{"defaultlang":"zh","titlegroup":{"articletitle":[{"lang":"zh","data":[{"name":"text","data":"可变胞并联机械臂样机的研制与误差分析"}]},{"lang":"en","data":[{"name":"text","data":"Development and error analysis of metamorphic parallel manipulators"}]}]},"contribgroup":{"author":[{"name":[{"lang":"zh","surname":"荣","givenname":"誉","namestyle":"eastern","prefix":""},{"lang":"en","surname":"RONG","givenname":"Yu","namestyle":"western","prefix":""}],"stringName":[],"aff":[{"rid":"aff1","text":"1"},{"rid":"aff2","text":"2"},{"rid":"aff3","text":"3"}],"role":["corresp","first-author"],"corresp":[{"rid":"cor1","lang":"en","text":"RONG Yu, E-mail:lixiangcg@126.com","data":[{"name":"text","data":"RONG Yu, E-mail:lixiangcg@126.com"}]}],"bio":[{"lang":"zh","text":["荣誉(1981-), 男, 吉林扶余人, 博士, 副教授, 2015年于燕山大学获得博士学位, 主要从事性能可变工业机械臂、变胞变尺度机构应用方面研究。E-mail:lixiangcg@126.com"],"graphic":[],"data":[[{"name":"bold","data":[{"name":"text","data":"荣誉"}]},{"name":"text","data":"(1981-), 男, 吉林扶余人, 博士, 副教授, 2015年于燕山大学获得博士学位, 主要从事性能可变工业机械臂、变胞变尺度机构应用方面研究。E-mail:"},{"name":"text","data":"lixiangcg@126.com"}]]}],"email":"lixiangcg@126.com","deceased":false},{"name":[{"lang":"zh","surname":"韩","givenname":"勇","namestyle":"eastern","prefix":""},{"lang":"en","surname":"HAN","givenname":"Yong","namestyle":"western","prefix":""}],"stringName":[],"aff":[{"rid":"aff2","text":"2"}],"role":[],"bio":[{"lang":"zh","text":["韩勇(1979-), 男, 河北秦皇岛人, 学士, 工程师, 主要从事工业机器人应用方面的研究。E-mail:hanyong@dicastal.com"],"graphic":[],"data":[[{"name":"bold","data":[{"name":"text","data":"韩勇"}]},{"name":"text","data":"(1979-), 男, 河北秦皇岛人, 学士, 工程师, 主要从事工业机器人应用方面的研究。E-mail:"},{"name":"text","data":"hanyong@dicastal.com"}]]}],"email":"hanyong@dicastal.com","deceased":false},{"name":[{"lang":"zh","surname":"刘","givenname":"双勇","namestyle":"eastern","prefix":""},{"lang":"en","surname":"LIU","givenname":"Shuang-yong","namestyle":"western","prefix":""}],"stringName":[],"aff":[{"rid":"aff2","text":"2"}],"role":[],"deceased":false},{"name":[{"lang":"zh","surname":"曲","givenname":"梦可","namestyle":"eastern","prefix":""},{"lang":"en","surname":"QU","givenname":"Meng-ke","namestyle":"western","prefix":""}],"stringName":[],"aff":[{"rid":"aff1","text":"1"},{"rid":"aff3","text":"3"}],"role":[],"deceased":false}],"aff":[{"id":"aff1","intro":[{"lang":"zh","label":"1","text":"河北科技师范学院 机电工程学院, 河北 秦皇岛 066004","data":[{"name":"text","data":"河北科技师范学院 机电工程学院, 河北 秦皇岛 066004"}]},{"lang":"en","label":"1","text":"College of mechanical and electrical engineering, Hebei Normal University of Science and Technology, Qinhuangdao 066004, China","data":[{"name":"text","data":"College of mechanical and electrical engineering, Hebei Normal University of Science and Technology, Qinhuangdao 066004, China"}]}]},{"id":"aff2","intro":[{"lang":"zh","label":"2","text":"中信戴卡股份有限公司 装备研制中心, 河北 秦皇岛 066004","data":[{"name":"text","data":"中信戴卡股份有限公司 装备研制中心, 河北 秦皇岛 066004"}]},{"lang":"en","label":"2","text":"Equipment Development Center, CiTiC Dicastal Wheel Manufacturing Co., Ltd, Qinhuangdao 066004, China","data":[{"name":"text","data":"Equipment Development Center, CiTiC Dicastal Wheel Manufacturing Co., Ltd, Qinhuangdao 066004, China"}]}]},{"id":"aff3","intro":[{"lang":"zh","label":"3","text":"燕山大学 河北省并联机器人与机电系统实验室, 河北 秦皇岛 066004","data":[{"name":"text","data":"燕山大学 河北省并联机器人与机电系统实验室, 河北 秦皇岛 066004"}]},{"lang":"en","label":"3","text":"Parallel Robot and Mechatronic System Laboratory of Hebei Province, Yanshan University, Qinhuangdao 066004, China","data":[{"name":"text","data":"Parallel Robot and Mechatronic System Laboratory of Hebei Province, Yanshan University, Qinhuangdao 066004, China"}]}]}]},"abstracts":[{"lang":"zh","data":[{"name":"p","data":[{"name":"text","data":"提出了一种通过驱动副锁定组合实现变胞的超冗余并联机械臂，其基础构型是3-PUPS并联机构，对机械臂进行了误差建模与分析，并通过标定系统测量了机械臂实验样机的定位误差。首先，提出了通过对3-PUPS机构各驱动副的组合锁定实现机械臂变胞的设计思路，从而使机械臂可以根据任务需求改变自身构型和性能；然后，采用含误差源的闭环矢量回路法，建立了机械臂3-PUPS机构的误差传递模型，并以此为基础，分析了机械臂的各误差源对其运动平台输出误差的影响规律；接着，根据各误差源对机械臂的输出误差影响程度，确定了各主要运动副配合零件的加工精度等级及公差，在此基础上研制出机械臂的实验样机；最后，采用一套高精度的工业机器人标定系统对机械臂的实验样机进行了定位误差测量，实验表明：机械臂的运动平台的位置误差均在0.005~0.038 mm之间，姿态误差均在0.010~0.044°之间，位置误差比通用式工业机器人的位置重复定位精度0.05 mm略有提高，姿态误差与通用式工业机器人的姿态重复定位精度0.045°相当。"}]}]},{"lang":"en","data":[{"name":"p","data":[{"name":"text","data":"A new type of hyper-redundant metamorphic parallel manipulator arm was proposed. It was based on the 3-PUPS parallel mechanism and it could change its configuration by locking driving joints. Error modeling and analysis of the manipulator were done, and the positioning error of the manipulator's experimental prototype was measured by a calibration system. First, the design idea of manipulator metamorphosis by locking driving joints was proposed so it could change its configuration and performance according to the requirements of the task. Then, using the closed loop vector loop method with error sources, the manipulator's error vector model was established, and the influence of each error source on the moving platform's output errors was analyzed. In addition, according to the influence of each error source on the output errors, the machining accuracy, grade, and tolerances of the manipulator's parts were determined. Based on these, the manipulator's experimental prototype was developed. Finally, the experimental prototype's errors were measured by a high precision calibration system for industrial robots. The experimental results show:the position errors of the manipulator's moving platform were between 0.005 mm and 0.003 8 mm, and the attitude errors were between 0.010° and 0.044°. The position errors were slightly higher than the position repeatability (0.05 mm) of the general industrial robot, and the attitude errors were equivalent to the attitude repetition positioning accuracy (0.045°) of the general industrial robot."}]}]}],"keyword":[{"lang":"zh","data":[[{"name":"text","data":"冗余"}],[{"name":"text","data":"变胞"}],[{"name":"text","data":"并联机械臂"}],[{"name":"text","data":"误差分析"}],[{"name":"text","data":"实验样机"}],[{"name":"text","data":"标定实验"}]]},{"lang":"en","data":[[{"name":"text","data":"redundant"}],[{"name":"text","data":"metamorphic"}],[{"name":"text","data":"parallel manipulator"}],[{"name":"text","data":"error analysis"}],[{"name":"text","data":"prototype"}],[{"name":"text","data":"calibration experiment"}]]}],"highlights":[],"body":[{"name":"sec","data":[{"name":"sectitle","data":{"label":[{"name":"text","data":"1"}],"title":[{"name":"text","data":"引言"}],"level":"1","id":"s1"}},{"name":"p","data":[{"name":"text","data":"机械臂被广泛应用于制造业、军事、航天等领域"},{"name":"sup","data":[{"name":"text","data":"["},{"name":"blockXref","data":{"data":[{"name":"xref","data":{"text":"1","type":"bibr","rid":"b1","data":[{"name":"text","data":"1"}]}},{"name":"text","data":"-"},{"name":"xref","data":{"text":"5","type":"bibr","rid":"b5","data":[{"name":"text","data":"5"}]}}],"rid":["b1","b2","b3","b4","b5"],"text":"1-5","type":"bibr"}},{"name":"text","data":"]"}]},{"name":"text","data":"，但是，针对一些特殊用途的专用机械臂例如：手术机械臂、空间飞行器捕获机械臂、放射性操作机械臂等的研究还有很大空间。上述各种特殊应用环境要求机械臂有高精度、高刚度、高灵活性且驱动器便于防护等性能，相比传统的串联结构机械臂，并联机构在精度、刚度、灵活性及驱动器防护方面更为突出，已有的并联结构机械臂有：Tricept构型机械臂、Delta构型机械臂"},{"name":"sup","data":[{"name":"text","data":"["},{"name":"xref","data":{"text":"6","type":"bibr","rid":"b6","data":[{"name":"text","data":"6"}]}},{"name":"text","data":"]"}]},{"name":"text","data":"、黄田等研发的TriVariant构型机械臂"},{"name":"sup","data":[{"name":"text","data":"["},{"name":"blockXref","data":{"data":[{"name":"xref","data":{"text":"7","type":"bibr","rid":"b7","data":[{"name":"text","data":"7"}]}},{"name":"text","data":"-"},{"name":"xref","data":{"text":"11","type":"bibr","rid":"b11","data":[{"name":"text","data":"11"}]}}],"rid":["b7","b8","b9","b10","b11"],"text":"7-11","type":"bibr"}},{"name":"text","data":"]"}]},{"name":"text","data":"、高峰等研发的拟人系列机械臂"},{"name":"sup","data":[{"name":"text","data":"["},{"name":"blockXref","data":{"data":[{"name":"xref","data":{"text":"12","type":"bibr","rid":"b12","data":[{"name":"text","data":"12"}]}},{"name":"text","data":"-"},{"name":"xref","data":{"text":"16","type":"bibr","rid":"b16","data":[{"name":"text","data":"16"}]}}],"rid":["b12","b13","b14","b15","b16"],"text":"12-16","type":"bibr"}},{"name":"text","data":"]"}]},{"name":"text","data":"、刘福才等研发的航天欠驱动机械臂"},{"name":"sup","data":[{"name":"text","data":"["},{"name":"xref","data":{"text":"17","type":"bibr","rid":"b17","data":[{"name":"text","data":"17"}]}},{"name":"text","data":"]"}]},{"name":"text","data":"等。上述各种并联机械臂与传统的串联机械臂的构型普遍采用固定不变的机构构型和结构参数，而机械臂的各种性能如灵活性、承载能力、刚度、精度等指标之间存在强耦合及互异性，即无法通过一种确定结构和尺寸参数使各种性能指标同时最优，这导致机械臂的结构和尺寸设计只能在各种指标之间权衡，很难精确优化设计。变胞机构可以通过自身的某些设定改变机构构型和自由度特性，从而间接使机构实现不同的最优机构学性能。"}]},{"name":"p","data":[{"name":"text","data":"并联机构不存在串联机构的直观物理运动轴线，因此，其制造、安装过程中产生的误差很难直接物理测量，这些大大限制了并联机构的应用领域。对并联机械臂误差分析，通过误差模型确定机械臂的零部件配合公差优选，通过误差测量与辨识优化完善机械臂的真实机构学模型，从而提高机械臂的精度。常用的并联机构误差分析方法主要有矢量链法"},{"name":"sup","data":[{"name":"text","data":"["},{"name":"blockXref","data":{"data":[{"name":"xref","data":{"text":"18","type":"bibr","rid":"b18","data":[{"name":"text","data":"18"}]}},{"name":"text","data":"-"},{"name":"xref","data":{"text":"19","type":"bibr","rid":"b19","data":[{"name":"text","data":"19"}]}}],"rid":["b18","b19"],"text":"18-19","type":"bibr"}},{"name":"text","data":"]"}]},{"name":"text","data":"和D-H变换矩阵法"},{"name":"sup","data":[{"name":"text","data":"["},{"name":"blockXref","data":{"data":[{"name":"xref","data":{"text":"20","type":"bibr","rid":"b20","data":[{"name":"text","data":"20"}]}},{"name":"text","data":"-"},{"name":"xref","data":{"text":"21","type":"bibr","rid":"b21","data":[{"name":"text","data":"21"}]}}],"rid":["b20","b21"],"text":"20-21","type":"bibr"}},{"name":"text","data":"]"}]},{"name":"text","data":"。"}]},{"name":"p","data":[{"name":"text","data":"本文提出一种基于3-PUPS机构的超冗余并联机械臂，通过对机械臂的各伺服电机抱闸的组合锁定实现机械臂的变胞变换，从而使机械臂在不同的任务用途下具有不同的机构学性能。采用闭环矢量回路建立机械臂的误差模型，并分析机械臂各误差源与其运动平台输出误差关系，进而确定机械臂的主要配合零件加工精度等级及配合公差数值，以此为基础研制机械臂的实验样机。通过一套专用机器人测量系统，测量机械臂实验样机位姿误差情况。"