[J]. 机器人. 1990,04:17-27

[7] 丛明,钱文瀚,张坚志. 自动装配线故障分析与研究[J]. 组合机床与自动化加工技术. 1994,10:39-45

[8] 王镛. 自动化装配技术的研究与发展[J]. 组合机床与自动化加工技术. 1990,11:47-51

[9] 李瑾,李婕,陈涛. 随夹的自动定位夹紧装置的设计[J]. 制造技术与机床. 2010,12:50-55

[10] 孙铭启. 机器人在装配作业中的应用[J]. 组合机床与自动化加工技术. 1994,09:33-35

[11] 姜中威. 自动化装配技术与柔性装配系统探索[J]. 黑龙江科技信息. 2004,10:11-17

[12] 平雪良,陶宇,叶晶,董宁. 基于坐标系的自动装配方法的研究与实现[J]. 机械设计. 2011,11:23-26

[13] 张肇富. 自动装配零件的检测装置[J]. 上海计量测试. 1997,06:13-17

[14] 张萍,廖文和,刘长毅. 基于装配特征的零件自动装配[J]. 机械制造与自动化. 2004,05:21-24

[15] 林绳宗. 国外制造业自动化现状及其发展趋向[J]. 世界产品与技术. 1996,02:47-50

毕业设计（论文）任务书

5、本毕业设计（论文）课题工作进度计划

起止日期工作内容

1.20~3.1

3.1～4.5

4.5～4.25

4.25～5.15

5.15～5.24

查阅资料，完成外文资料的翻译；

明确本题目的设计参数，技术条件，根据设计任务完成自动装配系统方案确定，绘自动装配夹具和机器人装配图；

完成自动装配夹具和机器人零件图的绘制；

撰写论文，指导老师审阅；

准备毕业论文答辩；

所在专业审核意见：

摘要

随着现代科技的迅速发展，装配自动化正在逐步发展成为当今世界装配的发展主流，逐步取代人工的手工装配。它已成为衡量一个国家机械发展水平的主要标志之一。自动装配技术的重要性还在于促进产品制造系统的整体优化，生产率得以全面提高，用少量调整工人服务于一定数量的自动装配设备，在一定程度上提高均衡生产水平。自动装配不会因为工人疲劳，疏忽，情绪，技术不熟练等因素影响而造成产品质量缺陷或不稳定。时间表明，当达到一定批量的与手工装配保持同一水平的自动化装配将会使成本下降。同时，在许多情况下，装配自动化所占用的生产面积比手工装配完成同样生产任务的工作面积要小的多。

本课题设计一种应用于工业生产装配线中的专用自动装配机械手，能通过自动控制操作工业机械手，实现多自由度的抓持与运动，代替人完成安全带卷加速敏感器组件的装配。

关键词：自动装配，机械手，气动，结构设计

ABSTRACT

With the rapid development of modern science and technology, assembly automation is gradually developed into the mainstream of development in the world and gradually replace the manual assembly .It has become one of the main signs to measure the level of development of a national machinery. The importance of Automatic assembly technology is to promote products manufacturing system overall optimization .productivity can be overall improved. Minor adjustment workers are used for a certain number of automatic assembly equipment, in certain extent, It improves the balance in the level of production. Automatic assembly can not affect product quality resulting from errors or instability because of the factors of worker’s fatigue, neglect, emotional, unskilled. It has shown that when a certain amount of automated assembly will decline costs than manual assembly. At the same time, in many cases, the production assembly automation occupies a smaller area than manual assembly in completing the same task.

This?subject?is?about?a?manipulator?used?in?production?assembly?line?to?complete?assembly?work.?It?is?automatic?controlled?with?mufti-function,?mufti-degree?of?freedom?.Its?entire?structure?consists?of?the?implementing?agencies,?drive?system,?control?system?and?other?components.

Key words: Automatic assembly ，Manipulator ，Air pressure drive ，Structural design

摘要II

ABSTRACTIII

第一章绪论1

1.1 自动装配机的概况1

1.1.1 自动装配机的定义1

1.1.2 自动装配机的组成1

1.1.3 自动装配机的传动结构1

1.1.4 自动装配机的控制系统2

1.1.5 自动装配机的适用性2

1.2. 机械手的发展趋势2

1.3 课题研究的目的及要求4

1.4 课题背景4

第二章总体方案设计与论证6

2.1 机械手的概况6

2.1.1 机械手的概述及分类6

2.1.2 机械手的组成结构7

2.2设计背景9

2.3机械手的坐标型式与自由度10

2.4机械手的主要参数10

2.5驱动方式和传动方式的选择11

2.5.1驱动方式的选择11

2.5.2传动方式的选择11

2.6各个自由度的实现12

2.6.1腕部纵向运动12

2.6.2手臂伸缩运动12

2.6.3底座升降运动12

第三章装配夹具的结构设计13

3.1 定位原理13

3.2 确定定位方式14

3.3 夹紧机构14

3.4 确定总体结构和尺寸15

第四章 1#机械手的结构设计18

4.1 路径规划18

4.2 手部结构设计18

4.2.1 手指的形状和分类18

4.2.2设计时考虑的几个问题19

4.2.3 手部夹紧气缸的设计20

4.3 手臂结构设计23

4.3.1 手臂伸缩结构设计23

4.3.2 手臂伸缩驱动力的计算23

4.3.3 手臂伸缩气缸的设计25

4.4 升降缸结构设计27

4.4.1 升降缸结构设计27

4.4.2 升降缸驱动力的计算27

4.4.3 升降气缸的设计28

第5章 2#机械手的结构设计30

5.1 路径规划30

5.2 手部结构设计31

5.2.1 手指的形状31

5.2.2 手部夹紧气缸的设计31

5.3各气缸的设计32

第六章总结33

致谢34

参考文献35

第一章绪论

1.1 自动装配机的概况

1.1.1 自动装配机的定义

装配是指将产品的若干个零部件通过紧配、卡扣、螺纹连接、粘合、铆合、焊接等方式组合到一起得到符合预定的尺寸精度及功能的成品（半成品）。由人工处理（接触、整理、抓取、移动、放置、施力等）每一个零部件而实现的装配，严格的讲，只能称为人工装配。不需要由人工处理（接触、整理、抓取、移动、放置等）零部件而完成的装配，可称为自动装配。介于两者之间的为半自动装配。

