机器人的运动学分析与模拟外文文献翻译、中英文翻译、外文翻译.doc
机器人的运动学分析与模拟外文文献翻译、中英文翻译、外文翻译
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附录一:机器人的运动学分析与模拟文摘:常见的方法,比如Denavit-Hartenberg方法,不能简单地用在特殊的机器人的运动分析与混合铰链很难获得这种方法的主要参数。因此,齐次变换理论来解决这个问题。首先,这种特殊结构的运动学特征分析的基础上闭链理论。在这样一个理论,闭链可以转换开连锁店,这使得它更容易分析这种结构。因此,它将成为更容易建立运动学方程,得到解决方案。然后,机器人模型可以建立Simmechanics与这些方程的解决方案。有必要设计一个机器人仿真的图形用户界面。之后,真正模型机器人和机器人将分别转移到一些空间点在同样的条件下。最后,所有数据将验证基于运动分析对比数据从模拟和真实的机器人。关键字：混合铰链结构 ，齐次变换，运动学分析，运动学仿真1 介绍 通常,我们使用Denavit-Hartenberg(d - h)方法来分析机器人的运动学。该方法的关键是建立一组d - h参数标明所有关节的坐标系的关系1。有很多研究串行链工业机器人,但是很少有研究在这样的工业机器人复杂的结构。例如,一种混合的大型通用工业机器人的铰链结构允许其在低能耗手臂向后移动。这个机器人的运动规律不同于其他机器人和d - h参数不能确定。提出了两个解决方案来处理这个特殊的结构。一是将结构转换为等效连续关节(关节转动或棱镜)。然后我们可以决定一个接一个的d - h参数基于d - h理论2。另一种是将闭链开连锁店,这样我们才能计算主动和被动关节之间的关系。然后,复杂结构转化为简单的串行结构3。第一种方法需要分析每一个共同的特点在这个混合的铰链,因此它是复杂和容易出错的4。同时,在第二个方法中,虽然一般理论分析介绍了所有封闭的链,分解结构不提出这个理论并不是由实验验证。考虑这两个方法,这将是容易确定关节的坐标系之间的关系如果我们知道的运动学特征的特殊结构。因此分析了特殊结构的运动特征基于封闭的开链理论。然后直接坐标系统建立在每个活动关节。该方法的优点是,它可以避免判断各运动副的运动结构5。此外,它方便构建下面提到的仿真模型。2 新型机器人的运动学特征图1显示了大型通用机器人ZX165U川崎公司。这种机器人可以保持它的平移运动人手端托盘包装。在这个过程中,更少的汽车工作,从而减少能源消耗。此外,阻尼器在基地是一个重要的组件在整个生产过程中保持对象的稳定和安全6。所有关节,除了联合2(JT2)在通常的机器人一样。在本文中,我们将只讨论旋转联合2如何影响整个机器人的运动学特征(7、8)。首先,我们从理论上分析了运动学特性的特殊结构。图2演示了一个混合系统组成的闭链结构。我是n链接和Li系统中某个midlink的名称。图2 b、c两种逻辑开链系统产生图2。这两个人造黄油的生产模式系统显示如下3,9。所有链接的闭链交叉与外部世界的决心(如L m和L m+4在图2)。然后所有并行链接连接到这些链接(L m和L m+4)发现。因此我们可以很容易地选择两个不同的路线(从L m到 L n),不存在并行链接的地方。最后,生成两个逻辑人造系统根据相应的选择路线。因此,所有静定链接存在于人造黄油的逻辑系统,如图所示。2 a,b。 图1工业机器人组成的混合铰链结构考虑到机器人的特点,我们正在研究,有完全8链接。所以n将等于8如果m等于1(见图2)。自由度(N)等于6(活动关节的数量)和被动关节(P)的数量等于3。我们假设主动关节变量的作为q A,i(i = 1、2 _,6)和被动关节的变量q P;j(j = 1、2、3)。在刚体动力学的理论基础和研究范围,刚性位移只是由六个主动关节完全10。相应的方程 (1)方程(1)显示了位移被动和主动关节之间的依赖关系,可以写成 (2) 还有其他两个几何约束。一个是链接L m +1是固定在底座上。另一个是封闭的链平行四边形结构。因此,从公式(2)我们可以获得 -q4 = -q5 = q3 = q2 （3） 即,Lm+1和Lm+2所做的一样。因此,机械手固定在连接Lm+5继续执行翻译一致。图3显示了机器人的仿真模型。只有联合2是仿真过程中旋转。图3显示了机器人的初始状态意味着所有关节的角度都是0。图3 b,c展示相应的机器人的状态当联合2 /4分别顺时针和逆时针方向移动。机械手保持平移运动,这与实际情况是一致的(见图3)。现在,我们可以得出结论,机器人执行平移运动的效应器,同时所有关节都是固定的,除了旋转接头2。 图2闭链系统和人造系统 图3机器人机械手的运动状态,只有JT2取数0，-/4,/43 运动学分析 运动学分析的目的是描述运动关节和效应器之间的关系。分析解决方案可以演示如何控制机器人运动,并建立动态方程和模型误差分析(11、12)。3.1正向运动学和齐次变换关节的位置和方向可以描述刚体坐标系统固定在关节10。所以我们建立坐标系统在每一个活动关节12。在图4中,ZX165U机器人的坐标系统。首先,建立了坐标系1,它伴随着基础坐标系0。为了方便起见,Z轴平行的轴旋转接头和Z轴的方向是由右手的旋转方向和固定的传统规则。第二个轴是完全符合一个特定轴在以前的坐标系统。最后一个轴是由右手规则了。尺寸参数坐标系统的图4所示,在Z1 - Z6与转动关节JT1-JT6 6是一致的, L1 = 670 mm, L3 = 1 100 mm,L4 = 270mm,L5 = 288mm,L6 = 1100mm,L7 = 228mm。根据齐次变换公式 （4） 我们可以获得所有矩阵:。字符“e”代表效应器协调;T指从坐标i-1到i之间的转换关系;D是指翻译向量从i-1到i之间的协调。在图4中,例如,坐标系统在那场1变化L 2距离,和转变L 1距离在2。然后逆时针方向旋转/2左右+ Y。然后它可以转化为协调2。转换矩阵 在T Y Z(左1)和T(左2)指翻译矩阵;L 1和L 2翻译长度沿相应的轴;R Y(h)是指旋转矩阵;h是逆时针方向旋转角的+Y。当其他矩阵计算,坐标变换矩阵的效应器基地协调获得(13、14)。正向运动学如下解决方案 图4 ZX165U齐次坐标系统Cji=(i+j),i,j=1,26。3.2逆运动学机器人逆运动学问题是计算所有相应的关节角度给出当机器人的姿态和位置13。换句话说,联合变量i(i=1,26)基于运动学方程可以确定如果值n,o,a,p和所需的几何参数是已知的14。方程(7)用于解决逆运动学方程。本文确定了前三个关节变量i(i=1,2,3)通过代数方法,和常见的逆变换方法15是用来确定最后三个联合变量i(i=4,5,6)。首先,只剩下1 h和其他变量是通过消去法消除Eq(16、17)。(7)等假设方程(11)替换回方程式。(8)和(9),那么情商。(12)。因此在方程式(10)和(11),双方的二次组件被添加在一起，整理得：方程(18)是情商的扣除双方乘以。(6)与所有从联合1 -联合3逆变换矩阵,所以我们得到以下方程:左边的一部分。(19)包含已知联合变量即。i,e、1、2和3,而另一侧包含联合变量4、5和6是解决。作为一个结果,解决单一的方案，5=04 仿真分析模型仿真可以验证运动学分析的正确性,并提供直观的理解和严格的数据(1、18)。机器人模型探讨了构建依赖MATLAB平台的强大功能。4.1工具箱和模型 有两个合格的需求(19、20)。第一个是建立一个精确的机器人模型。第二个是控制模型进行交流沟通的!模块数据基地,我们可以构建一个复杂的力学模型来实现机械结构的模拟。同时,司机和传感器模块连接Simmechanics的有效方法与仿真软件(21、22)。 如图5所示,该模型系统可以模拟系统控制的设计GUI。图所示。5,有六个活动关节,三个被动关节和三个固定关节。 