}]}]},{"name":"sec","data":[{"name":"sectitle","data":{"label":[{"name":"text","data":"2"}],"title":[{"name":"text","data":"超冗余变胞机械臂构型描述"}],"level":"1","id":"s2"}},{"name":"p","data":[{"name":"text","data":"本文提出的超冗余可变胞机械臂，如"},{"name":"xref","data":{"text":"图 1","type":"fig","rid":"Figure1","data":[{"name":"text","data":"图 1"}]}},{"name":"text","data":"所示，其采用3-PUPS对称并联机构(P代表移动副、U代表万向副、S代表球面副)，在固定平台与运动平台之间，通过3条相同的PUPS支链连接，其中，固定平台上3个驱动移动副滑轨的轴线交于固定平台中心点，且间隔120°均匀分布；在固定平台的每个移动驱动副滑块上，连接每个支链的驱动万向副组件，该组件通过电机对万向副靠近固定平台的转动副进行驱动；每个支链的移动副套筒组件一端与万向副连接，另一端通过球面副与运动平台连接，套筒组件的一端电机通过带轮带动丝杠驱动伸缩杆的移动运动，与运动平台连接的3个球面副呈等边三角形分布。"}]},{"name":"fig","data":{"id":"Figure1","caption":[{"lang":"zh","label":[{"name":"text","data":"图1"}],"title":[{"name":"text","data":"机械臂结构图"}]},{"lang":"en","label":[{"name":"text","data":"Fig 1"}],"title":[{"name":"text","data":"Structure of manipulator"}]}],"subcaption":[],"note":[],"graphics":[{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1710847&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1710847&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1710847&type=middle"}]}},{"name":"p","data":[{"name":"xref","data":{"text":"图 1","type":"fig","rid":"Figure1","data":[{"name":"text","data":"图 1"}]}},{"name":"text","data":"所示机械臂的3-PUPS机构通过螺旋理论"},{"name":"sup","data":[{"name":"text","data":"["},{"name":"blockXref","data":{"data":[{"name":"xref","data":{"text":"22","type":"bibr","rid":"b22","data":[{"name":"text","data":"22"}]}},{"name":"text","data":"-"},{"name":"xref","data":{"text":"23","type":"bibr","rid":"b23","data":[{"name":"text","data":"23"}]}}],"rid":["b22","b23"],"text":"22-23","type":"bibr"}},{"name":"text","data":"]"}]},{"name":"text","data":"分析可知运动平台有6个自由度，其每个支链有3个驱动副，整个机构有9个驱动副，所以其属于超冗余驱动系统，而超冗余并联机构因数学模型有无穷多组解而导致很难实现实时控制。通过对"},{"name":"xref","data":{"text":"图 1","type":"fig","rid":"Figure1","data":[{"name":"text","data":"图 1"}]}},{"name":"text","data":"所示的机械臂各支链伺服电机抱闸的组合锁定，可以使机械臂的实际机构构型实现变胞变换，从而使机械臂可以工作在对称或非对称的6自由度、5自由度、4自由度、3自由度构型，如3-UPS构型(锁定固定平台上3个移动驱动滑轨的电机抱闸)、3PRPS构成(锁定每个支链万向副的电机抱闸)、3-RPS构型(锁定每个支链固定平台移动驱动副电机、万向副电机的抱闸)等，这样就可以使机械臂在不同的任务状态变胞变换成不同的实际构型并具有不同的性能。经过分析，通过对3-PUPS机构进行电机抱闸组合锁定后，可以得到7种对称并联构型和26种非对称并联构型。为了建立机械臂的通用机构学模型，这里对其基础的3-PUPS构型进行机构学建模，然后通过对各锁定的变量赋常值就可以得到各种变胞后构型的数学模型。"}]},{"name":"p","data":[{"name":"xref","data":{"text":"图 2(a)","type":"fig","rid":"Figure2","data":[{"name":"text","data":"图 2(a)"}]}},{"name":"text","data":"是机械臂3-PUPS机构简图，"},{"name":"italic","data":[{"name":"text","data":"F"},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"("},{"name":"italic","data":[{"name":"text","data":"i"}]},{"name":"text","data":"=1，2，3)是固定平台与各支链驱动移动滑轨的连接点；"},{"name":"italic","data":[{"name":"text","data":"A"},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"("},{"name":"italic","data":[{"name":"text","data":"i"}]},{"name":"text","data":"=1，2，3)是各支链万向副靠近固定平台的转动副中心点，"},{"name":"italic","data":[{"name":"text","data":"B"},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"("},{"name":"italic","data":[{"name":"text","data":"i"}]},{"name":"text","data":"=1，2，3)是各支链万向副远离固定平台的转动副中心点，二者之间为万向副的回转中心点误差，"},{"name":"italic","data":[{"name":"text","data":"C"},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"("},{"name":"italic","data":[{"name":"text","data":"i"}]},{"name":"text","data":"=1，2，3)是各支链球面副的回转中心点。"},{"name":"italic","data":[{"name":"text","data":"O"}]},{"name":"text","data":"是固定平台的几何中心点，"},{"name":"italic","data":[{"name":"text","data":"O"}]},{"name":"text","data":"′是运动平台的几何中心点，且Δ"},{"name":"italic","data":[{"name":"text","data":"F"}]},{"name":"sub","data":[{"name":"text","data":"1"}]},{"name":"italic","data":[{"name":"text","data":"F"}]},{"name":"sub","data":[{"name":"text","data":"2"}]},{"name":"italic","data":[{"name":"text","data":"F"}]},{"name":"sub","data":[{"name":"text","data":"3"}]},{"name":"text","data":"和Δ"},{"name":"italic","data":[{"name":"text","data":"C"}]},{"name":"sub","data":[{"name":"text","data":"1"}]},{"name":"italic","data":[{"name":"text","data":"C"}]},{"name":"sub","data":[{"name":"text","data":"2"}]},{"name":"italic","data":[{"name":"text","data":"C"}]},{"name":"sub","data":[{"name":"text","data":"3"}]},{"name":"text","data":"均是等边三角形。将各尺寸参数化，"},{"name":"italic","data":[{"name":"text","data":"OA"},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"="},{"name":"italic","data":[{"name":"text","data":"a"},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"("},{"name":"italic","data":[{"name":"text","data":"i"}]},{"name":"text","data":"=1，2，3)、"},{"name":"italic","data":[{"name":"text","data":"AB"},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"=Δ"},{"name":"italic","data":[{"name":"text","data":"b"},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"("},{"name":"italic","data":[{"name":"text","data":"i"}]},{"name":"text","data":"=1，2，3)、"},{"name":"italic","data":[{"name":"text","data":"B"},{"name":"sub","data":[{"name":"text","data":"i"}]},{"name":"text","data":"C"},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"="},{"name":"italic","data":[{"name":"text","data":"l"},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"("},{"name":"italic","data":[{"name":"text","data":"i"}]},{"name":"text","data":"=1，2，3)、"},{"name":"italic","data":[{"name":"text","data":"O"}]},{"name":"text","data":"′"},{"name":"italic","data":[{"name":"text","data":"C"},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"="},{"name":"italic","data":[{"name":"text","data":"c"}]},{"name":"text","data":"("},{"name":"italic","data":[{"name":"text","data":"i"}]},{"name":"text","data":"=1，2，3)，各万向副靠近固定平台的转动副转角是"},{"name":"italic","data":[{"name":"text","data":"ψ"},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"("},{"name":"italic","data":[{"name":"text","data":"i"}]},{"name":"text","data":"=1，2，3)，远离固定平台的转动副转角是"},{"name":"italic","data":[{"name":"text","data":"θ"},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"("},{"name":"italic","data":[{"name":"text","data":"i"}]},{"name":"text","data":"=1，2，3)。根据前文对驱动副的设计，"},{"name":"italic","data":[{"name":"text","data":"a"},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"("},{"name":"italic","data":[{"name":"text","data":"i"}]},{"name":"text","data":"=1，2，3)、"},{"name":"italic","data":[{"name":"text","data":"l"},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"("},{"name":"italic","data":[{"name":"text","data":"i"}]},{"name":"text","data":"=1，2，3)、"},{"name":"italic","data":[{"name":"text","data":"ψ"},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"("},{"name":"italic","data":[{"name":"text","data":"i"}]},{"name":"text","data":"=1，2，3)是各支链的驱动参数。"},{"name":"xref","data":{"text":"图 2(b)","type":"fig","rid":"Figure2","data":[{"name":"text","data":"图 2(b)"}]}},{"name":"text","data":"是各万向副的误差矢量图，其靠近固定平台和远离固定平台的2个转动副中心点之间误差矢量是Δ"},{"name":"italic","data":[{"name":"text","data":"b"},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"("},{"name":"italic","data":[{"name":"text","data":"i"}]},{"name":"text","data":"=1，2，3)。"}]},{"name":"fig","data":{"id":"Figure2","caption":[{"lang":"zh","label":[{"name":"text","data":"图2"}],"title":[{"name":"text","data":"机械臂3-PUPS机构简图"}]},{"lang":"en","label":[{"name":"text","data":"Fig 2"}],"title":[{"name":"text","data":"Structure map of manipulator's 3-PUPS mechanism"}]}],"subcaption":[],"note":[],"graphics":[{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1710864&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1710864&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1710864&type=middle"}]}},{"name":"p","data":[{"name":"text","data":"在"},{"name":"xref","data":{"text":"图 2(a)","type":"fig","rid":"Figure2","data":[{"name":"text","data":"图 2(a)"}]}},{"name":"text","data":"中，定义固定平台坐标系"},{"name":"italic","data":[{"name":"text","data":"O"}]},{"name":"text","data":"-"},{"name":"italic","data":[{"name":"text","data":"xyz"}]},{"name":"text","data":"，"},{"name":"italic","data":[{"name":"text","data":"x"}]},{"name":"text","data":"轴与"},{"name":"italic","data":[{"name":"text","data":"F"}]},{"name":"sub","data":[{"name":"text","data":"1"}]},{"name":"italic","data":[{"name":"text","data":"O"}]},{"name":"text","data":"共线且方向相同，"},{"name":"italic","data":[{"name":"text","data":"z"}]},{"name":"text","data":"轴垂直于平面"},{"name":"italic","data":[{"name":"text","data":"F"}]},{"name":"sub","data":[{"name":"text","data":"1"}]},{"name":"italic","data":[{"name":"text","data":"F"}]},{"name":"sub","data":[{"name":"text","data":"2"}]},{"name":"italic","data":[{"name":"text","data":"F"}]},{"name":"sub","data":[{"name":"text","data":"3"}]},{"name":"text","data":"且方向向下，"},{"name":"italic","data":[{"name":"text","data":"y"}]},{"name":"text","data":"轴满足右手法则；定义运动平台坐标系"},{"name":"italic","data":[{"name":"text","data":"O"}]},{"name":"text","data":"′-"},{"name":"italic","data":[{"name":"text","data":"upw"}]},{"name":"text","data":"，"},{"name":"italic","data":[{"name":"text","data":"u"}]},{"name":"text","data":"轴与"},{"name":"italic","data":[{"name":"text","data":"C"}]},{"name":"sub","data":[{"name":"text","data":"1"}]},{"name":"italic","data":[{"name":"text","data":"O"}]},{"name":"text","data":"′共线且方向相同，"},{"name":"italic","data":[{"name":"text","data":"w"}]},{"name":"text","data":"轴垂直于平面"},{"name":"italic","data":[{"name":"text","data":"C"}]},{"name":"sub","data":[{"name":"text","data":"1"}]},{"name":"italic","data":[{"name":"text","data":"C"}]},{"name":"sub","data":[{"name":"text","data":"2"}]},{"name":"italic","data":[{"name":"text","data":"C"}]},{"name":"sub","data":[{"name":"text","data":"3"}]},{"name":"text","data":"且方向向下，"},{"name":"italic","data":[{"name":"text","data":"p"}]},{"name":"text","data":"轴满足右手法则；定义各分支万向副的基坐标系"},{"name":"italic","data":[{"name":"text","data":"A"},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"-"},{"name":"italic","data":[{"name":"text","data":"x"},{"name":"sub","data":[{"name":"text","data":"i"}]},{"name":"text","data":"y"},{"name":"sub","data":[{"name":"text","data":"i"}]},{"name":"text","data":"z"},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"("},{"name":"italic","data":[{"name":"text","data":"i"}]},{"name":"text","data":"=1，2，3)，"},{"name":"italic","data":[{"name":"text","data":"x"},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"轴与"},{"name":"italic","data":[{"name":"text","data":"A"},{"name":"sub","data":[{"name":"text","data":"i"}]},{"name":"text","data":"O"}]},{"name":"text","