1.1.2 自动装配机的组成

1. 零部件定向排列、输送、擒纵系统

将杂乱无章的零部件按便于机器自动处理的空间方位自动定向排列，随后顺利输送到后续的擒纵机构，为后续的机械手的抓取做准备。

2. 抓取-移位-放置机构

将由擒纵机构定点定位好的零（部件）抓住或用真空吸住，随后移动至另一位置（通常为装配工作位置）。

3. 装配工作机构

指用来完成装配工作主动作的机构，如将工件压入、夹合、螺联、卡人、粘合、焊接、铆合、粘合、焊接于上一零部件。

4.检测机构

用来对上一步装配好的部件或机器上一步工作成果进行检测，如缺零件检测、尺寸检测、缺损检测、功能检测、清料检测。

5. 工件的取出机构

用来将装配好的合格部件、不合格部件从机器上分类取出的机构。

1.1.3 自动装配机的传动结构

1) 按被装配工件在机器中的流动时间连贯性来分，有间隙运动式装配机和连续运动式装配机。

2）按装配机中工作位置数量来分，有单工位装配机和多工位装配机。

3）按装配机中工件的传动轨迹来分，有圆形工作台式装配机和环形工作台式装配机。

1.1.4 自动装配机的控制系统

通常采用PLC控制，PLC要接收各种信号的输入，向各执行机构发出指令。机器中配备多种传感器等信号采集器来监视机器中每一执行机构的运行情况，经判断后发出下一步的执行指令。人机界面用来显示机器的运行情况、运行记录，以及用来由操作者向机器发指令。

1.1.5 自动装配机的适用性

近年来,随着中国经济的发展,更多的企业出现劳资纠纷及一线员工不好管理的问题频频发生,更多的企业都在选择自动化机械装配,如同富士康在近来三年内要增加100万台机器人来解决员工问题。当然根据行业的不同,自动装配机的应用也自然不同。自动装配机根据行业的不同可分为以下几种：

1 电子电气类轻触开关装配机,继电器自动装配机,复位健装自动装配机,变压器自动装配机等

2 五金类脚轮自动装配机,轴承自动装配机,玩具自动装配机,齿轮自动装配机,牙箱自动装配机等

自动装配机还应用到家电,汽车行业,总而言之,自动装配机将是工厂工业化的一种趋势。

1.2. 机械手的发展趋势

国外机械手领域发展近几年有如下几个趋势:

(1)工业机械手性能不断提高(高速度、高精度、高可靠性、便于操作和维修)，而单机价格不断下降，平均单机价格从91年的10.3万美元降至97年的65万美元。

(2)机械结构向模块化、可重构化发展。例如关节模块中的伺服电机、减速机、检测系统三位一体化:由关节模块、连杆模块用重组方式构造机械手整机;国外已有模块化装配机械手产品问市。

(3)工业机械手控制系统向基于PC机的开放型控制器方向发展，便于标准化、网络化;器件集成度提高，控制柜日见小巧，且采用模块化结构:大大提高了系统的可靠性、易操作性和可维修性。

(4)机械手中的传感器作用日益重要，除采用传统的位置、速度、加速度等传感器外，装配、焊接机械手还应用了视觉、力觉等传感器，而遥控机械手则采用视觉、声觉、力觉、触觉等多传感器的融合技术来进行环境建模及决策控制;多传感器融合配置技术在产品化系统中已有成熟应用。

(5)虚拟现实技术在机械手中的作用已从仿真、预演发展到用于过程控制，如使遥控机械手操作者产生置身于远端作业环境中的感觉来操纵机械手。

(6)当代遥控机械手系统的发展特点不是追求全自治系统，而是致力于操作者与机械手的人机交互控制，即遥控加局部自主系统构成完整的监控遥控操作系统，使智能机械手走出实验室进入实用化阶段。美国发射到火星上的“索杰纳”机械手就是这种系统成功应用的最著名实例。

(7)机械手化机械开始兴起。从94年美国开发出“虚拟轴机床”以来，这种新型装置已成为国际研究的热点之一，纷纷探索开拓其实际应用的领域。

我国的工业机械手从80年代“七五”科技攻关开始起步，在国家的支持下，通过“七五”、“八五”科技攻关，目前己基本掌握了机械手操作机的设计制造技术、控制系统硬件和软件设计技术、运动学和轨迹规划技术，生产了部分机械手关键元器件，开发出喷漆、弧焊、点焊、装配、搬运等机械手;其中有130多台套喷漆机械手在二十余家企业的近30条自动喷漆生产线(站)上获得规模应用，弧焊机械手己应用在汽车制造厂的焊装线上。但总的来看，我国的工业机械手技术及其工程应用的水平和国外比还有一定的距离，如:可靠性低于国外产品；机械手应用工程起步较晚，应用领域窄，生产线系统技术与国外比有差距;在应用规模上，我国己安装的国产工业机械手约200台，约占全球已安装台数的万分之四。以上原因主要是没有形成机械手产业，当前我国的机械手生产都是应用户的要求，“一客户，一次重新设计”，品种规格多、批量小、零部件通用化程度低、供货周期长、成本也不低，而且质量、可靠性不稳定。因此迫切需要解决产业化前期的关键技术，对产品进行全面规划，搞好系列化、通用化、模块化设计，积极推进产业化进程.我国的智能机械手和特种机械手在“863”计划的支持下，也取得了不少成果。其中最为突出的是水下机械手，6000m水下无缆机械手的成果居世界领先水平，还开发出直接遥控机械手、双臂协调控制机械手、爬壁机械手、管道机械手等机种:在机械手视觉、力觉、触觉、声觉等基础技术的开发应用上开展了不少工作，有了一定的发展基础。但是在多传感器信息融合控制技术、遥控加局部自主系统遥控机械手、智能装配机械手、机械手化机械等的开发应用方面则刚刚起步，与国外先进水平差距较大，需要在原有成绩的基础上，有重点地系统攻关，才能形成系统配套可供实用的技术和产品，以期在“十五”后期立于世界先进行列之中。