图6显示了机器人的模块图(Kawasaki ZX165U)。 图5在Simmechanics生成模型 图6川崎ZX165U机器人的模块图 图7的GUI设计用于控制机器人模型包括以下功能设计GUI(见图7):(1) 控制仿真的过程;(2) (2)转发和审查关节角的信息;(3) (3)获得信息操纵者的姿势,然后保存数据。4.2.验证运动学分析 图8显示了真正的机器人ZX165U的照片。在实验中,机器人的效应器经过两种不同的方式,其中一个看起来像字母“W”而另一个看起来像一个“S”(参见无花果。9和10)。 图8机器人ZX165U的物理图像 图9 真实和模拟“W”路径 图10真实和模拟“S”路径ZX165U机器人可以驱动可及空间中任意点只要一组适当的值(联合角度或姿势)解决。在这个实验中,五组的数据点显示关节角度被放入控制器。然后控制器控制机器人通过这五个点线性插值(参见图9)和曲线插值(参见图10)。在这个过程中,机械手的姿势和位置可以在每一个对应点从教学吊坠。然后我们让机器人模型遵循虽然通过使用上述5点的相同的数据,但这一次我们使用GUI来输入数据。直观地,路径绘制在一个三维坐标系统只涉及到机器人的位置值,但不涉及姿势数据。保证10表示相反的。从图9和10可以明显看到,实际的路径匹配模拟路径在一定范围的小错误。这些小错误不能注意到,除非路径放大了许多倍。事实上,准确性已经接近0.02毫米,如表1和2所示。我们选择五套任意的数据流程上面,把所有的信息都在表格1中。表2显示了数据表明反向运动,以不同的方式获得。当真正的和仿真机器人移动到指定的姿势和位置相同,联合角度的数据将被记录下来。在表1和2中,“r -”和“s -”代表字分别“真实”和“模拟”。在表1中,模拟结果和实际结果之间的平均误差是0.0206毫米和0.037毫米的最大误差。具体来说,位置错误是0.0258毫米,0.0218毫米和0.0142毫米对应X,Y和z .这样的精度能满足任何工业需求。O,AandTstand X,Y,Z欧拉角,分别。此外,造成错误几乎可以忽略不计。实际上,我们永远不能看到机器人移动时由微小转移的距离。在表2中,平均误差是0.0011吗?通过粗略的计算错误的数据。没有JT4 5。这意味着模型机器人可以达到某个点在一个可接受的误差范围(小错误是不可知的)。正如在前一节中提到的,运动学分析是绝对正确的,可以通过数据的对比分析证明。5 结论分析和验证了运动学特征(平移运动)的一个新型机器人混合铰链结构。运动学分析的基础上,可以很容易地执行。然后建立了运动学方程,解决了用齐次变换理论。机器人模型建立运动学方程的解决方案可用于模拟和获得通过GUI设计的仿真数据。五组选择这些数据,进行了分析和比较。实际数据和仿真数据之间的误差计算分析。如表1和2所示,轻微的错误,这意味着仿真模型的完全可以满足实际的要求。此外,运动学分析的正确性证明的基础上适当的数据分析。本文希望为那些正在研究提供一些灵感或者去研究这种机器人混合铰链结构。表1的效应器的姿势从六个角度计算值(正向运动学)表2计算的6个关节角度的效应器姿势(反向运动)确认本研究重点科技项目支持的上海科委(批准号12111101004)。文献1. Bi LY, Liu LS (2012)基于模拟六轴机器人的设计和仿真。 Yang DH (ed）信息控制,自动化和机器人技术,133卷。施普林格,海德堡,页537 - 5442. Song T, He YY, Wang P et al (2013)系列工业机器人的运动学分析与混合铰链结构。 Mach Des Res 5:893. Fathi HG, Olivier C, Ruvinda G et al (2000)建模和控制设置点闭链机制:理论和实验。 IEEE Trans Control Syst Technol 8(8):8018154. Wang KS, Terje KL (1988)结构设计和机器人机械手的运动学。Robotica 6(4):2993095. Selig JM (2011）poin-tplane的几何约束刚体位移。 Acta Appl Math 116:1331556. Suguru A, Masahiro S (2006）人类与冗余自由度机器人手臂的运动:虚拟弹簧减震器假设解决伯恩斯坦的问题。IEEE机器人与自动化国际会议上提出,奥兰多,2006年5月7. Choi HB, Konno A, Uchiyama M (2009)封闭的四自由度并联机器人的运动学正解。 Int J Control Autom Syst 7(5):8588648. Pisla D, Gherman B, Vaida C et al (2012）五自由度混合并联机器人的运动学建模腹腔镜手术。 Robotica30(7):109511079. Gallardo-Alvarado J (2005)混合动力机械手的运动学螺旋理论的方法。Multibody Sys Dyn 14(3/4):34536610. Kuo SR, Yang YB (2013）刚体合格板理论的非线性结构分析涉及扭转操作。Eng Struct 47:21511. Wang ZY, Zhao ZQ, Pang ZF et al (2011)运动学分析和仿真的3自由度空间机器人机制由封闭的链。第二次国际会议上机械自动化和控制工程，2011年7月12. Wen GJ, Xu LH, He FL (2009）离线6自由度焊接机器人的运动学仿真。:9测量技术和机电一体化自动化国际会议上,张家界,2009年4月13. Xiao WL, Henning S, Torsten L et al (2011)封闭的逆运动学与奇点避免6 r机器人铣削。 Prod Eng Devel 5:10311014. Wu Y, Cheng LH, Fan GF et al (2014)6自由度搬运机器人的逆运动学解和优化。 Appl Mech Mater 635637:1355135915. Gao JR, Wang YZ, Chen ZP (2014)逆运动学的建模与仿真基于SimMechanics平面3 -RRR并联机器人。Adv Mater Res 898:51051316. Markus L (1994)应用程序一般消元法的机器人运动学。J Intell Rob Syst 11:10911617. Shi ZX, Ye MY, Luo YF et al (2011)分离的主要条款消除算法及其应用在5R机器人的逆运动学分析。:计算机科学国际会议和服务系统,南京,2011年6月18. Wang YS, Gai YX, Wu FY (2011)机器人运动学仿真系统基于开放GL。:IEEE会议机器人、自动化和机电一体化,青岛,2011年9月19. Phung AS, Malzahn J, Hoffmann F et al (2011)数据基于运动学模型的不同载荷的机械臂多灵活的链接。:IEEE机器人和仿生学国际会议上, Karon Beach, December 201120. Toz M, Kucuk S (2008)工业机器人机械手动力学仿真工具箱。Comput Appl Eng Educ18(2):31933021. Fatehi MH, Vali AR, Eghtesad M et al (2011)建模和控制3-PRS并联机器人和仿真基于SimMechanics MATLAB。:2号国际会议控制、仪表和自动化, Shiraz, December 201122. Dean-Leon E, Nair S, Knoll A (2012)使用的MATLAB工具箱为象征性的机器人动态建模用于控制设计。