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目录1英文文献翻译11.1 Research on a new 6 degrees of freedom combined parallel manipulator11.2中文翻译142专业阅读书目242.1机械制造基础242.2机械原理242.3机械设计252.4现代工程图学252.5机电传动控制262.6材料力学262.7互换性与技术测量262.8理论力学272.9机械设计课程设计272.10机械制造技术281英文文献翻译1.1 Research on a new 6 degrees of freedom combined parallel manipulator(Robotics and bionics, 2008, international society of robotics and biomimetic technology, 2008, IEEE International Conference).Abstract - a new type of six degree of freedom parallel manipulator, consisting of two free degree of freedom manipulator, is presented in this paper. The degree of freedom of the manipulator is analyzed and the position kinematics is modeled. The vector loop equation is derived through the Jacobi matrix. The working interval is determined by numerical.Key words: parallel manipulator;kinematics; working area;dexterity; reconfigurable structur1：Brief introductionDegree of freedom manipulator has been studied. Fang, Miller, Kong and Kok-Meng Lee have proposed a framework for reducing the degree of freedom, such as Tricept parallel mechanisms, which have been widely used in aircraft and automobiles.Flexible fixtures based on combined fixtures have become the main elements of modern development. In this paper, the author applies a six degree of freedom parallel manipulator to the design of flexible fixture. It consists of a space 3-RRS manipulator and a plane 3-RRR manipulator. Some properties of this mechanism are studied in detail: freedom, Jacobian matrix, working area and dexterity. Finally, two reconfigurable structures based on this mechanism are also proposed. These two reconfigurable structures can be applied to different industria.2：Description of a new type of parallel manipulatorFigure 1 shows the robotic arm studied in this article. It consists of two parallel manipulator arms. One of them is the planar 3-RRR manipulator and the other is the 3-RRS type manipulator. In addition to the ball joints associated with the mobile platform, all joints are rotated joints, and their axes are parallel to each other.Figure1：mechanical arm mode If the ball joint is replaced by three intersecting unit spinor, there will be five spinor associated with each arm of the 3-RRS type manipulator. Therefore, there is a special rotation that is opposite to all the joint rotation. It represents a point of force applied to the center of the space joint and the axis parallel to the rotating joint. Then, there will be three binding roles on the mobile platform. Generally speaking, the three power spinor is heterogeneous and linearly independent. So the possible movement is the translation of the normal fixed platform and the two-dimensional rotation of the space on a certain root line, which can be intersected at the same time at the same time.The planar 3-RRR manipulator has three degrees of freedom, including two-dimensional translational and one-dimensional rotation. Since the two combinations of manipulator have different degrees of freedom, the manipulator considered in this paper has six degrees of freedom.3： inverse kinematicsA schematic diagram