1.3 课题研究的目的及要求

主要任务：

2）明确本题目的设计参数，技术条件，根据设计任务完成自动装配系统方案的拟定，绘制全套自动装配夹具和机器人的机械零件图、装配图；

3）完成毕业设计说明书。

1.4 课题背景

装配过程是机械制造过程中必不可少的环节。人工操作的装配是一个劳动密集型的过程，生产率是工人执行某一具体操作所花费时间的函数，其劳动量在产品制造总劳动量中占有相当高的比例。随着先进制造技术的应用，制造零件劳动量的下降速度比装配劳动量下降速度快得多，如果仍旧采用人工装配的方式，该比值还会提高。据有关资料统计分析，一些典型产品的装配时间占总生产时间的53%左右，是花费最多的生产过程，因此提高装配效率是制造工业中急需解决的关键问题之一。

自动化装配具备如下优点。

1. 装配效率高，产品生产成本下降。尤其是在当前机械加工自动化程度不断得到提高的情况下，装配效率的提高对产品生产效率的提高具有更加重要的意义。

2 .自动装配过程一般在流水线上进行，采用各种机械化装置来完成劳动量最大和最繁重的工作，大大降低了工人的劳动强度。

3. 不会因工人疲劳、疏忽、情绪、技术不熟练等因素的影响而造成产品质量缺陷或不稳定。

4 .自动化装配所占用的生产面积比手工装配完成同样生产任务的工作面积要小得多。

5 .在电子、化学、宇航、国防等行业中，许多装配操作需要特殊环境，人类难以进人或非常危险，只有自动化装配才能保障生产安全。

随着科学技术的发展和进步，在机械制造业，CNC、FMC,FMS的出现逐步取代了传统的制造技术，它们不仅具备高度自动化的加工能力，而且具有对加工对象的灵活性。如果只有加工技术的现代化，没有装配技术的自动化，FMS就成了自动化孤岛。装配自动化的意义还在于它是CIMS的重要组成部分。

第二章总体方案设计与论证

在科学技术突飞猛进的今天，装配线机械手的设计思想主要是通过对以前及现有的最具有代表性的装配线机械手进行分析研究，吸收它们的优点，将各个优点结合起来，将不同结构进行组合变化，使之达到较理想的方案。从而达到较好的运动精度和工作稳定性，进而使之在市场上更具有竞争力。本次设计就是在分析、研究以往优秀的装配线机械手的基础上加以改进而成的。

2.1 机械手的概况

2.1.1 机械手的概述及分类

机械手是模仿着人手的部分动作，按给定程序、轨迹和要求实现自动抓取、搬运或操作的自动机械装置。在工业生产中应用的机械手被称为“工业机械手”。生产中应用机械手可以提高生产的自动化水平和劳动生产率:可以减轻劳动强度、保证产品质量、实现安全生产;尤其在高温、高压、低温、低压、粉尘、易爆、有毒气体和放射性等恶劣的环境中，它代替人进行正常的工作，意义更为重大。因此，在机械加工、冲压、铸、锻、焊接、热处理、电镀、喷漆、装配以及轻工业、交通运输业等方面得到越来越广泛的引用.

机械手的结构形式开始比较简单，专用性较强，仅为某台机床的上下料装置，是附属于该机床的专用机械手。随着工业技术的发展，制成了能够独立的按程序控制实现重复操作，适用范围比较广的“程序控制通用机械手”，简称通用机械手。由于通用机械手能很快的改变工作程序，适应性较强，所以它在不断变换生产品种的中小批量生产中获得广泛的引用。机械手一般分为三类。第一类是不需要人工操作的通用机械手，它是一种独立的不附属于某一主机的装置。它可以根据任务的需要编制程序，以完成各项规定工作。它的特点是除具备普通机械的物理性能外，还具备通用机械、记忆智能的三元机械。第二类是需要人工操作的，称为操作机。它起源于原子、军事工业，先是通过操作机来完成特定的作业，后来发展到用无线电信号操作机械手来进行探测月球、火星等。第三类是专用机械手，主要附属于自动机床或自动线上，用于解决机床上下料和工件传送。这种机械手在国外称为“Mechanical Hand”，它是为主机服务的，由主机驱动，除少数外，工作程序一般是固定的，因此是专用的。本项目要求设计的机械手模型可归为第一类，即通用机械手。