:IEEE机器人仿生学,国际会议上广州,2012年12月附录二:Kinematic analysis and simulation of a new-type robot with special structureAbstract Common methods, such as Denavit-Hartenberg(D-H) method, cannot be simply used in kinematic analysis of special robots with hybrid hinge as it is difficult to obtain the main parameters of this method. Hence, a homogeneous transformation theory is presented to solve this problem.Firstly, the kinematics characteristic of this special structure is analyzed on the basis of the closed-chain theory. In such a theory, closed chains can be transformed to open chains,which makes it easier to analyze this structure. Thus, it will become much easier to establish kinematics equations and get the solutions. Then, the robot model can be built in the Simmechanics(a tool box of MATLAB)with these equation solutions. It is necessary to design a graphical user interface(GUI) for robot simulation. After that, the model robot and real robot will respectively move to some spatial point sunder the same circumstances. At last, all data of kinematic analysis will be verified based on comparison between data got from simulation and real robot.Keywords Mixed hinge structure ? Homogeneous transformation ? Kinematic analysis ? Kinematic simulation1 IntroductionUsually,we use Denavit-Hartenberg(D-H)method to analyze the kinematics of robot.The key of this method is to establish a set of D-H parameters which indicate the relationship of the coordinate system so fall joints1.There are a lot of studies on the serial chain industry robots, however few studies are on such industry robots with complex structures. For example, a kind of large universal industry robot with hybrid hinge structure allows its arm to move backwards in low energy consumption.The motion law of this robot differs from that of other robots and its D-H parameters cannot be determined easily. Two solutions are proposed to deal with this special structure. One is to transform the structure into equivalent serial joints (revolute or prismatic joints). Then we can determine the D-H parameters one by one based on D-H theory 2. The other is to transform closed chains to open chains so that we can calculate the relationship between the active and passive joints. Then, the complex structure is transformed into simple serial structure 3. The first methodneedstoanalyzethecharacteristicsofeveryjointinthishybridhinge, thus it is sophisticated and error-prone 4. Meantime,in the second method,although a general theory to analyze all closed chains is introduced, the breakdown structure is not presented and this theory is not verified by experiments.Considering these two methods, it will be easier for us to determine the relationship between coordinate systems of joints if we know the kinematics characteristic of the special structure. Hence the motion characteristic of the special structure is analyzed based on the closed-to-open chain theory in the paper. Then the coordinate systems are directly established a teach active joint.The advantage of the method is that it can avoid judging the motion of each kinematic pair in the structure 5. In addition, it is convenient to build the simulation model mentioned below.2 Kinematics characteristic of new-type robotFigure 1 shows the large universal robotZX165U of Kawasaki Company. Such robots can keep the translationFig. 