data":"("},{"name":"italic","data":[{"name":"text","data":"i"}]},{"name":"text","data":"=1，2，3)共线且方向相同，"},{"name":"italic","data":[{"name":"text","data":"z"},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"轴垂直于平面"},{"name":"italic","data":[{"name":"text","data":"F"}]},{"name":"sub","data":[{"name":"text","data":"1"}]},{"name":"italic","data":[{"name":"text","data":"F"}]},{"name":"sub","data":[{"name":"text","data":"2"}]},{"name":"italic","data":[{"name":"text","data":"F"}]},{"name":"sub","data":[{"name":"text","data":"3"}]},{"name":"text","data":"且方向向下，"},{"name":"italic","data":[{"name":"text","data":"y"},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"轴满足右手法则；定义各支链摆动部分的连体坐标系"},{"name":"italic","data":[{"name":"text","data":"B"},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"-"},{"name":"italic","data":[{"name":"text","data":"u"},{"name":"sub","data":[{"name":"text","data":"i"}]},{"name":"text","data":"p"},{"name":"sub","data":[{"name":"text","data":"i"}]},{"name":"text","data":"w"},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"("},{"name":"italic","data":[{"name":"text","data":"i"}]},{"name":"text","data":"=1，2，3)，"},{"name":"italic","data":[{"name":"text","data":"w"},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"轴与"},{"name":"italic","data":[{"name":"text","data":"B"},{"name":"sub","data":[{"name":"text","data":"i"}]},{"name":"text","data":"C"},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"共线且方向相同，"},{"name":"italic","data":[{"name":"text","data":"p"},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"轴与对应万向副远离固定平台的转动副轴线共线，方向如"},{"name":"xref","data":{"text":"图 2(a)","type":"fig","rid":"Figure2","data":[{"name":"text","data":"图 2(a)"}]}},{"name":"text","data":"所示，"},{"name":"italic","data":[{"name":"text","data":"u"},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"轴满足右手法则。定义坐标系"},{"name":"italic","data":[{"name":"text","data":"O"}]},{"name":"text","data":"′-"},{"name":"italic","data":[{"name":"text","data":"upw"}]},{"name":"text","data":"从与坐标系"},{"name":"italic","data":[{"name":"text","data":"O"}]},{"name":"text","data":"-"},{"name":"italic","data":[{"name":"text","data":"xyz"}]},{"name":"text","data":"各轴平行开始，绕其自身"},{"name":"italic","data":[{"name":"text","data":"u"}]},{"name":"text","data":"轴旋转角度"},{"name":"italic","data":[{"name":"text","data":"α"}]},{"name":"text","data":"、再绕其自身"},{"name":"italic","data":[{"name":"text","data":"p"}]},{"name":"text","data":"轴旋转角度"},{"name":"italic","data":[{"name":"text","data":"β"}]},{"name":"text","data":"、再绕其自身"},{"name":"italic","data":[{"name":"text","data":"w"}]},{"name":"text","data":"轴旋转角度"},{"name":"italic","data":[{"name":"text","data":"γ"}]},{"name":"text","data":"得到任意姿态。"}]}]},{"name":"sec","data":[{"name":"sectitle","data":{"label":[{"name":"text","data":"2"}],"title":[{"name":"text","data":"机械臂3-PUPS机构的误差建模"}],"level":"1","id":"s3"}},{"name":"sec","data":[{"name":"sectitle","data":{"label":[{"name":"text","data":"2.1"}],"title":[{"name":"text","data":"机械臂的误差源及输出误差分析"}],"level":"2","id":"s3-1"}},{"name":"p","data":[{"name":"text","data":"并联机构的误差主要来自于几何误差"},{"name":"sup","data":[{"name":"text","data":"["},{"name":"xref","data":{"text":"24","type":"bibr","rid":"b24","data":[{"name":"text","data":"24"}]}},{"name":"text","data":"]"}]},{"name":"text","data":"，包括零部件制造误差、装配误差以及部件几何变形误差等。本文提出的机械臂的误差源主要有：固定平台上各驱动移动副滑轨的安装误差和滑块运动误差、各支链万向副的2个转动副中心点之间的位置误差、各支链套筒移动副的长度误差和扭转角误差、各支链球面副回转中心点的位置误差。机械臂的输出误差主要是其运动平台的位置误差和姿态角误差。为了建立机械臂的误差矢量回路，定义坐标系"},{"name":"italic","data":[{"name":"text","data":"O"}]},{"name":"text","data":"-"},{"name":"italic","data":[{"name":"text","data":"xyz"}]},{"name":"text","data":"中："},{"name":"italic","data":[{"name":"text","data":"A"},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"("},{"name":"italic","data":[{"name":"text","data":"i"}]},{"name":"text","data":"=1，2，3)的位置矢量是"},{"name":"italic","data":[{"name":"bold","data":[{"name":"text","data":"a"}]},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"，误差矢量是Δ"},{"name":"italic","data":[{"name":"bold","data":[{"name":"text","data":"a"}]},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"；"},{"name":"italic","data":[{"name":"text","data":"O"}]},{"name":"text","data":"′的位置矢量是"},{"name":"italic","data":[{"name":"bold","data":[{"name":"text","data":"p"}]}]},{"name":"sub","data":[{"name":"italic","data":[{"name":"text","data":"O"}]},{"name":"text","data":"′"}]},{"name":"text","data":"，误差矢量是Δ"},{"name":"italic","data":[{"name":"bold","data":[{"name":"text","data":"p"}]}]},{"name":"sub","data":[{"name":"italic","data":[{"name":"text","data":"O"}]},{"name":"text","data":"′"}]},{"name":"text","data":"；运动平台的姿态角误差分别是Δ"},{"name":"italic","data":[{"name":"text","data":"α"}]},{"name":"text","data":"、Δ"},{"name":"italic","data":[{"name":"text","data":"β"}]},{"name":"text","data":"、Δ"},{"name":"italic","data":[{"name":"text","data":"γ"}]},{"name":"text","data":"。坐标系"},{"name":"italic","data":[{"name":"text","data":"A"},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"-"},{"name":"italic","data":[{"name":"text","data":"x"},{"name":"sub","data":[{"name":"text","data":"i"}]},{"name":"text","data":"y"},{"name":"sub","data":[{"name":"text","data":"i"}]},{"name":"text","data":"z"},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"("},{"name":"italic","data":[{"name":"text","data":"i"}]},{"name":"text","data":"=1，2，3)中："},{"name":"italic","data":[{"name":"text","data":"B"}]},{"name":"text","data":"("},{"name":"italic","data":[{"name":"text","data":"i"}]},{"name":"text","data":"=1，2，3)与"},{"name":"italic","data":[{"name":"text","data":"A"},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"("},{"name":"italic","data":[{"name":"text","data":"i"}]},{"name":"text","data":"=1，2，3)间位置误差矢量是Δ"},{"name":"italic","data":[{"name":"bold","data":[{"name":"text","data":"b"}]},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"。坐标系"},{"name":"italic","data":[{"name":"text","data":"B"},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"-"},{"name":"italic","data":[{"name":"text","data":"u"},{"name":"sub","data":[{"name":"text","data":"i"}]},{"name":"text","data":"p"},{"name":"sub","data":[{"name":"text","data":"i"}]},{"name":"text","data":"w"},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"("},{"name":"italic","data":[{"name":"text","data":"i"}]},{"name":"text","data":"=1，2，3)中："},{"name":"italic","data":[{"name":"text","data":"C"},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"("},{"name":"italic","data":[{"name":"text","data":"i"}]},{"name":"text","data":"=1，2，3)的位置矢量是"},{"name":"italic","data":[{"name":"bold","data":[{"name":"text","data":"l"}]},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"，误差矢量是Δ"},{"name":"italic","data":[{"name":"bold","data":[{"name":"text","data":"l"}]},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"。坐标系"},{"name":"italic","data":[{"name":"text","data":"O"}]},{"name":"text","data":"′-"},{"name":"italic","data":[{"name":"text","data":"upw"}]},{"name":"text","data":"中："},{"name":"italic","data":[{"name":"text","data":"C"},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"("},{"name":"italic","data":[{"name":"text","data":"i"}]},{"name":"text","data":"=1，2，3)的位置矢量是"},{"name":"italic","data":[{"name":"bold","data":[{"name":"text","data":"c"}]},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"，误差矢量是Δ"},{"name":"italic","data":[{"name":"bold","data":[{"name":"text","data":"c"}]},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"。"}]},{"name":"p","data":[{"name":"text","data":"为了便于矢量计算，建立各坐标系之间的选择变换矩阵，其中，坐标系"},{"name":"italic","data":[{"name":"text","data":"A"},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"-"},{"name":"italic","data":[{"name":"text","data":"x"},{"name":"sub","data":[{"name":"text","data":"i"}]},{"name":"text","data":"y"},{"name":"sub","data":[{"name":"text","data":"i"}]},{"name":"text","data":"z"},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"("},{"name":"italic","data":[{"name":"text","data":"i"}]},{"name":"text","data":"=1，2，3)相对于坐标系"},{"name":"italic","data":[{"name":"text","data":"O"}]},{"name":"text","data":"-"},{"name":"italic","data":[{"name":"text","data":"xyz"}]},{"name":"text","data":"的旋转变换矩阵为："}]},{"name":"p","data":[{"name":"dispformula","data":{"label":[{"name":"text","data":"1"}],"data":[{"name":"text","data":" "},{"name":"text","data":"  "},{"name":"math","data":{"graphicsData":{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1710878&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1710878&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1710878&type=middle"}}}],"id":"gxjmgc-26-7-1698-E1"}}]},{"name":"p","data":[{"name":"text","data":"坐标系"},{"name":"italic","data":[{"name":"text","data":"B"},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"-"},{"name":"italic","data":[{"name":"text","data":"u"},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"italic","data":[{"name":"text","data":"p"},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"italic","data":[{"name":"text","data":"w"},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"("},{"name":"italic","data":[{"name":"text","data":"i"}]},{"name":"text","data":"=1，2，3)相对于坐标系"},{"name":"italic","data":[{"name":"text","data":"A"},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"-"},{"name":"italic","data":[{"name":"text","data":"x"},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"italic","data":[{"name":"text","data":"y"},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"italic","data":[{"name":"text","data":"z"},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"("},{"name":"italic","data":[{"name":"text","data":"i"}]},{"name":"text","data":"=1，2，3)的旋转变换矩阵为："}]},{"name":"p","data":[{"name":"dispformula","data":{"label":[{"name":"text","data":"2"}],"data":[{"name":"text","data":" "},{"name":"text","data":"  "},{"name":"math","data":{"graphicsData":{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1710901&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1710901&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1710901&type=middle"}}}],"id":"gxjmgc-26-7-1698-E2"}}]},{"name":"p","data":[{"name":"text","data":"式中："},{"name":"italic","data":[{"name":"text","data":"ψ"},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"是各万向副靠近固定平台转角，"},{"name":"italic","data":[{"name":"text","data":"θ"},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"是各万向副远离固定平台转动副转角。"