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内容简介：: Journal of Manufacturing Systems Vol. 15/No. 4 1996 GAPP: A Generative Assembly Process Planner Luc Laperrire, Universit6 du Quebec a Trois-Rivieres, Trois-Rivibres, Quebec, Canada Hoda A. EIMaraghy, University of Windsor, Windsor, Ontario, Canada Abstract This paper presents results of exhaustive research in automated assembly planning. A generative assembly process planner (GAPP) has been developed that takes as input a solid model of the product to be assembled and out- puts its feasible assembly sequences. Once the product has been modeled as a solid using a commercial solid modeler, the resulting solid models boundary representation (B-Rep) file is interpreted by the GAPP to generate mating informa- tion among parts in the form of a relational graph. This graph becomes the input of a search graph process whose con- strained expansion reveals all feasible assembly sequences from a geometric, stability, and accessibility point of view. The relative goodness of different feasible assembly sequences can be determined using pertinent criteria such as the number of reorientations involved or the clustering of similar assembly operations into successive ones. The expansion engine is very flexible and enables many different types of assembly problems to be handled uniformly, for example, finding disassembly repair sequences not requir- ing complete product disassembly or generating assembly sequences that force the building of predefined subassem- blies. Examples with real industrial products are provided to illustrate the potential of using this tool. Keywords: Assembly, Disassembly, Assembly Sequence, Assembly Planning Introduction Shorter product lifecycles, smaller batches, and just-in-time production have drastically reduced the time spent for assembly planning activities. This has called for the development of efficient software tools to assist the planner. Among the tasks the planner has to perform, the choice of an appropriate assembly sequence is a cru- cial one because of its economical impact. Earlier research in assembly planning focused on methods for automatically generating the numerous assembly sequences of a given product, as well as investigating potential compact assembly sequence representation schemes./-s Most of the reasoning was left to be done a posteriori by the human planner, for example elim- inating unfeasible assembly sequences with respect to some constraints and/or evaluating and selecting a few good feasible ones based on some cost criteria. Today there are many assembly planners that can automatically generate all possible assembly sequences of a product and discard all those that are unfeasible with respect to some constraints. 6s Current research focuses on the formalization of such constraints used to reduce assembly sequence count and on the formalization of different relevant cost criteria that can be used to select better assem- bly sequences among all feasible ones. 912 This paper describes the developed integrated approach to assembly planning, where generation, elimination, and evaluation of assembly sequences are all performed in a single process. The resulting software tool, called the generative assembly process planner (GAPP) is implemented in C+ and runs the OSF/MOTIF window interface on a Silicon Graphics workstation. Figure 1 shows a block diagram of the software. A screen dump of the window interface is also presented in Figure 18 at the end of the paper. The next section of the paper describes the prod- ucts graph model, which is generated automatically from the products solid model and is used as input to the assembly sequence enumeration engine briefly described in the third section. Next are outlined some constraints used to eliminate unfeasible assembly sequences and, as a result, reduce search space. The fifth section briefly describes the role of cost criteria. Practical applications are presented next, and the last section discusses accomplishments. Product Graph Model General Description Assembly operations can be viewed as establish- ing contacts and attachments among parts or sub- assemblies using collision-free paths. One central element in assembly planning is therefore the knowl- edge of mating information among parts. This kind of information lends itself to a binary relation on the set of parts that can be more appropriately represent- ed in the form of a graph model, where vertices are parts and edges are mating relations among them. 13 282 Journal o/ManuJacturing Systems Vol. l 5/40.4 1996 User input Products solid model I1 Feasibil,ly constraints (on or o I I Eva,oat,on cr,teria,% ofre,at,ve,mpooce, Search method . I . 1 . 1 . Boundary representation file Products graph model I I Assembly sequences enumeration engine I . I . S,II . Outputs Linear sequence of (optimal) assembly operations I moved subassembly I fixed subassembly directions of insertion L . . . J Figure 1 Block Diagram of the GAPP Figure 2 shows a simple four-blocks product along with its graph model. As can be seen, three types of mating relations are possible. They are defined as follows: 1. Two components have a contact relationship between them if they are in constant physical contact in the assembled product. 2. Two components have a blocking relationship between them if they are not in constant physi- cal contact in the product and if a linear transla- tion of one of them in one of the orthogonal directions results in a collision with the other. 3. Two components have a free relationship between them if they are not in constant physi- cal contact in the product and if a linear transla- tion of one of them in any of the orthogonal directions does not result in a collision with the other. Figure 3 shows an example of two parts having a free relationship between them. Note that although blocking and free mating rela- tions do not involve contact, they imply that colli- sion-free paths with respect to the chosen coordinate system may or may not exist. These noncontact mat- ing relations play an important role in determining feasible assembly sequences from a geometric inter- ference point of view. Clearly, the above definitions are such that the graph model of any product is always a complete graph (that is, every part has at least one of the above three mating relations with every other part). Generating the graph model is therefore a geometric reasoning process that mainly consists of identifying which parts have which types of mating relations with 283 Journal of Manufacturing Systems Vol. 15/No. 4 1996 Z x J- Block a Block b i Block c Contact Blocking - - Block d Figure 2 Four Blocks Product Along with Its Graph Model Block a Z x.L, Plane surface P of block a Plane surface of block b Pz Figure 4 Identification of First Contact Between Surfaces of Two Blocks Z xft , Block b Free . Figure 3 Two Blocks Having a Free Relationship Between Them which other parts. For a product with n components, n (n - 1) / 2 mating relations must be identified. Automatic Generation of Graph Model from Solid Model A method has been developed that builds the inter- nal computer representation of the graph model auto- matically from the information contained