1 Industry robot consisting of hybrid hinge structuresmotion of its end-effector when it is palletizing. During this process, fewer motors work, thus less energy is consumed.Furthermore, the damper settled on the base is an important component to keep the object stable and safe in the whole process 6. All joints except the joint 2 (JT2) are the same as those in usual robots. In this paper, we will only discuss how the spinning of joint 2 affects the kinematics characteristic of the whole robot 7, 8.Firstly, we theoretically analyze the kinematics characteristic of the special structure. Figure 2a demonstrates a mixed system consisting of closed chain structure. There are n links and L i is the name of a certain mid-link in the system. Figures 2b, c are two kinds of logic open-chain systems generated from Fig. 2a. The producing mode of these two open-chain systems is shown as following 3, 9.All links with which the closed chain intersects with out-side world are determined (such as L m and L m?4 in Fig. 2a).And then all parallel links connected to these links (L m and L m?4 ) are figured out. Thus we can easily choose two different routes (from L m to L n ), where no parallel link exists. Finally, two logic open-chain systems are generated according to corresponding selected routes. As a result, all non-redundant links exist in the logic open-chain systems,as shown in Figs. 2a, b.Considering the characteristic of the robot we are studying, there are totally 8 links. So n will be equal to 8 if m is equal to 1 (see Fig. 2). The degree of freedom (DOF)(N) is equal to 6 (the number of active joints), and the number of passive joints (P) is equal to 3. We assume thevariables of the active joints as q A;i (i = 1, 2, _, 6) and the variables of the passive joints as q P;j (j = 1, 2, 3). In the theoretical basis and research scope of rigid body dynamics, rigid displacement is only determined by the six active joints exclusively 10. The relative equation is (1)Equation (1) shows the displacement dependency between passive and active joints, which can be written as (2)There are other two geometric constraints. One is that link is fixed on the base. The other is that the closed chain is a parallelogram structure. Consequently, from Eq. (2) we can obtain-q4 = -q5 = q3 = q2 （3） Namely, the moves the same as the L m?3 does. So the manipulator fixed on the link keeps executing translation consistently. Figure 3 shows the simulation model of the robot. Only the joint 2 is rotating in the simulation process. Figure 3a shows the initial state of the robot meaning that all the angles of joints are 0. Figures 3b, c demonstrate the corresponding status of the robot when the joint 2 moves clockwise and anticlockwise respectively. The manipulator keeps translation motion all the time, which is consistent with the actual situation (see Fig. 3).Now, we can make a conclusion that the end-effector of the robot executes translation motion while all joints are fixed except the rotating joint 2.Fig. 3 Motion status of robot manipulator when only JT2 moves to 0, - and 3 Kinematics analysisThe aim of kinematics analysis is to describe the kinematic relationship between joints and end-effector. The analysis solutions can demonstrate how to control robot motion, and establish the dynamic equation and the model for error analysis 11, 12.3.1 