}]},{"name":"p","data":[{"name":"text","data":"坐标系"},{"name":"italic","data":[{"name":"text","data":"O"}]},{"name":"text","data":"′-"},{"name":"italic","data":[{"name":"text","data":"upw"}]},{"name":"text","data":"相对于坐标系"},{"name":"italic","data":[{"name":"text","data":"O"}]},{"name":"text","data":"-"},{"name":"italic","data":[{"name":"text","data":"xyz"}]},{"name":"text","data":"的旋转变换矩阵为："}]},{"name":"p","data":[{"name":"dispformula","data":{"label":[{"name":"text","data":"3"}],"data":[{"name":"text","data":" "},{"name":"text","data":"  "},{"name":"math","data":{"graphicsData":{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1710930&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1710930&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1710930&type=middle"}}}],"id":"gxjmgc-26-7-1698-E3"}}]},{"name":"p","data":[{"name":"text","data":"式中：坐标系"},{"name":"italic","data":[{"name":"text","data":"O"}]},{"name":"text","data":"′-"},{"name":"italic","data":[{"name":"text","data":"upw"}]},{"name":"text","data":"从与坐标系"},{"name":"italic","data":[{"name":"text","data":"O"}]},{"name":"text","data":"-"},{"name":"italic","data":[{"name":"text","data":"xyz"}]},{"name":"text","data":"各轴平行开始，绕其自身"},{"name":"italic","data":[{"name":"text","data":"u"}]},{"name":"text","data":"轴旋转角度"},{"name":"italic","data":[{"name":"text","data":"α"}]},{"name":"text","data":"、再绕其自身"},{"name":"italic","data":[{"name":"text","data":"p"}]},{"name":"text","data":"轴旋转角度"},{"name":"italic","data":[{"name":"text","data":"β"}]},{"name":"text","data":"、再绕其自身"},{"name":"italic","data":[{"name":"text","data":"w"}]},{"name":"text","data":"轴旋转角度"},{"name":"italic","data":[{"name":"text","data":"γ"}]},{"name":"text","data":"得到任意姿态。"}]},{"name":"p","data":[{"name":"text","data":"坐标系"},{"name":"italic","data":[{"name":"text","data":"O"}]},{"name":"text","data":"′-"},{"name":"italic","data":[{"name":"text","data":"upw"}]},{"name":"text","data":"相对于坐标系"},{"name":"italic","data":[{"name":"text","data":"O"}]},{"name":"text","data":"-"},{"name":"italic","data":[{"name":"text","data":"xyz"}]},{"name":"text","data":"的姿态误差旋转变换矩阵为："}]},{"name":"p","data":[{"name":"dispformula","data":{"label":[{"name":"text","data":"4"}],"data":[{"name":"text","data":" "},{"name":"text","data":"  "},{"name":"math","data":{"graphicsData":{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1710960&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1710960&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1710960&type=middle"}}}],"id":"gxjmgc-26-7-1698-E4"}}]},{"name":"p","data":[{"name":"text","data":"式中：Δ"},{"name":"italic","data":[{"name":"text","data":"α"}]},{"name":"text","data":"、Δ"},{"name":"italic","data":[{"name":"text","data":"β"}]},{"name":"text","data":"、Δ"},{"name":"italic","data":[{"name":"text","data":"γ"}]},{"name":"text","data":"是运动平台的姿态角"},{"name":"italic","data":[{"name":"text","data":"α"}]},{"name":"text","data":"、"},{"name":"italic","data":[{"name":"text","data":"β"}]},{"name":"text","data":"、"},{"name":"italic","data":[{"name":"text","data":"γ"}]},{"name":"text","data":"的对应误差。"}]}]},{"name":"sec","data":[{"name":"sectitle","data":{"label":[{"name":"text","data":"2.2"}],"title":[{"name":"text","data":"机械臂的误差建模"}],"level":"2","id":"s3-2"}},{"name":"p","data":[{"name":"text","data":"基于"},{"name":"xref","data":{"text":"图 2(a)","type":"fig","rid":"Figure2","data":[{"name":"text","data":"图 2(a)"}]}},{"name":"text","data":"中的构型及矢量回路，建立机械臂3-PUPS机构的含误差全矢量闭环约束方程，有："}]},{"name":"p","data":[{"name":"dispformula","data":{"label":[{"name":"text","data":"5"}],"data":[{"name":"text","data":" "},{"name":"text","data":"  "},{"name":"math","data":{"graphicsData":{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1710984&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1710984&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1710984&type=middle"}}}],"id":"gxjmgc-26-7-1698-E5"}}]},{"name":"p","data":[{"name":"text","data":"如果忽略机构的全部误差，建立机械臂3-PUPS机构的基本尺寸全矢量闭环约束方程，有："}]},{"name":"p","data":[{"name":"dispformula","data":{"label":[{"name":"text","data":"6"}],"data":[{"name":"text","data":" "},{"name":"text","data":"  "},{"name":"math","data":{"graphicsData":{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1710997&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1710997&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1710997&type=middle"}}}],"id":"gxjmgc-26-7-1698-E6"}}]},{"name":"p","data":[{"name":"text","data":"用式(5)减去式(6)对应项，有："}]},{"name":"p","data":[{"name":"dispformula","data":{"label":[{"name":"text","data":"7"}],"data":[{"name":"text","data":" "},{"name":"text","data":"  "},{"name":"math","data":{"graphicsData":{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1711019&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1711019&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1711019&type=middle"}}}],"id":"gxjmgc-26-7-1698-E7"}}]},{"name":"p","data":[{"name":"text","data":"根据"},{"name":"xref","data":{"text":"图 2(a)","type":"fig","rid":"Figure2","data":[{"name":"text","data":"图 2(a)"}]}},{"name":"text","data":"的几何关系可知："},{"name":"italic","data":[{"name":"bold","data":[{"name":"text","data":"w"}]},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"sup","data":[{"name":"text","data":"T"}]},{"name":"italic","data":[{"name":"bold","data":[{"name":"text","data":"c"}]},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"=0，"},{"name":"italic","data":[{"name":"bold","data":[{"name":"text","data":"w"}]},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"sup","data":[{"name":"text","data":"T"}]},{"name":"text","data":"Δ"},{"name":"italic","data":[{"name":"bold","data":[{"name":"text","data":"c"}]},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"=0(Δ"},{"name":"italic","data":[{"name":"bold","data":[{"name":"text","data":"c"}]},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"("},{"name":"italic","data":[{"name":"text","data":"i"}]},{"name":"text","data":"=1，2，3)简化为平面"},{"name":"italic","data":[{"name":"text","data":"C"}]},{"name":"sub","data":[{"name":"text","data":"1"}]},{"name":"italic","data":[{"name":"text","data":"C"}]},{"name":"sub","data":[{"name":"text","data":"2"}]},{"name":"italic","data":[{"name":"text","data":"C"}]},{"name":"sub","data":[{"name":"text","data":"3"}]},{"name":"text","data":"内的误差矢量)。因此，在式(7)各项点乘"},{"name":"italic","data":[{"name":"bold","data":[{"name":"text","data":"w"}]},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"sup","data":[{"name":"text","data":"T"}]},{"name":"text","data":"并将"},{"name":"italic","data":[{"name":"text","data":"ψ"},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"("},{"name":"italic","data":[{"name":"text","data":"i"}]},{"name":"text","data":"=1，2，3)和"},{"name":"italic","data":[{"name":"text","data":"θ"},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"("},{"name":"italic","data":[{"name":"text","data":"i"}]},{"name":"text","data":"=1，2，3)代入进行线性化整理，有："}]},{"name":"p","data":[{"name":"dispformula","data":{"label":[{"name":"text","data":"8"}],"data":[{"name":"text","data":" "},{"name":"text","data":"  "},{"name":"math","data":{"graphicsData":{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1711043&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1711043&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1711043&type=middle"}}}],"id":"gxjmgc-26-7-1698-E8"}}]},{"name":"p","data":[{"name":"text","data":"式中Δ"},{"name":"italic","data":[{"name":"bold","data":[{"name":"text","data":"φ"}]}]},{"name":"sub","data":[{"name":"italic","data":[{"name":"text","data":"O"}]},{"name":"text","data":"′"}]},{"name":"text","data":"=[Δ"},{"name":"italic","data":[{"name":"text","data":"α"}]},{"name":"text","data":" Δ"},{"name":"italic","data":[{"name":"text","data":"β"}]},{"name":"text","data":" Δ"},{"name":"italic","data":[{"name":"text","data":"γ"}]},{"name":"text","data":"]"},{"name":"sup","data":[{"name":"text","data":"T"}]},{"name":"text","data":"是3-PUPS机构运动平台的姿态角误差矢量。"}]},{"name":"p","data":[{"name":"text","data":"将式(8)整理成矩阵形式，有："}]},{"name":"p","data":[{"name":"dispformula","data":{"label":[{"name":"text","data":"9"}],"data":[{"name":"text","data":" "},{"name":"text","data":"  "},{"name":"math","data":{"graphicsData":{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1711062&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1711062&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1711062&type=middle"}}}],"id":"gxjmgc-26-7-1698-E9"}}]},{"name":"p","data":[{"name":"text","data":"式中：[Δ"},{"name":"italic","data":[{"name":"bold","data":[{"name":"text","data":"p"}]}]},{"name":"sub","data":[{"name":"italic","data":[{"name":"text","data":"O"}]},{"name":"text","data":"′"}]},{"name":"sup","data":[{"name":"text","data":"T"}]},{"name":"text","data":" Δ"},{"name":"italic","data":[{"name":"bold","data":[{"name":"text","data":"φ"}]}]},{"name":"sub","data":[{"name":"italic","data":[{"name":"text","data":"O"}]},{"name":"text","data":"′"}]},{"name":"sup","data":[{"name":"text","data":"T"}]},{"name":"text","data":"]"},{"name":"sup","data":[{"name":"text","data":"T"}]},{"name":"text","data":"是机械臂3-"},{"name":"italic","data":[{"name":"text","data":"PUPS"}]},{"name":"text","data":"机构运动平台的误差矢量，Δ"},{"name":"italic","data":[{"name":"bold","data":[{"name":"text","data":"ε"}]}]},{"name":"text","data":"=[Δ"},{"name":"italic","data":[{"name":"bold","data":[{"name":"text","data":"a"}]}]},{"name":"sub","data":[{"name":"text","data":"1"}]},{"name":"sup","data":[{"name":"text","data":"T"}]},{"name":"text","data":" Δ"},{"name":"italic","data":[{"name":"bold","data":[{"name":"text","data":"b"}]}]},{"name":"sub","data":[{"name":"text","data":"1"}]},{"name":"sup","data":[{"name":"text","data":"T"}]},{"name":"text","data":" Δ"},{"name":"italic","data":[{"name":"bold","data":[{"name":"text","data":"l"}]}]},{"name":"sub","data":[{"name":"text","data":"1"}]},{"name":"sup","data":[{"name