of kinematics is given in Figure 2. All joints of the manipulator are represented in the diagram. Here are six movable rotatable joint variables, expressed as theta I and ETA I, where i= 1, 2, 3. The moving coordinate system m is at the center of the triangle P1P2P3, the coordinate system o is at the center of the triangle C1C2C3, and the base coordinate system O is fixed on the ground and the origin is the same as o in the initial condition state, and the I and zeta I are passive auxiliary joint angles, which can be used for computer simulation calculation or for the calculation of velocity and dynamics. . As shown, the length of the link is expressed in terms of 1, L, a and B.Figure 2: six degrees of freedom parallel manipulatorThe inverse kinematics problem gives the mobile platform posture needed to calculate the required joint angle. Since the secondary arm is made up of two robotic arms, the position of the platform C1C2C3 needs to be obtained from the first step, and then all the angles of the driving joints can be known.In the spherical joint coordinate system UVW, the coordinates are PI (i=1,2,3). If we convert the homogeneous transformation matrix T to the coordinate system o in the Euler angle (alpha, beta, gamma) in the X-Y-Z, the spherical joint coordinates can be written as:In here：The (XM, YM, ZM) T here represents the position of UVW in the coordinate system o. C and s represent the sin and COS functions, respectively. The link DiEi-EiPi (i=1,2,3) is constrained by the rotational joints of plane y=0, y = x and y = x, respectively. The relationship between the six postural variables can be derived from the constraint equation.The length of the EiPi of the link is equal to the distance between the ith spherical joint Pi and Ei. So there are three equations in this relation, and then we can get the expression of driving joint angle theta I:Pij (I = 1, 2, 3 J = x, y, z) indicates the position of Pi with J in the coordinate system o. It is assumed that the posture of the mobile platform in the coordinate system O is (Xm, Ym, Zm, Zm), and the posture in the coordinate system is (XM, YM, ZM, alpha, beta, gamma) T, and the pose of the platform C1C2C3 can be expressed as:The angle of the ETA I in the 3-RRR manipulator can also be obtained by the above method.Here: Dij (J = 1, 2, 3) is an equation of the same form as eij in 3.Now there is a general solution to the configuration of a corner and two arms, so we can conclude that there are 64 possible robotic arm positions corresponding to a given end actuators position.4： The Jacobian matrixAccording to Fig. two, the vector link in the manipulator arm can be written as:The differential of time on both sides of the equation is used. Then the Li and Bi points are used to eliminate the passive variables by the two sides equation.It can be simplified to:Here, Omega theta and Omega are the angular variables that drive joints. Jiq and Jix are matrices derived from Eq. (8). Vo1 and VO2 respectively represent the output variables of the two arms. The first variable represents the coordinate system o, and the other represents the coordinates