Forward kinematics and homogeneous transformationThe position of joints and orientations of rigid bodies can be described by coordinate systems fixed on joints 10. So we build coordinate system on every active joint 12.In Fig. 4, the coordinate system of ZX165U robot is established. First of all, the coordinate system 1 is established and it coincides with the base coordinate system 0.For convenience, the Z axis is parallel to the axis of each rotating joint and the direction of Z axis is determined by the rotation direction and fixed conventionally by right hand rule. The second axis is exactly consistent with one of the certain axes in previous coordinate system. Finally, the last axis is determined by the right hand rule again.The dimension parameters in the coordinate system are Shown in Fig. 4,in which the axes Z 1 Z 6 are consistent with the revolute joints JT1JT6, L 1 = 670 mm, L 3 = 1 100 mm,L 4 = 270mm,L 5 = 288mm,L 6 = 1100mm,L 7 = 228mm.According to homogeneous transformation formula (4)we can obtain all matrices:. The character e represents end-effector coordinate;refers to the transformation relationship from the coordinate i-1 to i;i refers to the revolution relationship from the coordinate i-1 to i; D refers to the translation vector from the coordinate i-1 to i. In Fig. 4, for example, coordinate system 1 shifts L 2 distance along the?Y, and shifts L 1 distance along the ?Z, then anticlockwise rotates around the ?Y. Then it can be transformed to coordinate 2. The transformation matrix iswhere T Z (L 1 ) and T Y (L 2 ) refer to translation matrices; L 1and L 2 are translation lengths along the corresponding axes;R Y (h) refers to rotation matrix; h is anticlockwise rotation angle around the +Y. When other matrices are computed, the transformation matrix from end-effector coordinate to base coordinate is obtained 13, 14. The solution to the forward kinematics is as followsWhereFig. 4 Homogeneous coordinate system of Kawasaki ZX165U3.2 Inverse kinematicsThe issue of robot inverse kinematics is to calculate all the corresponding joint angles when the pose and location of robot are given 13. In other words, the joint variables h i(i = 1, 2, _, 6) can be determined based on kinematics equation if the values of n, o, a, p and the needed geometric parameters are known 14. Equation (7) is used to get the solution to the inverse kinematics equation. This paper determines the first three joint variables h i (i = 1, 2, 3) by means of algebraic method, and the common inverse transformation method 15 is used to determine the last three joint variables h i (i = 4, 5, 6).First of all, there is only h 1 left and other variables are Eliminated by elimination method16,17for Eq.(7),such asAssumeEquation (11) is substituted back into Eqs. (8) and (9).Thus Eq. (12) is obtained.therefore,In Eqs. (10) and (11), the quadratic components of both sides are added together, and we getAlso are determined as follows.Equation (18) is deducted by multiplying both sides of Eq. (6) with all inverse transformation matrices from joint1 to joint 3,So we get the equation below:The left part of Eq. (19) contains known joint variables i.e., and , while the other side contains the joint variables and to be solved. As a result,Get rid of the singular solution, =0,4 Analysis of simulationModel