":"text","data":"T"}]},{"name":"text","data":" Δ"},{"name":"italic","data":[{"name":"bold","data":[{"name":"text","data":"a"}]}]},{"name":"sub","data":[{"name":"text","data":"2"}]},{"name":"sup","data":[{"name":"text","data":"T"}]},{"name":"text","data":" Δ"},{"name":"italic","data":[{"name":"bold","data":[{"name":"text","data":"b"}]}]},{"name":"sub","data":[{"name":"text","data":"2"}]},{"name":"sup","data":[{"name":"text","data":"T"}]},{"name":"text","data":" Δ"},{"name":"italic","data":[{"name":"bold","data":[{"name":"text","data":"l"}]}]},{"name":"sub","data":[{"name":"text","data":"2"}]},{"name":"sup","data":[{"name":"text","data":"T"}]},{"name":"text","data":" Δ"},{"name":"italic","data":[{"name":"bold","data":[{"name":"text","data":"a"}]}]},{"name":"sub","data":[{"name":"text","data":"3"}]},{"name":"sup","data":[{"name":"text","data":"T"}]},{"name":"text","data":" Δ"},{"name":"italic","data":[{"name":"bold","data":[{"name":"text","data":"b"}]}]},{"name":"sub","data":[{"name":"text","data":"3"}]},{"name":"sup","data":[{"name":"text","data":"T"}]},{"name":"text","data":" Δ"},{"name":"italic","data":[{"name":"bold","data":[{"name":"text","data":"l"}]}]},{"name":"sub","data":[{"name":"text","data":"3"}]},{"name":"sup","data":[{"name":"text","data":"T"}]},{"name":"text","data":"]"},{"name":"sup","data":[{"name":"text","data":"T"}]},{"name":"text","data":"是机械臂3-"},{"name":"italic","data":[{"name":"text","data":"PUPS"}]},{"name":"text","data":"机构的误差源矢量，Δ"},{"name":"italic","data":[{"name":"bold","data":[{"name":"text","data":"ε"}]}]},{"name":"text","data":"∈"},{"name":"italic","data":[{"name":"bold","data":[{"name":"text","data":"R"}]}]},{"name":"sup","data":[{"name":"text","data":"27×1"}]},{"name":"text","data":"，"},{"name":"italic","data":[{"name":"bold","data":[{"name":"text","data":"J"}]}]},{"name":"sub","data":[{"name":"text","data":"1"}]},{"name":"text","data":"∈"},{"name":"italic","data":[{"name":"bold","data":[{"name":"text","data":"R"}]}]},{"name":"sup","data":[{"name":"text","data":"3×6"}]},{"name":"text","data":"，"},{"name":"italic","data":[{"name":"bold","data":[{"name":"text","data":"J"}]}]},{"name":"sub","data":[{"name":"text","data":"2"}]},{"name":"text","data":"∈"},{"name":"italic","data":[{"name":"bold","data":[{"name":"text","data":"R"}]}]},{"name":"sup","data":[{"name":"text","data":"3×27"}]},{"name":"text","data":"，"},{"name":"italic","data":[{"name":"bold","data":[{"name":"text","data":"O"}]}]},{"name":"sub","data":[{"name":"text","data":"1×3"}]},{"name":"text","data":"为3阶0向量，且有："}]},{"name":"p","data":[{"name":"dispformula","data":{"label":[],"data":[{"name":"text","data":" "},{"name":"text","data":"  "},{"name":"math","data":{"graphicsData":{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1711086&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1711086&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1711086&type=middle"}}}],"id":"gxjmgc-26-7-1698-FE1"}}]},{"name":"p","data":[{"name":"text","data":"机械臂3-PUPS机构的误差源与运动平台输出误差之间的传递方程如式(9)所示，如果"},{"name":"italic","data":[{"name":"bold","data":[{"name":"text","data":"J"}]}]},{"name":"sub","data":[{"name":"text","data":"1"}]},{"name":"text","data":"和"},{"name":"italic","data":[{"name":"bold","data":[{"name":"text","data":"J"}]}]},{"name":"sub","data":[{"name":"text","data":"2"}]},{"name":"text","data":"均是可逆矩阵，就可以在已知机械臂的各误差源误差数值条件下，通过式(9)求解出机械臂的运动平台输出误差；还可以通过设定机械臂的运动平台输出误差大小，分析出机械臂各误差源的误差分布情况。"}]}]}]},{"name":"sec","data":[{"name":"sectitle","data":{"label":[{"name":"text","data":"3"}],"title":[{"name":"text","data":"机械臂3-PUPS机构的灵敏度"}],"level":"1","id":"s4"}},{"name":"sec","data":[{"name":"sectitle","data":{"label":[{"name":"text","data":"3.1"}],"title":[{"name":"text","data":"机械臂的灵敏度分析"}],"level":"2","id":"s4-1"}},{"name":"p","data":[{"name":"text","data":"为了便于量化分析机械臂的误差性能，在"},{"name":"xref","data":{"text":"图 2","type":"fig","rid":"Figure2","data":[{"name":"text","data":"图 2"}]}},{"name":"text","data":"中，给定机械臂的主要尺寸参数值为：固定平台可变尺寸"},{"name":"italic","data":[{"name":"text","data":"a"},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"∈(200，300) mm、运动平台球面副分布半径"},{"name":"italic","data":[{"name":"text","data":"c"}]},{"name":"text","data":"=90 mm、各分支丝杠长度为500 mm、各分支套筒长度为450 mm、各分支伸缩杆长度为500 mm、各分支最大直径为90 mm。"}]},{"name":"p","data":[{"name":"text","data":"为了深入分析机械臂的各误差源对其运动平台输出误差的影响规律，如果"},{"name":"italic","data":[{"name":"bold","data":[{"name":"text","data":"J"}]}]},{"name":"sub","data":[{"name":"text","data":"1"}]},{"name":"text","data":"是可逆矩阵，对式(9)进行变换，有:"}]},{"name":"p","data":[{"name":"dispformula","data":{"label":[{"name":"text","data":"10"}],"data":[{"name":"text","data":" "},{"name":"text","data":"  "},{"name":"math","data":{"graphicsData":{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1711103&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1711103&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1711103&type=middle"}}}],"id":"gxjmgc-26-7-1698-E10"}}]},{"name":"p","data":[{"name":"text","data":"式中："},{"name":"italic","data":[{"name":"bold","data":[{"name":"text","data":"G"}]}]},{"name":"text","data":"=("},{"name":"bold","data":[{"name":"italic","data":[{"name":"text","data":"J"}]}]},{"name":"sub","data":[{"name":"text","data":"1"}]},{"name":"sup","data":[{"name":"text","data":"-1"}]},{"name":"text","data":")"},{"name":"italic","data":[{"name":"bold","data":[{"name":"text","data":"J"}]}]},{"name":"sub","data":[{"name":"text","data":"2"}]},{"name":"text","data":"，"},{"name":"bold","data":[{"name":"italic","data":[{"name":"text","data":"G"}]}]},{"name":"text","data":"∈"},{"name":"italic","data":[{"name":"bold","data":[{"name":"text","data":"R"}]}]},{"name":"sup","data":[{"name":"text","data":"6×27"}]},{"name":"text","data":"，"},{"name":"italic","data":[{"name":"bold","data":[{"name":"text","data":"G"}]}]},{"name":"text","data":"是机械臂的误差传递逆矩阵。"}]},{"name":"p","data":[{"name":"text","data":"因为式(10)中机械臂的运动平台输出误差矢量内部位置误差和姿态误差量纲不统一，故将式(10)拆解为位置误差、姿态误差子矩阵表达，有："}]},{"name":"p","data":[{"name":"dispformula","data":{"label":[{"name":"text","data":"11"}],"data":[{"name":"text","data":" "},{"name":"text","data":"  "},{"name":"math","data":{"graphicsData":{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1711126&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1711126&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1711126&type=middle"}}}],"id":"gxjmgc-26-7-1698-E11"}}]},{"name":"p","data":[{"name":"text","data":"式中："},{"name":"italic","data":[{"name":"bold","data":[{"name":"text","data":"G"}]},{"name":"sub","data":[{"name":"text","data":"P"}]}]},{"name":"text","data":"∈"},{"name":"italic","data":[{"name":"bold","data":[{"name":"text","data":"R"}]}]},{"name":"sup","data":[{"name":"text","data":"3×27"}]},{"name":"text","data":"是机械臂的输出位置误差子矩阵，具体值是矩阵"},{"name":"italic","data":[{"name":"bold","data":[{"name":"text","data":"G"}]}]},{"name":"text","data":"的前3行；"},{"name":"italic","data":[{"name":"bold","data":[{"name":"text","data":"G"}]},{"name":"sub","data":[{"name":"text","data":"φ"}]}]},{"name":"text","data":"∈"},{"name":"italic","data":[{"name":"bold","data":[{"name":"text","data":"R"}]}]},{"name":"sup","data":[{"name":"text","data":"3×27"}]},{"name":"text","data":"是机械臂的输出姿态误差子矩阵，具体值是矩阵"},{"name":"italic","data":[{"name":"bold","data":[{"name":"text","data":"G"}]}]},{"name":"text","data":"的后3行。"}]},{"name":"p","data":[{"name":"text","data":"通过式(11)就可以在已知机械臂的各误差源数值条件下，求出其运动平台的输出位置误差和姿态误差。"}]},{"name":"p","data":[{"name":"text","data":"为了量化评估机械臂的输出误差，对式(11)取范数，有："}]},{"name":"p","data":[{"name":"dispformula","data":{"label":[{"name":"text","data":"12"}],"data":[{"name":"text","data":" "},{"name":"text","data":"  "},{"name":"math","data":{"graphicsData":{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1711143&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1711143&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1711143&type=middle"}}}],"id":"gxjmgc-26-7-1698-E12"}}]},{"name":"p","data":[{"name":"text","data":"因为本文提出的机械臂3-PUPS机构属于轴对称并联机构，其3个支链具有相同的性质，因此，仅需要分析1个支链内各误差源对机构的输出误差影响，就能够揭示出其误差特性。通过式(9)可知，每个支链中的运动平台球面副回转中心位置误差Δ"},{"name":"italic","data":[{"name":"text","data":"c"},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"("},{"name":"italic","data":[{"name":"text","data":"i"}]},{"name":"text","data":"=1，2，3)因简化为平面"},{"name":"italic","data":[{"name":"text","data":"C"}]},{"name":"sub","data":[{"name":"text","data":"1"}]},{"name":"italic","data":[{"name":"text","data":"C"}]},{"name":"sub","data":[{"name":"text","data":"2"}]},{"name":"italic","data":[{"name":"text","data":"C"}]},{"name":"sub","data":[{"name":"text","data":"3"}]},{"name":"text","data":"内的误差矢量而在计算过程中被消去，说明其对机械臂的输出误差影响较小。故对于每个单独的支链而言，其误差源主要有Δ"},{"name":"italic","data":[{"name":"bold","data":[{"name":"text","data":"a"}]},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"，Δ"},{"name":"italic","data":[{"name":"bold","data":[{"name":"text","data":"b"}]},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"，Δ"},{"name":"italic","data":[{"name":"bold","data":[{"name":"text","data":"l"}]},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"("},{"name":"italic","data":[{"name":"text","data":"i"}]},{"name":"text","data":"=1，2，3)3个误差矢量，现以支链1为对象，分析上述Δ"},{"name":"italic","data":[{"name":"bold","data":[{"name":"text","data":"a"}]}]},{"name":"sub","data":[{"name":"text","data":"1"}]},{"name":"text","data":"，Δ"},{"name":"italic","data":[{"name":"bold","data":[{"name":"text","data":"b"}]}]},{"name":"sub","data":[{"name":"text","data":"1"}]},{"name":"text","data":"，Δ"},{"name":"italic","data":[{"name":"bold","data":[{"name":"text","data":"l"}]}]},{"name":"sub","data":[{"name":"text","data":"1"}]},{"name":"text","data":"3个误差源对机械臂的运动平台输出误差影响规律。为了逐一量化分析某一误差源的单独影响，在计算时令其余各误差源数值均为0，被分析对象的误差源矢量绝对值‖Δ"},{"name":"italic","data":[{"name":"bold","data":[{"name":"text","data":"a"}]}]},{"name":"sub","data":[{"name":"text","data":"1"}]},{"name":"text","data":"‖，‖Δ"},{"name":"italic","data":[{"name":"bold","data":[{"name":"text","data":"b"}]}]},{"name":"sub","data":[{"name":"text","data":"1"}]},{"name":"text","data":"‖，‖Δ"},{"name":"italic","data":[{"name":"bold","data":[{"name":"text","data":"l"}]}]},{"name":"sub","data":[{"name":"text","data":"1"}]},{"name":"text","data":"‖从0.001~0.01 mm变化时，机械臂的运动平台输出位置误差和姿态误差矢量的绝对值变化规律，如"},{"name":"xref","data":{"text":"图 3","type":"fig","rid":"Figure3","data":[{"name":"text","data":"图 3"}]}},{"name":"text","data":"所示。"