O.Here, the 3-RRR type planar manipulator has only three outputs, so VO2 can be written as J2x.Here is the third column, bij (J = 1, 2) is the jth column of Bi.Then the second equations of (9) can be written as:Because Jacobian matrix represents the relationship between input speed and output speed, we can describe the input speed in an equation.Because the output speed v = Vo1 + VO2, equation (11) becomes:From the equation (10) we can come to the following:The right form of (13) in the first matrix is described by J3, and (13) is replaced by (12).Then we can get the Jacobian matrix of the manipulator.5：Work intervalAs we all know, compared with the same series, the parallel manipulator has a smaller working range. Therefore, it is necessary to analyze the shape of the working area to enhance the performance of the parallel manipulator.The workable interval is defined as such a space, which can be reached by reference points in at least one direction. We select a point on the w axis, which is a distance from the center of gravity m of the mobile platform as a reference point. Here are three steps to get the working space of this manipulator. The first step is to find the boundary of the 3-RRS type manipulator and use the spherical coordinates query method. The boundary of planar 3-RRR manipulator can easily be calculated from the normal boundary search method. This is the second step. Then, the working area is moved along the boundary of the plane curve obtained in the second step, and the final envelope is the working area of the parallel manipulator. Of course, the constraints of practical situations need to be considered when designing practical arms.The structural parameters of the manipulator are selected as follows: r=50mm, R=80mm, R =260mm, L=l=130mm, a=b=140mm. Assuming that the orientation is 0, the working range of the manipulator can be programmed by MATLAB, as shown in Figure three (a), (b), and (c), which represent the forward view, the overlook and the left view respectively. It can be observed from Fig. 3 that the workable interval is about the symmetry of the movement direction of the three drives.Figure 3: a workable range of workable arms6： DexterityThe dexterity of a manipulator can be considered as the ability of a manipulator to change its position and direction, or the force and torque in any direction. This can be measured by the kinematic performance index of the manipulator. The Jacobian matrix represents the mapping between the speed and force between the actuator and the actuator at the end of the manipulator, so its characteristics are usually used to measure dexterity.The exponent of dexterity of manipulator is taken as the condition number, and the minimum singularity and maneuverability are proposed. The conditional number of Jacobian matrix can be obtained from 1 (isotropy) to infinity (singularity), which measures the degree of morbidity. This is used as the dexterity index in this article. The condition number of the Jacobian matrix can be defined as:The sigma Max and sigma min represent the largest and minimum singular values of Jacobian matrix respectively.The