simulation can verify the correctness of the kinematic analysis, and provide intuitive understanding and rigorous data 1, 18. The robot model discussed in this paper is built relying on the powerful function of the MATLAB platform.4.1 The toolbox and the modelThere are two qualified requirements 19, 20. The first one is to build an accurate robot model. The second one is to control the model for communication. With module database, we can build a complex mechanical model to realize the simulation of the mechanical structure. Meantime,driver and the sensor modules are effective ways to connectSimmechanics with Simulink 21, 22.As shown in Fig. 5, the model system can simulate the system controlled by the designed GUI. As shown in Fig. 5, there are six active joints, three passive joints and three fixed joints.Figure 6 shows the module chart of the robot (KawasakiZX165U).Fig. 5 Generated model in SimmechanicsFig. 6 Module chart of Kawasaki ZX165U robotThe following functions are included in the designed GUI (see Fig. 7):(i) controlling the process of simulation;(ii) forwarding and reviewing the information of joint angle;(iii) obtaining the information of manipulator pose and then saving the data.4.2 Verification of the kinematics analysisFigure 8 shows the picture of the real robot ZX165U. In experiment, the end-effector of the robot goes through two different ways, among which one looks like the letter W while the other looks like an S (see Figs. 9 and 10).Fig. 7 GUI designed for controlling the robot modelFig. 8 Physical picture of the robot ZX165UFig. 9 Real and simulation W pathsFig. 10 Real and simulation S paths The ZX165U robot can be driven to any arbitrary points in a reachable space as long as a set of appropriate values(joint angles or poses) are settled. In this experiment, five groups of data about points which indicate joint angles are put into the controller. Then the controller controls the robot to pass through these five points by linear interpolation (see Fig. 9) and curve interpolation (see Fig. 10).During this process, the pose and position of manipulator can be obtained at each corresponding point from teaching pendant. Then we let the robot model follow the same process by using the same data of 5 points mentioned above, but this time we use GUI to input data. Intuitively,the paths are drawn in a 3D coordinate system which only involves position values of robot but does not involve pose data. Figure 10 indicates the reverse. From Figs. 9 and 10, it can be apparently seen that the actual path matches the simulation path within a certain range of minor errors. These minor errors cannot be noticed unless the paths are magnified by many times. As a matter of fact, the accuracy is already close to 0.02 mm, as shownin Tables 1 and 2. We selected five arbitrary sets of data from process above and put all information in Table 1. Table 2 shows the data indicating inverse kinematics that are obtained in different ways. When the real and simulation robots move to the same designated pose and position, the data of their joint angles will be recorded. In Tables 1 and 2, r- ands- stand for words real and simulation respectively. In Table 1, the mean error between simulation result and actual result is 0.0206 mm with the maximum error of 0.037mm. Specifically, the