in the B-Rep file resulting from the products solid model, using the ICEM/DDN commercial hybrid solid modeler. The method mainly consists of analyzing the parts surface information contained in the B-Rep file. In particular, mathematical tests involving surface pairs each on a different part help determine whether the parts to which these surfaces belong are in contact, blocked, or free. Figures 4 and 5 show an example for the identi- fication of the contact mating relation between blocks a and b in Figure 2, from an analysis of their mat- ing surfaces definition contained in the B-Rep file. In Figure 4, n and n2 are the unit normal vectors of the bold surfaces of blocks a and b, respec- tively. The distance between the two blocks is denot- ed by d. Pl and P2 are points on the surfaces. Assume the limits of the planes of blocks a and b, with respect to the chosen Cartesian system, are (Xmi,1, Xmaxl, Yminl, Ymaxl, Zminl, Zmaxl) and (Xmi.2 , Xmax2 , Ymin2. Ym,x2, Zmin2, Zm2), respectively. For identification of the contact between these two surfaces, three condi- tions must be satisfied: nl n2 = nix * n2 + nly * n2y + nl * n2z .I- Figure 5 Identification of Another Contact Between Surfaces of Two Blocks a_l p2xn l=0 Inl I where P,P2 = (Pz - P,.) i + (Pzy - Ply) j + (P2z - Pu) k and 2 2 In, (2) (3) (4) Xminl Pz Xm,l andyminl P2y Ymaxl or Xmin2 Plx Xmax2 and Ymi.2 Ply Ymax2 (5) All the information required for the above geo- metric reasoning is directly extracted or computed from the B-Rep file. In Figure 5, nl and nz are the unit normal vectors of the bold surfaces of blocks a and b, respec- tively. Assume the limits of the cylinders of blocks a and b, with respect to the chosen Cartesian system, are (Xminl , Xmaxl , Ymlnl, Ym.l, Zmi.l, Zm,x0 and (Xmin2, Xmax2, Ymin2, Y.,.2, Zraln2, Zmax2), respectively. For the identification of the contact between these two surfaces, three other conditions must be satisfied: 284 Journal of Manufacturing Systems Vol. 15/No. 4 1996 , result i ,loo,.,ooo 1=,ooo,ooo 1 FM(el,b)= 1 l oo|n|ooo OlllJ lll 1 011 Figure 6 Freedom Matrices Associated with a Relation Between Two Parts nl nz = 0 (6) Xmin2 Xminl Xmax2 and Xmin2 ( Xmaxl Xmax2 Ymin2 Yminl Ymax2 and Ymin2 Ymaxl Ymax2 Zmi.1 Z ax2 (7) diameter 1 = diameter 2 (8) The same conditions used to determine if surfaces are in contact are also used for blocking and free mating relations identification. For example, a blocking between two planar surfaces requires con- ditions (1) and (5) to be satisfied, but not condition (2), whereas a free relationship between the same type of surfaces only requires condition (1) to be sat- isfied, but not conditions (2) and (5). Building Freedom Matrices A part in 3-D space has a maximum of six degrees of freedom: three translations and three rotations. In assembly planning, it is more appropriate to talk about half degrees of freedom by further considering the actual direction (+ or -) of a translation or rota- tion) 4 This gives a total of 12 half degrees of free- dom for the same part: (Tx, Tx., Ty+, Ty., T+, T., Rx+, Rx., R_, Ry_, R+, R:_). The letters T and R stand for translation and rotation, respectively. Once a contact, blocking, or free relationship has been identified (conditions satisfied) between any pairof surfaces between two parts, the tmderlying half degrees of freedom this relation provides to the parts implied are represented in an appropriate 3 x 4 matrix, called the freedom matrix, where there exists a correspondence between each entry in the matrix and the half degree of freedom it represents: Tx Rx+R- Tz+L-Rz+Rz-J Freedom matrices are built automatically for every contact surface pair. A freedom matrix func- tion, FM (argl, arg2), has been developed where argl is a mating relation and arg2 is a part. The function returns a freedom matrix representing this parts half degrees of freedom provided by that rela- tion. Every half degree of freedom that is available or not is represented by the entry 1 or 0 in the matrix, respectively. Such information is used for computing geometric interference in disassembly operations. Figure 6 shows a simple example or freedom matrix computation, using the two contact relations identified in Figures 4 and 5. The freedom matrices associated with both planar contact (Figure 4) and cylindrical contact (Figure 5) are shown. To obtain the resulting freedom matrix at the part level, all that is required is to perform a positionwise logical and between the entries of each of the surface- level freedom matrices previously generated. Limits of the Model For now, every part of the product to be assem- bled must be modeled using block, cylinder, cone, sphere, revolution, and slab (sweep) primitives and their Boolean combination. Although the solid mod- eler used enables complex objects to be modeled- for example, using air-tight B-spline envelopes from which a solid can be computed-the format of such solids in the B-Rep file is complex and its interpre- tation using some condition(s) to identify mating relations has not been formalized yet. Another limitation lies in the automatic computa- tion of the rotational part of freedom matrices. For now, only the translational part is generated auto- matically from the B-Rep file analysis using the concepts described so far. The rotational part, if nec- essary, must be supplied manually. Complete automation of the graph model generation is there- fore limited to this wide and representative category of products whose parts and subassemblies can be assembled from single translations (this is also a fundamental design-for-assembly rule). Finally, the GAPP can process products whose parts and subassemblies can be assembled in direc- tions complying with those of the chosen orthogonal coordinate system. Because the B-Rep file explicit- ly represents surface normals using standard 4 x 4 homogeneous matrices, it is possible to identify 285 Journal of Manufacturing Systems Vol. 15/No. 4 1996 assembly directions other than those aligned with the coordinate system. Extending the approach for such cases has not been investigated. Assembly Sequences Enumeration After having derived from the solid model a more suitable assembly representation scheme in the form of a graph model, an algorithmic engine is next used to exploit this model and extract assembly sequences out of it. Basic Enumeration Principle Homem de Mello and Sanderson have developed a mathematically robust and systematic assembly sequence enumeration engine? The process starts by putting the products graph model as the root node of a search graph. Search graph expansion is accom- plished through the computation of the cutsets in the root node (a cutset is a set of edges in the graph, the removal of which increases the number of graph components by onemS). To every cutset there corre- sponds a new node in the layer underneath. Any new node has the graph representation of its parent node minus the edges in the cutsets from which it was generated. Then the cutsets in the graph representa- tions of the newly generated nodes are computed, yielding another layer, and so on. This process stops when a node has been generated where all edges have been removed. Note that this disassembly approach is close to that used by the human planner. In the GAPP, assembly sequences generated this way are represented compactly in a graph of assembly states (Figure 7). 