}]},{"name":"fig","data":{"id":"Figure3","caption":[{"lang":"zh","label":[{"name":"text","data":"图3"}],"title":[{"name":"text","data":"机械臂的误差源与输出误差关系曲线"}]},{"lang":"en","label":[{"name":"text","data":"Fig 3"}],"title":[{"name":"text","data":"Relation curves between error sources and output errors of manipulator"}]}],"subcaption":[],"note":[],"graphics":[{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1711164&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1711164&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1711164&type=middle"}]}},{"name":"p","data":[{"name":"text","data":"在"},{"name":"xref","data":{"text":"图 3","type":"fig","rid":"Figure3","data":[{"name":"text","data":"图 3"}]}},{"name":"text","data":"中可知，随着‖Δ"},{"name":"italic","data":[{"name":"bold","data":[{"name":"text","data":"a"}]}]},{"name":"sub","data":[{"name":"text","data":"1"}]},{"name":"text","data":"‖和‖Δ"},{"name":"italic","data":[{"name":"bold","data":[{"name":"text","data":"b"}]}]},{"name":"sub","data":[{"name":"text","data":"1"}]},{"name":"text","data":"‖从0.001 m增加到0.01 mm，‖Δ"},{"name":"italic","data":[{"name":"bold","data":[{"name":"text","data":"p"}]}]},{"name":"sub","data":[{"name":"italic","data":[{"name":"text","data":"O"}]},{"name":"text","data":"′"}]},{"name":"text","data":"‖和‖Δ"},{"name":"italic","data":[{"name":"bold","data":[{"name":"text","data":"φ"}]}]},{"name":"sub","data":[{"name":"italic","data":[{"name":"text","data":"O"}]},{"name":"text","data":"′"}]},{"name":"text","data":"‖均呈现波动方式迅速增大，这说明误差源Δ"},{"name":"italic","data":[{"name":"bold","data":[{"name":"text","data":"a"}]},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"和Δ"},{"name":"italic","data":[{"name":"bold","data":[{"name":"text","data":"b"}]},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"("},{"name":"italic","data":[{"name":"text","data":"i"}]},{"name":"text","data":"=1，2，3)对机械臂的运动平台输出误差影响相对较大；随着‖Δ"},{"name":"italic","data":[{"name":"bold","data":[{"name":"text","data":"l"}]},{"name":"text","data":"B"}]},{"name":"sub","data":[{"name":"text","data":"1"}]},{"name":"text","data":"‖从0.001 m增加到0.01 mm，‖Δ"},{"name":"italic","data":[{"name":"bold","data":[{"name":"text","data":"p"}]}]},{"name":"sub","data":[{"name":"italic","data":[{"name":"text","data":"O"}]},{"name":"text","data":"′"}]},{"name":"text","data":"‖和‖Δ"},{"name":"italic","data":[{"name":"bold","data":[{"name":"text","data":"φ"}]}]},{"name":"sub","data":[{"name":"italic","data":[{"name":"text","data":"O"}]},{"name":"text","data":"′"}]},{"name":"text","data":"‖均以较为平稳的曲线缓慢增大，这说明误差源Δ"},{"name":"italic","data":[{"name":"bold","data":[{"name":"text","data":"l"}]},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"("},{"name":"italic","data":[{"name":"text","data":"i"}]},{"name":"text","data":"=1，2，3)对机械臂的运动平台输出误差影响相对较小。"}]},{"name":"p","data":[{"name":"text","data":"如果想使机械臂在具有较高精度的条件下尽量降低配合零部件的加工成本，需要将驱动移动副滑轨、万向副的机械零件选择较高的精度等级和较小的配合公差，而套筒移动副机械零件的精度等级可以适当降低且配合公差可以适当增大。"}]}]},{"name":"sec","data":[{"name":"sectitle","data":{"label":[{"name":"text","data":"3.2"}],"title":[{"name":"text","data":"机械臂的主要配合零件精度等级及配合公差"}],"level":"2","id":"s4-2"}},{"name":"p","data":[{"name":"text","data":"机械臂的主要运动副配合关系主要有：固定平台驱动移动副滑轨的丝杠轴与轴承及轴承座配合、万向副的十字轴与对应轴承及轴承孔配合、套筒移动副丝杠轴与轴承及轴承座配合、套筒移动副的防轴向旋转导向杆与丝杠螺母总成导向孔的轴承配合、伸缩杆与套筒端盖导向孔轴承配合、球面副球轴承与轴配合。因为各伺服电机驱动的同步带轮均采用顶丝或键实现周向锁定，故不考虑其配合。基于前文误差分析揭示的各误差源对机械臂的运动平台输出误差影响规律，在保证机械臂有较高精度的同时，尽量降低加工精度等级以降低加工制造成本，制定了机械臂的各配合关系精度等级及配合公差，如"},{"name":"xref","data":{"text":"表 1","type":"table","rid":"Table1","data":[{"name":"text","data":"表 1"}]}},{"name":"text","data":"所示。"}]},{"name":"table","data":{"id":"Table1","caption":[{"lang":"zh","label":[{"name":"text","data":"表1"}],"title":[{"name":"text","data":"机械臂的配合精度等级及公差"}]},{"lang":"en","label":[{"name":"text","data":"Table 1"}],"title":[{"name":"text","data":"Accuracy class and tolerances of manipulator"}]}],"note":[],"table":[{"head":[[{"style":"class:table_top_border","data":[{"name":"text","data":"配合关系"}]},{"style":"class:table_top_border","data":[{"name":"text","data":"精度等级"}]},{"style":"class:table_top_border","data":[{"name":"text","data":"配合公差/mm"}]}]],"body":[[{"style":"class:table_top_border2","data":[{"name":"text","data":"固定平台移动滑轨丝杠轴与轴承"}]},{"style":"class:table_top_border2","data":[{"name":"text","data":"IT6"}]},{"style":"class:table_top_border2","data":[{"name":"inlineformula","data":[{"name":"math","data":{"graphicsData":{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1711226&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1711226&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1711226&type=middle"}}}]}]}],[{"data":[{"name":"text","data":"万向副十字轴与轴承"}]},{"data":[{"name":"text","data":"IT6"}]},{"data":[{"name":"inlineformula","data":[{"name":"math","data":{"graphicsData":{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1711245&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1711245&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1711245&type=middle"}}}]}]}],[{"data":[{"name":"text","data":"套筒移动副丝杠轴与轴承"}]},{"data":[{"name":"text","data":"IT7"}]},{"data":[{"name":"inlineformula","data":[{"name":"math","data":{"graphicsData":{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1711263&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1711263&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1711263&type=middle"}}}]}]}],[{"data":[{"name":"text","data":"套筒移动副导向杆与丝杠螺母导向轴承"}]},{"data":[{"name":"text","data":"IT8"}]},{"data":[{"name":"inlineformula","data":[{"name":"math","data":{"graphicsData":{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1711283&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1711283&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1711283&type=middle"}}}]}]}],[{"data":[{"name":"text","data":"伸缩杆与套筒端盖导向孔轴承"}]},{"data":[{"name":"text","data":"IT9"}]},{"data":[{"name":"inlineformula","data":[{"name":"math","data":{"graphicsData":{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1711305&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1711305&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1711305&type=middle"}}}]}]}],[{"style":"class:table_bottom_border","data":[{"name":"text","data":"球面副球轴承与轴"}]},{"style":"class:table_bottom_border","data":[{"name":"text","data":"IT8"}]},{"style":"class:table_bottom_border","data":[{"name":"inlineformula","data":[{"name":"math","data":{"graphicsData":{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1711327&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1711327&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1711327&type=middle"}}}]}]}]],"foot":[]}]}}]},{"name":"sec","data":[{"name":"sectitle","data":{"label":[{"name":"text","data":"3.3"}],"title":[{"name":"text","data":"机械臂的实验样机的研制"}],"level":"2","id":"s4-3"}},{"name":"p","data":[{"name":"text","data":"基于前文给定的机械臂各结构参数尺寸，采用"},{"name":"xref","data":{"text":"表 1","type":"table","rid":"Table1","data":[{"name":"text","data":"表 1"}]}},{"name":"text","data":"中所列各精度等级及配合公差，加工制造出机械臂的零部件并进行装配，研制出超冗余变胞机械臂的实验样机，如"},{"name":"xref","data":{"text":"图 4","type":"fig","rid":"Figure4","data":[{"name":"text","data":"图 4"}]}},{"name":"text","data":"所示。"}]},{"name":"fig","data":{"id":"Figure4","caption":[{"lang":"zh","label":[{"name":"text","data":"图4"}],"title":[{"name":"text","data":"机械臂实验样机图"}]},{"lang":"en","label":[{"name":"text","data":"Fig 4"}],"title":[{"name":"text","data":"Experimental prototype of manipulator"}]}],"subcaption":[],"note":[],"graphics":[{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1711183&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1711183&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1711183&type=middle"}]}}]}]},{"name":"sec","data":[{"name":"sectitle","data":{"label":[{"name":"text","data":"4"}],"title":[{"name":"text","data":"机械臂实验样机的误差实验"}],"level":"1","id":"s5"}},{"name":"p","data":[{"name":"text","data":"为了验证"},{"name":"xref","data":{"text":"图 4","type":"fig","rid":"Figure4","data":[{"name":"text","data":"图 4"}]}},{"name":"text","data":"所示的机械臂实验样机运动平台在空间的位置、姿态定位能力，通过一套高精度的专用工业机器人标定系统ABBIRB2600C对其进行位姿测量。具体测量方法为：首先，将机械臂实验样机固定平台朝下、运动平台朝上倒置固定在测量基座上；接着，将高精度标定用工业机器人ABB IRB2600C的测量手腕与机械臂实验样机的运动平台连接在一起，让ABB机器人的测量手腕跟随机械臂的运动平台运动，并将ABB机器人设定为随动测量模式；然后，让机械臂的实验样机在空间6个测试点做30次重复位姿定位运动，并通过ABB机器人测量机械臂的运动平台在每个测试点实际位姿数据；最后，将每个测试点的30次实测位姿数据求解平均值并与对应点的理论位姿数据相减求出机械臂在各测试点的位置、姿态误差值。6个测试点的位置、姿态坐标，如"},{"name":"xref","data":{"text":"表 2","type":"table","rid":"Table2","data":[{"name":"text","data":"表 2"}]}},{"name":"text","data":"所示。"