position errors are 0.0258 mm, 0.0218mm and 0.0142 mm corresponding to X, Y and Z. Such precision can satisfy any industrial requirement.O,A and T stand for X, Y, Z Euler angles, respectively. Furthermore, the pose Error is almost negligible.Actually,we can never see the robot moving when it is shifted by a tiny distance. In Table 2, the mean error is 0.0011? by rough calculation with the wrong dataNo.5 without JT4. It means that the model robot can reach a certain point within an acceptable error range (tiny error is in cognizable). Just as mentioned in the previous section, the kinematics analysis is absolutely correct and can be proved by the comparison analysis of the data.5 ConclusionsThis paper analyzes and verifies the kinematics characteristic (translation motion) of a new-type robot with a mixed hinge structure. On the basis of that, the kinematic analysis can be easily carried out. Then the kinematic equation is established and solved with homogeneous transformation theory. The robot model built with kinematic equation solution can be used for simulation and acquire the simulation data via a designed GUI. Five groups of these data are selected, analyzed and compared. The error between real data and simulation data is calculated through the analysis. As shown in Tables 1 and 2, the errors are slight,which means that the simulation of the model can absolutely meet the actual requirement. Furthermore, the correctness of kinematics analysis is proved on the basis of the appropriate data analysis. This article hopes to provide some inspiration for those who are studying or going to study this kind of robot with a hybrid hinge structure.Table 1 Values of the end-effector pose calculated from six angles (forward kinematics)Table 2 Angles of six joints calculated from the end-effector pose (inverse kinematics)Acknowledgements This research was supported by the Key Scientific and Technological Project of Shanghai Science and Technology Commission (Grant No. 12111101004).References1. Bi LY, Liu LS (2012) 6-axis robot design and simulation based on simulation X. In: Yang DH (ed) Informatics in control, automation and robotics, vol 133. Springer, Heidelberg, pp 5375442. Song T, He YY, Wang P et al (2013) Kinematic analysis of series industrial robot with hybrid hinge structure. Mach Des Res 5:893. Fathi HG, Olivier C, Ruvinda G et al (2000) Modeling and set point control of closed-chain mechanisms: theory and experiment. IEEE Trans Control Syst Technol 8(8):8018154. Wang KS, Terje KL (1988) Structure design and kinematics of a robot manipulator. Robotica 6(4):2993095. Selig JM (2011) On the geometry of point-plane constraints on rigid-body displacements. Acta Appl Math 116:1331556. Suguru A, Masahiro S (2006) Human-like movements of robotic arms with redundant DOFs: virtual spring-damper hypothesis to tackle the Bernstein problem. In: Proceedings of IEEE international conference on robotics and automation, Orlando, May 20067. Choi HB, Konno A, Uchiyama M (2009) Closed-form forward kinematics solutions of a 4-DOF parallel robot. Int J Control Autom Syst 7(5):8588648. Pisla D, Gherman B, Vaida C et al (2012) Kinematic modeling of a 5-DOF hybrid parallel robot for laparoscopic surgery. Robotica 30(7):1095
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