2 Every path from top to bottom rep- resents a disassembly sequence. Going from the bot- tom up gives the corresponding assembly sequence. Figure 7 Unconstrained Graph of Assembly States of Four Blocks in Figure 2 of the root node are inherited by each new child node. Some edges of the inherited cutsets, which are not part of the new child node, must first be deleted. For example, child5 was obtained from cutset e, e3, es. The edges in this cutset must not be part of any cutsets of child5. They are, therefore, deleted from the inherited set, yielding the new cutsets: 1 - ea, 2 - e, 3 - e4), 4- e4, 5 - , and 6- e2, e4. Updating the Cutsets In reality, one cannot afford to compute a new set of cutsets every time a new node is generated in the search graph because of the underlying combinator- ial complexity that this computation involvesJ 6 A method has been developed that ensures that only the set of cutsets in the root node of the graph of assembly states is ever generated. Any other cutset in any newly generated node is simply obtained by updating the set of cutsets of the root node. Figure 8 is used to describe the approach. After the six cutsets of the root node have been computed, six new states of the graph are generated. The six cutsets Out of this new list, the first and second, as well as the third and fourth, are combined because they both represent the same cutset. The fifth, which was removed from the root node to generate child5, is eliminated as it became empty. Therefore, the list becomes: 1 - e, 2 - e4, 3 - ea, e4. An algorithm is then used to check if the remain- ing sets of edges are indeed cutsets (that is, yielding 286 Journal Of 44anujbcturing Systems Vol. 15ANo. 4 1996 Child 1 Child 2 Child 3 Child 4 Child 5 Child 6 Cutsets of root node J e, e, e, e3, , , e, e, e, es, e, e, e, e, e, es Inherited by child 5 e, ez, e2, e3, es, e3, e, e, e, eE, e, e3, eE, e2, e, es Remove edges not in child 5 ez, eTJ, e, e, , e2, e, I Combine similar, remove empty , e, e2, 04 ( Eliminate non-cutset 1 , e,) Figure 8 Determination of Cutsets of New Child Node by Analyzing Ones Inherited from Its Parent exactly one more subassembly in the child state than in the parent state). Applying this algorithm for the above sets of edges eliminates the last one. The cut- sets of child5 are then: 1 - e, 2 - e4. This process is repeated for every new child node to determine their cutsets by means of a simple analysis of the ones inherited from their parent. Note that only contact-type edges are considered at this stage in the cutsets computations; that is, inclusion of other relation types (like e6 in this example) would not help identify more potential subassemblies and would simply decrease the computational efficiency. Blocking and free relations are considered only when geometric interference issues are addressed. .L x 1 Blocka Cutset Block c Blockd FM(e, b) FM(e, b) FM(e2, b) Result ollo V l Fl 000 0=0 /oooo/q,oo/n/,o ooo / LOl 111 LlOllj LlOll OOllj Figure 9 Cutset in Graph Model of Four Blocks and Corresponding Freedom Matrices Using Feasibility Constraints The engine described earlier does not consider the physical feasibility of the disassembly operations associated with each cutset. Three feasibility con- straints are used to ensure that the generated assem- bly sequences are indeed feasible. They are: 1. Geometric interference constraints, 2. Stability constraints, and 3. Accessibility constraints These can be turned on or off by the user for com- parison purposes (see Figure 18). Geometric Interference Figure 9 illustrates how freedom matrices are used to compute automatically the geometric feasi- bility of separating two subassemblies in a disas- sembly operation. It is desired to determine if an operation that splits the four blocks into the two sub- assemblies b and a, c, d is geometrically feasi- ble. The cutset e, ez, e6 is associated with this operation (note that all types of relations must be considered here in the cutsets). The freedom matri- ces of block b relative to the relations in this cut- set, also shown in Figure 9, are used to compute the geometric feasibility of this operation. In particular, by performing a positionwise logical and between the binary entries of the freedom matrices, the resulting matrix contains all zeros in the first two columns associated with translations. The interpretation is that this operation is not geometrical- ly feasible because there does not exist a disassembly direction along which part b can be removed. 287 Journal of Manufacturing Systems gol. 15/No. 4 1996 Stability Another important constraint during assembly execution is stability. Among all possible assembly sequences, many must be discarded due to stability problems. Because the four blocks in Figure 2 are not very interesting from a stability point of view, consider instead the flashlight in Figure 10. Note that although the represented disassembly operation is geometrically feasible, it clearly results in a high- ly unstable configuration. Following is a brief description of the stability model used by the GAPP. Stability is computed by first finding a subgraph of the graph model called the stability-directed subgraph. It is build by a progressive graph-grow- ing procedure using an algorithm. The basic con- struction principle is to find, for every component in the original graph model, which other component stabilizes (or secures) it, using which relations. The first step is to identify a part considered fixed (or grounded) in the complete product (usually the one with the lower z-coordinate assuming the z-axis is pointing upward). This part is put in the set P of processed components. Then the algorithm starts and picks another part not yet in P. It checks if this component is secured by any relation with the parts in P. If so, the relation(s) is (are) added to the set A of arcs. The arc(s) point(s) from the secured component to the securing component. As an example, in Figure 11 the component head was chosen as the initially fixed (or ground- ed) component and put in set P. Assume the part reflector was then chosen by the algorithm. Because this part is implicitly attached to the head by a snap fit, this part is in turn added to P and the relation between the reflector and head becomes an arc in the stability subgraph. This arc points from the Cap =- Spring Body Flashlights graph model I _ battery2 battery1 Reflector J- H Bulb r., . _- Lens Head Figure 10 Geometrically Feasible Disassembly Operation that Can Be Applied to Completely Assembled Flashlight reflector to the head and is added to the set A. Assume the cap is chosen next. This part is not secured by any of the parts in P at this stage. Another part is then chosen, say, the bulb. This part is secured by an implicit screwing to the reflector, already in P. The bulb is then added in turn to P and the arc pointing from the bulb to the reflector is added to A. The process continues until all parts have been successfully processed. A much more detailed description of the stability subgraph