}]},{"name":"table","data":{"id":"Table2","caption":[{"lang":"zh","label":[{"name":"text","data":"表2"}],"title":[{"name":"text","data":"机械臂的实验测试点位姿坐标"}]},{"lang":"en","label":[{"name":"text","data":"Table 2"}],"title":[{"name":"text","data":"Experimental test point coordinate of manipulator"}]}],"note":[],"table":[{"head":[[{"rowspan":"2","style":"class:table_top_border","data":[{"name":"text","data":"测试点编号"}]},{"colspan":"6","style":"class:table_top_border","data":[{"name":"text","data":"位置、姿态坐标"}]}],[{"style":"class:table_top_border2","data":[{"name":"italic","data":[{"name":"text","data":"X"}]},{"name":"text","data":"/mm"}]},{"style":"class:table_top_border2","data":[{"name":"italic","data":[{"name":"text","data":"Y"}]},{"name":"text","data":"/mm"}]},{"style":"class:table_top_border2","data":[{"name":"italic","data":[{"name":"text","data":"Z"}]},{"name":"text","data":"/mm"}]},{"style":"class:table_top_border2","data":[{"name":"italic","data":[{"name":"text","data":"α"}]},{"name":"text","data":"/(°)"}]},{"style":"class:table_top_border2","data":[{"name":"italic","data":[{"name":"text","data":"β"}]},{"name":"text","data":"/(°)"}]},{"style":"class:table_top_border2","data":[{"name":"italic","data":[{"name":"text","data":"γ"}]},{"name":"text","data":"/(°)"}]}]],"body":[[{"style":"class:table_top_border2","data":[{"name":"text","data":"PE1"}]},{"style":"class:table_top_border2","data":[{"name":"text","data":"0"}]},{"style":"class:table_top_border2","data":[{"name":"text","data":"0"}]},{"style":"class:table_top_border2","data":[{"name":"text","data":"1 300"}]},{"style":"class:table_top_border2","data":[{"name":"text","data":"0"}]},{"style":"class:table_top_border2","data":[{"name":"text","data":"0"}]},{"style":"class:table_top_border2","data":[{"name":"text","data":"0"}]}],[{"data":[{"name":"text","data":"PE2"}]},{"data":[{"name":"text","data":"500"}]},{"data":[{"name":"text","data":"500"}]},{"data":[{"name":"text","data":"1 200"}]},{"data":[{"name":"text","data":"15"}]},{"data":[{"name":"text","data":"15"}]},{"data":[{"name":"text","data":"35"}]}],[{"data":[{"name":"text","data":"PE3"}]},{"data":[{"name":"text","data":"-500"}]},{"data":[{"name":"text","data":"-500"}]},{"data":[{"name":"text","data":"1 200"}]},{"data":[{"name":"text","data":"-15"}]},{"data":[{"name":"text","data":"-15"}]},{"data":[{"name":"text","data":"-35"}]}],[{"data":[{"name":"text","data":"PE4"}]},{"data":[{"name":"text","data":"500"}]},{"data":[{"name":"text","data":"-500"}]},{"data":[{"name":"text","data":"1 200"}]},{"data":[{"name":"text","data":"15"}]},{"data":[{"name":"text","data":"15"}]},{"data":[{"name":"text","data":"35"}]}],[{"data":[{"name":"text","data":"PE5"}]},{"data":[{"name":"text","data":"-500"}]},{"data":[{"name":"text","data":"500"}]},{"data":[{"name":"text","data":"1 200"}]},{"data":[{"name":"text","data":"-15"}]},{"data":[{"name":"text","data":"-15"}]},{"data":[{"name":"text","data":"-35"}]}],[{"style":"class:table_bottom_border","data":[{"name":"text","data":"PE6"}]},{"style":"class:table_bottom_border","data":[{"name":"text","data":"0"}]},{"style":"class:table_bottom_border","data":[{"name":"text","data":"0"}]},{"style":"class:table_bottom_border","data":[{"name":"text","data":"1 500"}]},{"style":"class:table_bottom_border","data":[{"name":"text","data":"10"}]},{"style":"class:table_bottom_border","data":[{"name":"text","data":"10"}]},{"style":"class:table_bottom_border","data":[{"name":"text","data":"-30"}]}]],"foot":[]}]}},{"name":"p","data":[{"name":"text","data":"在测量过程中，让机械臂实验样机按照"},{"name":"xref","data":{"text":"表 2","type":"table","rid":"Table2","data":[{"name":"text","data":"表 2"}]}},{"name":"text","data":"中PE1-PE6的顺序反复定位30次，并通过ABB机器人进行测量统计，测量过程如"},{"name":"xref","data":{"text":"图 5","type":"fig","rid":"Figure5","data":[{"name":"text","data":"图 5"}]}},{"name":"text","data":"所示。"}]},{"name":"fig","data":{"id":"Figure5","caption":[{"lang":"zh","label":[{"name":"text","data":"图5"}],"title":[{"name":"text","data":"ABB机器人对机械臂的位姿测量实验"}]},{"lang":"en","label":[{"name":"text","data":"Fig 5"}],"title":[{"name":"text","data":"Pose measurement experiment of the manipulator with ABB robot"}]}],"subcaption":[],"note":[],"graphics":[{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1711203&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1711203&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1711203&type=middle"}]}},{"name":"p","data":[{"name":"text","data":"经过对"},{"name":"xref","data":{"text":"图 5","type":"fig","rid":"Figure5","data":[{"name":"text","data":"图 5"}]}},{"name":"text","data":"中测量数据的统计计算，得到机械臂的运动平台在每个测试点的位置、姿态误差数值，如"},{"name":"xref","data":{"text":"表 3","type":"table","rid":"Table3","data":[{"name":"text","data":"表 3"}]}},{"name":"text","data":"所示。"}]},{"name":"table","data":{"id":"Table3","caption":[{"lang":"zh","label":[{"name":"text","data":"表3"}],"title":[{"name":"text","data":"采用ABB机器人对机械臂的位姿测量偏差"}]},{"lang":"en","label":[{"name":"text","data":"Table 3"}],"title":[{"name":"text","data":"Pose errors of manipulator pose test points with ABB robot"}]}],"note":[],"table":[{"head":[[{"rowspan":"2","style":"class:table_top_border","data":[{"name":"text","data":"测试点编号"}]},{"colspan":"6","style":"class:table_top_border","data":[{"name":"text","data":"位置、姿态坐标"}]}],[{"style":"class:table_top_border2","data":[{"name":"text","data":"Δ"},{"name":"italic","data":[{"name":"text","data":"X"}]},{"name":"text","data":"/mm"}]},{"style":"class:table_top_border2","data":[{"name":"text","data":"Δ"},{"name":"italic","data":[{"name":"text","data":"Y"}]},{"name":"text","data":"/mm"}]},{"style":"class:table_top_border2","data":[{"name":"text","data":"Δ"},{"name":"italic","data":[{"name":"text","data":"Z"}]},{"name":"text","data":"/mm"}]},{"style":"class:table_top_border2","data":[{"name":"text","data":"Δ"},{"name":"italic","data":[{"name":"text","data":"α"}]},{"name":"text","data":"/(°)"}]},{"style":"class:table_top_border2","data":[{"name":"text","data":"Δ"},{"name":"italic","data":[{"name":"text","data":"β"}]},{"name":"text","data":"/(°)"}]},{"style":"class:table_top_border2","data":[{"name":"text","data":"Δ"},{"name":"italic","data":[{"name":"text","data":"γ"}]},{"name":"text","data":"/(°)"}]}]],"body":[[{"style":"class:table_top_border2","data":[{"name":"italic","data":[{"name":"text","data":"PE"}]},{"name":"text","data":"1"}]},{"style":"class:table_top_border2","data":[{"name":"text","data":"0.006"}]},{"style":"class:table_top_border2","data":[{"name":"text","data":"0.010"}]},{"style":"class:table_top_border2","data":[{"name":"text","data":"0.005"}]},{"style":"class:table_top_border2","data":[{"name":"text","data":"0.018"}]},{"style":"class:table_top_border2","data":[{"name":"text","data":"0.016"}]},{"style":"class:table_top_border2","data":[{"name":"text","data":"0.011"}]}],[{"data":[{"name":"italic","data":[{"name":"text","data":"PE"}]},{"name":"text","data":"2"}]},{"data":[{"name":"text","data":"0.018"}]},{"data":[{"name":"text","data":"0.020"}]},{"data":[{"name":"text","data":"0.016"}]},{"data":[{"name":"text","data":"0.021"}]},{"data":[{"name":"text","data":"0.026"}]},{"data":[{"name":"text","data":"0.031"}]}],[{"data":[{"name":"italic","data":[{"name":"text","data":"PE"}]},{"name":"text","data":"3"}]},{"data":[{"name":"text","data":"0.036"}]},{"data":[{"name":"text","data":"0.032"}]},{"data":[{"name":"text","data":"0.038"}]},{"data":[{"name":"text","data":"0.040"}]},{"data":[{"name":"text","data":"0.041"}]},{"data":[{"name":"text","data":"0.033"}]}],[{"data":[{"name":"italic","data":[{"name":"text","data":"PE"}]},{"name":"text","data":"4"}]},{"data":[{"name":"text","data":"0.021"}]},{"data":[{"name":"text","data":"0.023"}]},{"data":[{"name":"text","data":"0.019"}]},{"data":[{"name":"text","data":"0.026"}]},{"data":[{"name":"text","data":"0.020"}]},{"data":[{"name":"text","data":"0.030"}]}],[{"data":[{"name":"italic","data":[{"name":"text","data":"PE"}]},{"name":"text","data":"5"}]},{"data":[{"name":"text","data":"0.037"}]},{"data":[{"name":"text","data":"0.032"}]},{"data":[{"name":"text","data":"0.037"}]},{"data":[{"name":"text","data":"0.032"}]},{"data":[{"name":"text","data":"0.040"}]},{"data":[{"name":"text","data":"0.044"}]}],[{"style":"class:table_bottom_border","data":[{"name":"italic","data":[{"name":"text","data":"PE"}]},{"name":"text","data":"6"}]},{"style":"class:table_bottom_border","data":[{"name":"text","data":"0.010"}]},{"style":"class:table_bottom_border","data":[{"name":"text","data":"0.009"}]},{"style":"class:table_bottom_border","data":[{"name":"text","data":"0.007"}]},{"style":"class:table_bottom_border","data":[{"name":"text","data":"0.010"}]},{"style":"class:table_bottom_border","data":[{"name":"text","data":"0.013"}]},{"style":"class:table_bottom_border","data":[{"name":"text","data":"0.011"}]}]],"foot":[]}]}},{"name":"p","data":[{"name":"text","data":"通过"},{"name":"xref","data":{"text":"表 3","type":"table","rid":"Table3","data":[{"name":"text","data":"表 3"}]}},{"name":"text","data":"的测量数据可知，机械臂实验样机的运动平台在测试点定位时位置误差均小于0.04 mm，姿态误差均小于0.045°，基本达到了同样尺寸级别的通用工业机器人精度水平。"}]}]},{"name":"sec","data":[{"name":"sectitle","data":{"label":[{"name":"text","data":"5"}],"title":[{"name":"text","data":"结论"}],"level":"1","id":"s6"}},{"name":"p","data":[{"name":"text","data":"提出了一种基于3-PUPS机构的超冗余并联机械臂，通过对机械臂的各伺服电机抱闸的组合锁定实现机械臂的变胞变换，从而使机械臂在不同的任务用途具有不同的机构学性能。采用矢量闭环回路法，对机械臂3-PUPS机构进行了误差建模，推导出机械臂的各运动副关节误差源输入误差和运动平台输出误差之间的传递方程。通过单独分析各误差源的误差数值变化对机械臂的运动平台输出误差影响，建立了各误差源与机械臂的输出误差之间关系曲线，表明：固定平台移动副滑轨误差、万向副误差对机械臂的输出误差影响较大，各支链末端球面副的位置误差对机械臂的输出误差影响较小。以误差分析为依据，确定了机械臂的主要配合零件加工精度等级及配合公差数值，并研制出机械臂的实验样机。通过一套专用工业机器人位姿测量系统对机械臂实验样机进行了位姿测量实验，表明：机械臂实验样机在测试点的位置误差均小于0.04 mm，姿态误差均小于0.045°，基本达到了同样尺寸级别的通用工业机器人精度水平。"}]}]}],"footnote":[],"reflist":{"title":[{"name":"text","data":"参考文献"}],"data":[{"id":"b1","label":"1","citation":[{"lang":"zh","text":[{"name":"text","data":"熊有伦.智能制造[J].科技导报, 2013, 31(10):3."}]},{"lang":"en","text":[{"name":"text","data":"XIONG Y L. Intelligent manufacturing[J]."},{"name":"italic","data":[{"name":"text","data":"Science and Technology Review"}]},{"name":"text","data":", 2013, 31(10):3. (in Chinese)"}]}]},{"id":"b2","label":"2","citation":[{"lang":"zh","text":[{"name":"text","data":"蔡鹤皋.对我国机器人产业发展的思考[J].集成技术, 2015, 4(5):1-4."}]},{"lang":"en","text":[{"name":"text","data":"CAI H G. Thoughts on the development of China's robot industry[J]."},{"name":"italic","data":[{"name":"text","data":"Integration Technology"}]},{"name":"text","data":", 2015, 4(5):1-4. (in Chinese)"}]}]},{"id":"b3","label":"3","citation":[{"lang":"zh","text":[{"name":"text","data":"黄田, 陈闯, 王辉.一种新型并联动力头动力学参数辨识方法研究[J].机械工程学报, 2013, 49(19):31-39."}]},{"lang":"en","text":[{"name":"text","data":"HUANG T, CHEN CH, WANG H. Identification of dynamic parameters of a novel 3-DOF spindle head[J]."},{"name":"italic","data":[{"name":"text","data":"Journal of Mechanical Engineering"}]},{"name":"text","data":", 2013, 49(19):31-39. (in Chinese)"}]}]},{"id":"b4","label":"4","citation":[{"lang":"zh","text":[{"name":"text","data":"田士涛, 吴清文, 贺帅.空间机械臂锁紧机构等效线性化分析及验证[J].光学 精密工程, 2016, 24(3):590-599."}]},{"lang":"en","text":[{"name":"text","data":"TIAN SH T, WU Q W, HE SH. Linear analysis and practical tests of fixation mechanisms in space robotic arm[J]."},{"name":"italic","data":[{"name":"text","data":"Opt. Precision Eng"}]},{"name":"text","data":"., 2016, 24(3):590-599. (in Chinese)"}]}]},{"id":"b5","label":"5","citation":[{"lang":"zh","text":[{"name":"text","data":"姜力, 周扬, 孙奎.七自由度冗余机械臂避障控制[J].光学 精密工程, 2013, 21(7):1795-1802."}]},{"lang":"en","text":[{"name":"text","data":"JIANG L, ZHOU Y, SUN K. Obstacle avoidance control for 7-DOF redundant manipulators[J]."