condition number is restricted to 1 to infinity, from the singular configuration at infinity to the dexterity at 1. The structural parameters of the manipulator are the same as those shown in Figure four. We assume that the mobile platform is parallel to the fixed platform, and the height of Z is 200mm, and the condition number of the Jacobian matrix of the work area is shown in Figure four.It is clear that the dexterity is the best in the center of the workspace and decreases gradually as the center moves outward. However, the number of these conditions can satisfy the requirements of parallel manipulator.Figure 4: dexterity under the initial parameter setting7：Reconfigurable analysisA: 3-RRRS parallel mechanism with six degrees of freedomAs shown in Figure five, the 3-RRRS mechanism has a reconfigurable composite mechanism for help, as shown in Figure 1. The first R joint axis vector is perpendicular to plane B1B2B3, and the second and third R key axis vectors are parallel to B1B2B3. Finally, the arm is connected to the mobile platform through joints. Suppose that the reference coordinate system of each arm is at the center of the second R joints, similar to the B-xiyizi shown in Figure five. Under initial configuration, the kinematic spinor of each chain can be expressed as follows:The matrix T is a full rank matrix, which represents the linear independence of the kinematic spinor of each chain. There is no inverse helix that acts on kinematic constraints. Therefore, the degree of freedom of the 3-RRRS mechanism is 6. joints of each chain, which can be flexibly selected as the actuated joints of two.Figure 5: a six degree of freedom mechanism with three armsB: 3-RRRS-UPR parallel mechanism with four degrees of freedomFig.6: four degree of freedom mechanism for three arms with a beam chain.This constraint chain has a U joint, a P joint and a R joint. The rest of the structure andThe 3-RRRS mechanism is the same. This binding force acting on 3RRRS-UPR can be analyzed by the spinor theory. The reference coordinate system of the constraint chain is located at the center of the U joint, similar to the xoyozo shown in Figure six. Under initial configuration, the kinematic spinor of each chain can be expressed as follows:From (13), mobile platforms do not move along the x0 axis and the Y0 axis. This mechanism has three rotational freedoms and a translational freedom along the Z0 axis.1.2中文翻译（机器人技术和仿生学，2008，机器人与仿生技术国际学会，2008，IEEE国际会议）摘要本文提出了由两个少自由度机械臂组成的一种新型六自由度并联机械臂，对这种机械臂的自由度进行了分析和位置运动学建模。通过雅可比矩阵导出了矢量环方程。工作区间通过数值方法被确定为考虑干扰检查。此外，根据灵巧度标准来评估机制的性能。为了满足不同的配置需求，基于提出的六自由度并联机构。给出了两个可重构的结构。这项工作提供了新型机械臂的发展基础。关键词并联机械臂，运动学，工作区间，灵巧度，可重构结构一、简介并联机构已经在许多领域被广泛使用，例如飞机模拟器，机器人，机床。由于其更好的刚度和精度，较轻的重量，更大的承载，更高的速度和加速度以及不那么强有力的执行器。最经典的六自由度并联机构机械臂是Gough的轮胎试验机Stewart的运动模拟器。但有些并联机械臂少于六自由度，例如Delta和3-UPU型机械臂。最近几年，缩减自由度的机械臂尤其是三自由度机械臂已经被集中研究。Fang, Miller，Kong和Kok-Meng Lee已经提出集中缩减自由度的架构，如Tricept并联机构已经被广泛地应用于飞机和汽车。基于组合固定装置的柔性固定装置已成为现代发展方向的主要元素。在本文中，作者应用一种六自由度并联机械臂到柔性固定装置的设计中。它由一个空间的3-RRS型机械臂和一个平面的3-RRR型机械臂构成。这种机制的一些特性被具体研究：自由度，雅克比矩阵，工作区间以及灵巧度等。最后，基于这种机制的两种可重构结构也被提出来，这两种可重构结构可以用于不同的工业领域。二、新型并联机械臂的描述图一展示了本文中研究的机械臂。它由两个并联机械臂组成。