and the algorithm used to build it can be found in Lavoie and Laperri6re. v Once the stability subgraph D = P, A has been constructed, stability can be computed by the fol- lowing simple rule: if a cutset breaks at least one outgoing edge of the fixed subassembly or more than one outgoing edge of the moved subassembly, Cutset associated with Figure 10 X Cutset Moved subassembly fixed Flashlights stability subgraph Fixed subassembly Figure 11 Using Stability Subgraph to Estimate Disassembly Operations Stability 288 Journal qf Manufacturing Systems Vol. 15/No. 4 1996 then the corresponding disassembly operation is considered unfeasibleJ 7 Going back to Figure 11, it can be seen that the cutset under investigation breaks the flashlight into the following two subassemblies: cap spring body and head lens reflector bulb batteryl battery2. The former is the moved subassembly (grasped), and the latter is the fixed subassembly (because it contains the head initially chosen as grounded). This cutset breaks one outgoing edge of the moved sub- assembly: body head. Thus the rule above is not violated so far. But it is also seen from the figure that two outgoing edges of the fixed subassembly are broken by the cutset: batteryl body and bat- tery2 body. Thus by taking away the body, the bat- teries become unsecured and fall instantaneously (unless special fixtures are supplied, which is not considered for now). Experiments with this stability model have shown surprising results on how stringent the stability con- straint can sometimes be. For the flashlight product in Figure 1 O, by turning on only the geometric inter- ference constraint, there were 331 nodes expanded in the graph of assembly states, giving 12 896 paths (assembly sequences). By adding the stability con- straint in the expansion process, 17 nodes with 14 paths were generated (Figure 12). This drastic reduction is explained by the fact that for this prod- uct the stability constraint leads to the elimination of many nodes in the higher levels of the search graph, close to the root node. Accessibility Consider the removal of part a in Figure 13. The restricted access of a tool to hold and remove it makes the corresponding disassembly operation very difficult or impossible to execute. Such a constraint is used during graph of assembly states expansion to eliminate those state transitions that imply unfeasible operations with respect to accessibility. The notion of accessibility is implemented using models and con- cepts whose preliminary description can be found in Sere, Laperrire, and MascleJ 8 Search for Optimal Solutions In spite of considering all the above constraints, the graph of assembly states usually contains more than one feasible solution. To make a choice, one must then reason on pertinent criteria to determine the relative goodness of the feasible alternatives. Up to now, four such criteria have been used in the GAPP. They are: 1. Reorientations 2. Parallelism 3. Stability 4. Clustering Note that stability appears at two levels: as a con- straint to eliminate unstable states during graph expansion, and as a criterion to evaluate the relative stability of those states that have successfully passed the stability constraint test (using the stability sub- graph described earlier). ltiiiiiiiii iiiiiii l - ,.:. . b L% %. % % %.%,%,%.% Figure 12 Graph of Assembly States of Flashlight Considering Both Geometric Interference and Stability Figure 13 Typical Example of Inaccessible Component (in this case, a) in a Geometrically Feasible and Stable Disassembly Operation 289 Journal of Manufacturing Systems Vol. 15/No. 4 1996 By triggering one criterion on and leaving all three others off prior to search graph expansion, one can generate the optimal assembly sequence with respect to this criterion. By further providing relative importance (in terms of a percentage) to each criteri- on, optimal solutions with respect to all four criteria and their relative importance can also be obtained (see the window interface in Figure 18, where each criterions weight is represented as a slider from 0 to 100). Typically, this is useful for comparing different solutions in concurrent engineering. 13 Practical Examples Generation of Repair Disassembly Sequences of an Electrical Switch Some components within a product may be expected to fail during service and be replaced peri- odically. The disassembly sequences allowing access to these components generally do not require total product disassembly. Consider, for example, the insulators of the elec- trical switch in Figure 14, shown along with its graph model in Figure 15. The goal is to partly dis- assemble this product to get to the insulators and replace them. To generate a repair plan, all that is required is the identification of the contact relations of the graph model that should not be broken in the repair disassembly plan. In this particular example, these relations could be: ( central_body, switchcase ) ( terminal_blocks, switch_case ) ( spark_covers, switch_case ) ( sparkcovers, terminal_blocks ) ( actuator, central_body ) These relations are not part of any cutset used in the search process. This ensures that the generated disas- sembly plan will preserve the above relations and avoid total disassembly. A first disassembly sequence generated for this example is presented below: 1. remove (screws)from (switch_case central_body spark covers insulators terminal_blocks actua- tor switch cover) along z+ 2. remove (switchcover) from (switch_case cen- tral_body spark_covers insulators terminal_blocks actuator) along z+ switch_cover screws (4) insulators (3) terminalblocks I actuator spark_covers (3) centralbody switch_case Figure 14 Exploded View of Simplified Electrical Switch Assembly 1 - switch_case 2 - central_body 3 - spark_covers 4 - insulators 5 - terminal blocks 6 - actuator 7 - switch cover 8 - screws- Figure 15 Graph Model of Electrical Switch in Figure 14 3. remove (insulators)from (switch_case cen- tral_body sparkcovers terminal_blocks actua- to O along z+ It has been generated using only the geometric interference constraint turned on. Breadth-first was the chosen search mode. All cost criteria were turned off (sliders to zero). Note that the spark_covers were left in place, as required by the specification of the above relations to be preserved. Another test was performed with the same para- meters, except that the accessibility constraint was 290 Journal qf Manufacturing Systems Vol. 15/No. 4 1996 also turned on. No solution was returned by the GAPP. The reason is that the spark_covers were rec- ognized to interfere with the final removal of the insulators. Because the spark_covers were at the same time specified not to be disassembled in the preserved relation list above, no solution could be found. A more appropriate solution is shown below: 1. remove (screws)from (switch_case central_body spark_covers insulators terminalblocks actua- tor switch_cover) along z+ 2. remove (switch_cover)from (switch_case cen- tral_body spark_covers insulators terminal_blocks actuator) along z+ 3. remove (spark_covers)from (switch_case cen- tral_body insulators terminalblocks actuator) along z+ 4. remove (insulators)from (switch_case