},{"name":"italic","data":[{"name":"text","data":"Opt. Precision Eng"}]},{"name":"text","data":"., 2013, 21(7):1795-1802. (in Chinese)"}]}]},{"id":"b6","label":"6","citation":[{"lang":"en","text":[{"name":"text","data":"JAIME G A, ALBERT B S, EDUARDO C C. An application of screw theory to the kinematic analysis of a Delta-type robot[J]."},{"name":"italic","data":[{"name":"text","data":"Journal of Mechanical Science and Technology"}]},{"name":"text","data":", 2014, 28(9):3785-3792."}]}]},{"id":"b7","label":"7","citation":[{"lang":"zh","text":[{"name":"text","data":"黄田, 李亚, 李思维.一种三自由度并联机构几何误差建模、灵敏度分析及装配工艺设计[J].中国科学, 2002, 32(5):628-635."}]},{"lang":"en","text":[{"name":"text","data":"HUANG T, LI Y, LI S W. Criteria for conceptual design of reconfigurable PKM modules theory and application[J]."},{"name":"italic","data":[{"name":"text","data":"Science in China, Ser.E"}]},{"name":"text","data":", 2002, 32(5):628-635. (in Chinese)"}]}]},{"id":"b8","label":"8","citation":[{"lang":"zh","text":[{"name":"text","data":"刘海涛, 黄田. 5自由度大工作空间/支链行程比混联机械手的概念设计与尺度综合[J].机械工程学报, 2007, 43(6):14-20."}]},{"lang":"en","text":[{"name":"text","data":"LIU H T, HUANG T. Kinematic design of 5-DOF hybrid robot with large workspace/limb stroke ratio[J]."},{"name":"italic","data":[{"name":"text","data":"Journal of Mechanical Engineering"}]},{"name":"text","data":", 2007, 43(6):14-20. (in Chinese)"}]}]},{"id":"b9","label":"9","citation":[{"lang":"zh","text":[{"name":"text","data":"李彬, 黄田, 刘海涛. Exechon混联机器人的三自由度并联机构模块位置分析[J].中国机械工程, 2010, 21(11):2785-2789."}]},{"lang":"en","text":[{"name":"text","data":"LI B, HUANG T, LIU H T. Position analysis of a 3-DOF PKM module for a 5-DOF hybrid robot exechon[J]."},{"name":"italic","data":[{"name":"text","data":"China Mechanical Engineering"}]},{"name":"text","data":", 2010, 21(11):2785-2789. (in Chinese)"}]}]},{"id":"b10","label":"10","citation":[{"lang":"zh","text":[{"name":"text","data":"李曚. 可重构混联机械手模块TriVariant的设计理论与方法[D]. 天津: 天津大学, 2005: 29-55."},{"name":"uri","data":{"text":[{"name":"text","data":"http://cdmd.cnki.com.cn/article/cdmd-10056-2006050010.htm"}]}}]},{"lang":"en","text":[{"name":"text","data":"LI M. "},{"name":"italic","data":[{"name":"text","data":"Design Theory and Methodology of the TriVariant a"}]},{"name":"text","data":" 5-"},{"name":"italic","data":[{"name":"text","data":"DOF Reconfigurable PKM Module"}]},{"name":"text","data":"[D]. Tianjin: Tianjin University, 2005: 29-55. (in Chinese)"}]}]},{"id":"b11","label":"11","citation":[{"lang":"zh","text":[{"name":"text","data":"刘海涛. 少自由度机器人机构一体化建模理论、方法及工程应用[D]. 天津: 天津大学, 2010: 3-87."},{"name":"uri","data":{"text":[{"name":"text","data":"http://www.wanfangdata.com.cn/details/detail.do?_type=degree&id=Y1874715"}]}}]},{"lang":"en","text":[{"name":"text","data":"LIU H T. "},{"name":"italic","data":[{"name":"text","data":"Unified Parameter Modeling of Lower Mobility Robotic Manupulators"}]},{"name":"text","data":": "},{"name":"italic","data":[{"name":"text","data":"Theory"}]},{"name":"text","data":", "},{"name":"italic","data":[{"name":"text","data":"Methodology and Application"}]},{"name":"text","data":"[D]. Tianjin: Tianjin University, 2010: 3-87. (in Chinese)"}]}]},{"id":"b12","label":"12","citation":[{"lang":"zh","text":[{"name":"text","data":"李研彪, 金振林, 计时鸣.一种新型3-DOF串并混联拟人机械臂的研制[J].中国科学E辑:技术科学, 2009, 39(12):1983-1991."}]},{"lang":"en","text":[{"name":"text","data":"LI Y B, JIN ZH L, JI SH M. Design of a novel 3-DOF hybrid mechanical arm[J]."},{"name":"italic","data":[{"name":"text","data":"Sci China Ser E-Tech Sci"}]},{"name":"text","data":", 2009, 52(12):3592-3600. (in Chinese)"}]}]},{"id":"b13","label":"13","citation":[{"lang":"zh","text":[{"name":"text","data":"李研彪. 新型6-DOF串并混联拟人机械臂的性能分析与设计[D]. 秦皇岛: 燕山大学, 2009: 17-37."},{"name":"uri","data":{"text":[{"name":"text","data":"http://cdmd.cnki.com.cn/Article/CDMD-10216-2010018445.htm"}]}}]},{"lang":"en","text":[{"name":"text","data":"LI Y B. "},{"name":"italic","data":[{"name":"text","data":"Analysis and Design of a Novel"}]},{"name":"text","data":" 6-"},{"name":"italic","data":[{"name":"text","data":"DOF Hybrid Mechanical Arm"}]},{"name":"text","data":"[D]. Qinhuangdao: Yanshan University, 2009: 17-37. (in Chinese)"}]}]},{"id":"b14","label":"14","citation":[{"lang":"zh","text":[{"name":"text","data":"金振林, 曹舜, 高峰.新型机器人肩关节及其运动学分析[J].中国机械工程, 2009, 20(14):1639-1642."}]},{"lang":"en","text":[{"name":"text","data":"JIN ZH L, CAO SH, GAO F. Arc spline tool path generation for triangular mesh surface machining[J]."},{"name":"italic","data":[{"name":"text","data":"China Mechanical Engineering"}]},{"name":"text","data":", 2009, 20(14):1639-1642. (in Chinese)"}]}]},{"id":"b15","label":"15","citation":[{"lang":"zh","text":[{"name":"text","data":"李研彪, 金振林, 计时鸣.一种并联结构拟人肩关节的误差分析[J].应用基础与工程科学学报, 2009, 17(3):446-451."}]},{"lang":"en","text":[{"name":"text","data":"LI Y B, JIN ZH L, JI SH M. Error analysis of a parallel anthropopathic shoulder[J]."},{"name":"italic","data":[{"name":"text","data":"China Mechanical Engineering"}]},{"name":"text","data":", 2009, 17(3):446-451. (in Chinese)"}]}]},{"id":"b16","label":"16","citation":[{"lang":"zh","text":[{"name":"text","data":"王跃灵, 金振林, 李研彪.球面3-RRR并联机构动力学建模与鲁棒-自适应迭代学习控制[J].机械工程学报, 2010, 46(1):68-73."}]},{"lang":"en","text":[{"name":"text","data":"WANG Y L, JIN ZH L, LI Y B. Dynamic modeling and robust-adaptive iterative learning control of 3-rrr spherical parallel mechanism[J]"},{"name":"italic","data":[{"name":"text","data":". Journal of Mechanical Engineering"}]},{"name":"text","data":", 2010, 46(1):68-73. (in Chinese)"}]}]},{"id":"b17","label":"17","citation":[{"lang":"zh","text":[{"name":"text","data":"秦利. 考虑重力效应的空间机器人系统建模与控制研究[D]. 秦皇岛: 燕山大学, 2014: 11-77."},{"name":"uri","data":{"text":[{"name":"text","data":"http://cdmd.cnki.com.cn/Article/CDMD-10216-1015009064.htm"}]}}]},{"lang":"en","text":[{"name":"text","data":"QIN L. "},{"name":"italic","data":[{"name":"text","data":"Research on Modeling and Control for Space Robot System with Gravity Effect Consideration"}]},{"name":"text","data":"[D]. Qinhuangdao: Yanshan University, 2014: 11-77. (in Chinese)"}]}]},{"id":"b18","label":"18","citation":[{"lang":"zh","text":[{"name":"text","data":"孟兆新, 肖定福, 尹航.并联式曲线送料平台机构误差补偿方法的研究[J].北京林业大学学报, 2016, 38(9):95-101."}]},{"lang":"en","text":[{"name":"text","data":"MENG ZH X, XIAO D F, YIN H. Mechanism error compensation method of parallel curve feeding platform[J]."},{"name":"italic","data":[{"name":"text","data":"Journal of Beijing Forestry University"}]},{"name":"text","data":", 2016, 38(9):95-101. (in Chinese)"}]}]},{"id":"b19","label":"19","citation":[{"lang":"en","text":[{"name":"text","data":"NZUE R M, BRETHE J F, VASSELIN E. Comparison of serial and parallel robot repeatability based on different performance criteria[J]."},{"name":"italic","data":[{"name":"text","data":"Mechanism and Machine Theory"}]},{"name":"text","data":", 2013, 40(7):136-155."}]}]},{"id":"b20","label":"20","citation":[{"lang":"zh","text":[{"name":"text","data":"侯雨雷, 段艳宾, 窦玉超. 65 m射电望远镜天线副面调整机构标定研究[J].中国机械工程, 2013, 24(12):3318-3328."}]},{"lang":"en","text":[{"name":"text","data":"HOU Y L, DUAN Y B, DOU Y CH. Calibration of adjusting mechanism for sub reflector of a 65 meters radio telescope[J]."},{"name":"italic","data":[{"name":"text","data":"China Mechanical Engineering"}]},{"name":"text","data":", 2013, 24(12):3318-3328. (in Chinese)"}]}]},{"id":"b21","label":"21","citation":[{"lang":"en","text":[{"name":"text","data":"CHANAL H, DUC E, HASCOET J Y. Reduction of a parallel kinematics machine tool inverse kinematics model with regard to machining behaviour[J]."},{"name":"italic","data":[{"name":"text","data":"Mechanism and Machine Theory"}]},{"name":"text","data":", 2009, 44(7):1371-1385."}]}]},{"id":"b22","label":"22","citation":[{"lang":"zh","text":[{"name":"text","data":"黄真, 赵永生, 赵铁石.高等空间机构学[M].北京:高等教育出版社, 2006:277-283."}]},{"lang":"en","text":[{"name":"text","data":"HUANG ZH, ZHAO Y SH, ZHAO T SH."},{"name":"italic","data":[{"name":"text","data":"Advanced Spatial Mechanism"}]},{"name":"text","data":"[M]. Beijing:Higher Education Press, 2006:277-283. (in Chinese)"}]}]},{"id":"b23","label":"23","citation":[{"lang":"zh","text":[{"name":"text","data":"曾达幸, 黄真.基于螺旋理论的转动解耦并联机构型综合[J].中国科学(E辑), 2011, 41(5):585-591."}]},{"lang":"en","text":[{"name":"text","data":"ZENG D X, HUANG Z. Type synthesis of the rotationaldecoupledparallel mechanism based on screwtheory[J]."},{"name":"italic","data":[{"name":"text","data":"Sci China Tech Sci"}]},{"name":"text","data":", 2011, 41(5):585-591.(in Chinese)"}]}]},{"id":"b24","label":"24","citation":[{"lang":"zh","text":[{"name":"text","data":"党鹏飞. 并联机床运动精度及参数辩识方法研究[D]. 沈阳: 东北大学, 2015: 1-17."},{"name":"uri","data":{"text":[{"name":"text","data":"http://www.wanfangdata.com.cn/details/detail.do?_type=degree&id=Y2996106"}]}}]},{"lang":"en","text":[{"name":"text","data":"DANG P F. "},{"name":"italic","data":[{"name":"text","data":"Research on the Kinematic Accuracy and Parameter Identification Method of Parallel Kinematic Machine"}]},{"name":"text","data":"[D]. Shenyang: Northeastern University, 2015: 1-17. (in Chinese)."}]}]}]},"response":[],"contributions":[],"acknowledgements":[],"conflict":[],"supportedby":[],"articlemeta":{"doi":"10.3788/OPE.20182607.1698","clc":[[{"name":"text","data":"TP242.6"}]],"dc":[],"publisherid":"gxjmgc-26-7-1698","citeme":[],"fundinggroup":[{"lang":"zh","text":[{"name":"text","data":"国家科技支撑计划资助项目（No.2015BAI06B01）；河北省高等学校科学技术研究青年基金资助项目（No.QN2015185，No.QN2018024）；秦皇岛市科技计划资助项目（No.201703A003）；河北科技师范学院博士启动基金资助项目（No.2015YB004）"}]}],"history":{"received":"2017-08-09","accepted":"2017-10-08","ppub":"2018-07-25","opub":"2020-06-16"},"copyright":{"data":[{"lang":"zh","data":[{"name":"text","data":"版权所有©《光学 精密工程》编辑部2018"}],"type":"copyright"},{"lang":"en","data":[{"name":"text","data":"Copyright ©2018 Optics and Precision Engineering. All rights reserved."}],"type":"copyright"}],"year":"2018"}},"appendix":[],"type":"research-article","ethics":[],"backSec":[],"supplementary":[],"journalTitle":"光学 精密工程","issue":"7","volume":"26","originalSource":[]}