其中一个是平面的3-RRR型机械臂，另一个是空间的3-RRS型机械臂。除了与移动平台相联系的球关节，所有关节都是转动关节，而且它们的轴都是互相平行的。图一：机械臂模型如果球关节被三个相交的单元旋量代替，那会有五个与3-RRS型机械臂的每个臂联系的旋量。因此存在一个特别的旋量与所有的关节旋量相反，它代表了一个力应用于空间关节中心的一个点和平行于转动关节的轴。然后，然后,就会有三个约束力作用于移动平台。通常来说，这三力旋量是异面和线性独立的。所以可能的运动是顺着正常固定的平台的平移和关于某根线的空间二维旋转，这种于东可以是三力旋量在同一时间相交。平面的3-RRR型机械臂有三个自由度，包括平面二维的平移和一维旋转。由于两组合机械臂分别有不同的自由度，因此本文中所考虑的机械臂都拥有六个自由度。三、逆运动学在图二中给出了运动学的图解示意图。机械臂的所有关节都在图中有所表示。这里有六个活动的可旋转的关节变量，表示为i 和i ，这里i= 1, 2, 3。移动的坐标系m是在三角形P1P2P3的中心，坐标系o是在三角形C1C2C3的中心，而且基坐标系O被固定在地面上且原点同一样o在初始条件状态下，i和i是被动辅助关节角，可以被用来计算机仿真计算或者用于速度和动力学计算。如图所示，链接的长度用1，L，a和b表示。图二：六自由度并联机械臂图解逆运动学问题给出了计算所需要的驱动关节角度的移动平台姿势。由于次机械臂是由两个机械臂组成，因此平台C1C2C3的姿势需要从第一步得出，然后所有的驱动关节的角度都可以知道。在球关节坐标系uvw中的坐标是pi(i=1,2,3) ，如果我们将它们根据X-Y-Z中的欧拉角(,)用齐次变换矩阵T转换到坐标系o中，这个球关节坐标可以写为：在这里：这里的(xm, ym, zm)T表示uvw在坐标系o中原点的位置。c和s分别表示sin和cos函数。链接DiEi-EiPi(i=1,2,3)被分别在平面y=0, y = -3x和y = 3x的旋转关节所约束。六个姿势变量的关系可以由约束方程推导出来：链接的EiPi长度等于 ith球关节Pi 和Ei间的距离。因此在这关系中存在三个方程，然后我们可以得到驱动关节角i的表达式：这里：Pij（i = 1, 2, 3 j = x, y, z）表示在坐标系o中Pi伴随j的位置。假设在坐标系O中的移动平台的姿势是(Xm, Ym, Zm, , , )T，它在坐标系o中的姿势是(xm, ym, zm, , , )T，平台C1C2C3的姿势可以表示为：3-RRR型机械臂中i 的角度可以同样由上述方法得出：在这里：Dij（j = 1, 2, 3）是同(3)式中eij 一样形式的等式。现在已有一个角和两个臂的配置的通用解决方法，因此我们可以得出结论：对应于一个给出的末端执行器位置，总共存在64种可能的机械臂姿势。四、雅克比矩阵根据图二，机械臂中链接的矢量环可以写为：对等式两边进行关于时间的微分，然后分别用li和bi点乘两边等式消掉被动变量得：这里ki表示平行于特殊机械臂ith驱动关节轴的单位向量，k是指向正Z轴的单位向量。然后我们可以得到两个方程：可以简化为：这里 和 是驱动关节的角变量，Jiq 和Jix 是由Eq. (8) 推导出的矩阵。vo1 和vo2 分别表示两个机械臂的输出变量，第一个变量代表坐标系o 另一个代表坐标是O。这里3-RRR型平面机械臂只有三个输出，因此vo2 可以写为，J2x变为：这里是的第三列，bij（j = 1, 2）是bi 的jth列。然后（9）的第二个等式可以写为：由于雅克比矩阵表示了输入速度和输出速度的关系，因此我们可以在一个方程式中描述输入速度因为输出速度v = vo1 + vo2 ，等式(11) 变为：从等式(10)中我们可以得出：由J3 来描述第一个矩阵中(13)的右式，并把(13)代入(12)，可得： 然后我们可以得到机械臂的雅克比矩阵： 五、工作区间众所周知，与同系列的相比，并联机械臂有较小的工作区间。因此，有必要分析工作区间的形状来加强并联机械臂的表现。可获得的工作区间被定义为这样一块空间，它能被参考点至少在一个方向上达到。我们在w轴选取一个点，这在移动平台的重心m 作为参考点之上的一段距离。这里有三个步骤来得到这个机械臂的工作区间。第一步是寻找空间3-RRS型机械臂的边界，使用球坐标查询方法。平面3-RRR机械臂的边界很容易从普通边界查找方法算出，这是第二步。然后，沿着第二步得到的平面曲线的边界移动空间工作区，最终的包络线是并联机械臂的工作区间。当然，实际情况的约束在设计实用的机械臂时需要被考虑。机械臂的架构参数被选取为：r=50mm，R=80mm，R=260mm，L=l=130mm，a=b=140mm。假设取向是0，机械臂的工作区间可以通过MATLAB编程得到，如图三(a), (b), (c)所示，它们分别表示正视图，俯视图和左视图。从图三中可以观察到，可达到的工作区间是关于三个驱动器的移动方向匀称的。图三：机械臂可达到的工作区间六、灵巧度机械臂的灵巧度可以被认为是机械臂可以任意改变其位置和方向，或者任意方向的作用力和扭矩的能力。这已经可以用机械臂的运动学性能指标来测量。雅克比矩阵表示了在机械臂的末端执行器和驱动器之间速度和力两者的映射，因此它的特性通常被用来衡量灵巧度。机械臂灵巧度不同的指数作为条件数，最小奇异性和可操纵性被提出。雅克比矩阵的条件数可以从1（各向同性）到无穷（奇异性），这衡量了病态性程度。这被用来作为本文中灵巧度指标。雅克比矩阵的条件数可以被定义为：在这里max 和min 分别表示雅克比矩阵的最大和最小奇异值。条件数被限制在1到无穷，它从在无穷处的奇异位形到在1处的灵巧。机械臂的架构参数和如图四给出的一样。我们假设移动平台平行于固定平台而且Z的高度是200mm，工作区间的雅克比矩阵的条件数如图四所示。图中很明显的显示了灵巧度在工作区间的中心是最好的，且按照中心向外移动逐渐减小。但是这些条件数的值可以满足并联机械臂的要求。图四：初始参数设定下的灵巧度七、可重构分析A、具有六自由度的3-RRRS平行机制如图五所示的3-RRRS机制，它有可重构的组合机制求助，如图一所示。第一个R关节的轴向量垂直于平面B1B2B3，第二个和第三个R关键的轴向量平行于B1B2B3。最后，臂通过关节被连接到移动平台。假设每个臂的参考坐标系处于第二个R关节的中心，类似于图五所示的B-xiyizi。在初始配置下，每条链的运动学旋量可以如下表示：螺旋矩阵可以如下表示为： 矩阵T是一个满秩矩阵，它代表了每条链的运动学旋量的线性无关。这里没有作用于运动学约束的反螺旋。因此，3-RRRS机制的自由度是6.每条链的两个关节可以被灵活地选为驱动关节。图五：具有三臂的六自由度机制B、具有四自由度的3-RRRS-UPR平行机制进一步的重构，3RRRS-UPR型具有中心约束链的平行机制如图6所示。图六：有约束链的三臂的四自由度机制这个约束链有一个U关节，一个P关节和一个R关节构成。剩下的结构和3-RRRS机制相同。这个通过约束链作用于3RRRS-UPR的约束力可以通过旋量理论被分析。约束链的参考坐标系被定位在U关节的中心，类似于如图六所示的xoyozo。在初始配置下，每条链的运动学旋量可以如下表示：反螺旋可以由下面公式获得：从(13)中看，移动平台不会沿着x0轴和y0轴移动。这个机制有三个旋转自由和沿z0轴的一个平移自由。24
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