cen- tral_body terminal_blocks actuator) along z+ Note that the sparkcovers have been removed to provide better access to the tool before removing the insulators. This new solution required the relation (spark_covers, switch_case) to be removed from the list of relations not to be broken during the expansion process. Depth-first search was used in this case. Another approach where only the part or sub- assembly to be replaced is specified instead of the relations not to be broken is being implemented. Generation of Assembly Sequences that Build Predefined Subassemblies Consider the air cylinder in Figure 16. A first assem- bly sequence generated by the GAPP is shown below: 1. fit (bearing_oring) (bearing) along z- 2. fit (bearing_oring bearing) (body) along z- 3.fit (piston_rod) (bearing_oring bearing body) along z- 4. fit (piston_oring) (piston) along z- 5. fit (piston_oring piston) (bearing_oring bearing body piston_rod) along z- 6. screw (pistonscrew) (bearing_oring bearing body piston_rod piston_oring piston) along z- 7. against (cover_oring cover) along z- 8. reorient (cover_oring cover) 180 degrees 9. against (cover._oring cover) (bearing_oring bearing body piston_rod piston_oring p i s - ton pistonscrew) along z- / beadng_oring bearing body IF piston_ring piston pistonscrew piston oring cover oring cover ,- cover screws (2) Figure 16 Exploded View of Air Cylinder 10. screw (cover_screws) (bearing_oring bearing body piston_rod piston_oring piston piston_screw cover_oring cover) along z- This solution was obtained using clustering as the only criterion turned on. This has led to the genera- tion of an assembly sequence where, as much as pos- sible, consecutive operations are of the same type (as determined by the operation name, such as fit, against, and so on, and neglecting reorientation operations, which are not considered during cluster- ing). However, in trying to do so, it can be seen that this solution does not build one inherent subassem- bly of that product, that is, the piston, piston_rod, piston_oring, piston_screw. Another solution is shown below where the input graph model was that of Figure 17: 1. against (piston) (piston_rod) along z- 2. against (cover_oring body) along z- 291 Journal of Manufacturing Systems Vol. 15/No. 4 1996 3. screw (piston_screw) (piston piston_rod) along z- 4. fit (piston_oring) (piston piston_rod piston_screw) along z- 5. fit (bearing_oring) (bearing) along z- 6. fit (bearing_oring bearing) (cover_oring body) along z- 7. fit (piston piston_rod piston_screw piston_oring) (cover_oring body bearing_oring bearing) along z- 8. against (cover) (cover_oring body bearing_ oring bearing piston piston_rod piston_screw piston_oring) along z- 9. screw (cover_screws) (cover_oring body bear- ing_oring bearing piston piston_rod piston_ screw piston_oring cover) along z- Note that this unconnected graph model encom- passes the inherent subassembly (one component of the graph) along with the subassembly bearing_oring bearing body cover_oring, for demonstration purposes. As a result, the solution returned builds the required subassemblies. On the other hand, assuming that each operation name requires a different tool, then this new solution requires one more tool change than the previous one. Conclusions This paper presented an approach for integrating assembly sequence generation, elimination, and evaluation. Compared to other works reported in the literature, the developed GAPP presents: an efficient method for computing the cutsets, a rather straight- forward method for computing geometric interfer- ence based on freedom matrices, and a new stability model for computing stability constraints, all embedded in a functional computer software that can be easily used to tackle different kinds of assem- bly problems. 2 - bearing 3 - body 4 - piston_ring 5 - piston 6 - piston_screw 7 - piston_oring 8 - cover_oring 9 - cover /r 1 n 10 - cover_screws kS) Figure 17 Unconnected Graph Model of Air Cylinder The product to be assembled is first described in a relational graph model. The data structures underly- ing this model are built from the products B-Rep file resulting from solid modeling. An important piece of information resulting from the B-Rep file analysis is the freedom matrix. The freedom matrix approach is explicit because it directly specifies which assembly directions are available. On the other hand, this approach is limited to assembly directions aligned with the chosen coordinate system. Although the approach works for a vast variety of mechanical products compatible with this limitation, it would be desirable to investigate how the generalization of the model to arbitrary directions could be implemented using the same basic approach. Once the graph model has been generated, Homem De Mello and Sandersons engine is used to find a sequence of mutually exclusive cutsets in the prod- ucts graph model and its subgraphs. From a purely mathematical point of view, the combinatorial com- plexity behind this computation when used with the expansion of graph of assembly states is nontrivial. 1 However, the computation of feasibility constraints, including geometric interference, stability, and acces- Figure 18 Screen Dump of GAPPs Window Interface 292 Journal of Manufacturing Systems Vol. 15/No. 4 1996 sibility, as the search graph is expanded greatly reduces this combinatorial complexity. Experience with the system has shown that search space reduc- tion is not always the same using the same constraint for different products. For example, the electrical switch in Figure 14 is highly geometrically con- strained by nature. Thus the geometric interference constraint leads to the most significant reduction for that product. For the flashlight in Figure 10, it is the stability constraint that leads to the most important reduction in the number of possible solutions. Many standard AI search modes are available for the GAPP: breadth-first, depth-first, best-first, and hill climbing. Hill climbing is not guaranteed to return optimal solutions. However, as this search method picks only the best node at each newly gen- erated level of the search graph and flushes any other node generated so far, it is an appropriate search method for products with larger number of parts. For a product whose graph model consists of n connected parts, this search method returns a good (but not necessarily optimal) solution in only n-1 steps, making the search almost instantaneous. References 1. A. Bourjault, Contribution une approche mthodologique de lassemblage automatisr: llaboration automatique des srquences oprra- toires, Th+se dltat, Universit6 de Besangon, Franche-Comtr, France (1984). 2. T.L. DeFazio and D.E. Whitney, Simplified Generation of All Mechanical Assembly Sequences, 1EEE Transactions on Robotics and Automation (vRA-3, n6, 1987), pp640-658. 3. L.S. Homem de Mello andA.C. Sanderson, A Correct and Complete Algorithm for the Generation of Mechanical Assembly Sequences, IEEE Transactions on Robotics and Automation (v7, n2, 1991 ), pp228-240. 4. M. Shpitalni, G. Elber, and E. Lenz, Automatic Assembly of Three Dimensional Structures via Connectivity Graphs, Annals of CI

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