外文翻译---旋转机械轴心轨迹识别方法研究

机械毕业设计英文外文翻译论述压痕测试法和原子力显微镜的SI可跟踪力计量学The SI traceable force metrology of indentations test method and atomic force microscope machiningIntroduction:The SI traceable force metrology is an important aspect in the field of mechanical engineering. The measurement of forces accurately and precisely is critical in various applications, such as materials testing, quality control, and design analysis. This paper aims to discuss the indentations test method and atomic force microscope (AFM) machining, which are two techniques used in SI traceable force metrology.Indentations Test Method:Indentations test method is a widely used technique for measuring the mechanical properties of materials. It involves applying a known force on the surface of a material and measuring the resulting indentation depth or hardness. In order to ensure the accuracy and reliability of the measurements, itis essential to have a SI traceable force calibration. The force calibration is typically done using a certified force standard, such as a deadweight machine or a force transducer, which provides SI traceable force values. The force applied during the indentation test is then traceable to the SI unit of force, the newton (N).Atomic Force Microscope (AFM) Machining:AFM is a powerful tool used for imaging and manipulating materials at the nanoscale. It operates by scanning a sharp probe over the surface of a material, while measuring the forces between the probe and the surface. The forces can be measured using a variety of techniques, including optical interferometry, piezoresistive sensors, and capacitive sensors. In order to achieve SI traceability in AFM force measurements, it is necessary to calibrate the AFM system using a SI traceable force standard.The AFM machining is particularly useful for measuring forces at the nanoscale. It allows for the precise control and manipulation of materials, enabling the fabrication ofstructures with nanoscale features. The force measurements obtained from AFM can be used to characterize the mechanical properties of materials, such as the elastic modulus, adhesion strength, and friction coefficient. Furthermore, AFM can be used for force spectroscopy, which involves mapping the force-distance relationship between the probe and the surface.Conclusion:In conclusion, the SI traceable force metrology is essential for accurate and reliable force measurements in mechanical engineering. The indentations test method and AFM machining are both techniques that can be used for SI traceable forcemeasurements. The indentations test method is a non-destructive technique that can be used on a wide range of materials, while AFM machining allows for precise measurements at the nanoscale. Both techniques require the calibration of force standards to ensure SI traceability.。

Kinematics and trajectory planning of a cucumber harvesting robot manipulatorZhang Libin, W ang Y an, Y ang Qinghua, Bao Guanjun, Gao Feng, Xun Yi(The MOE Key Laboratory of Mechanical Manufacture and Automation, Zhejiang University of Technology, Hangzhou 310012, China)Abstract:In order to reduce cucumber harvesting cost and improve economic benefits, a cucumber harvesting robot was developed. The cucumber harvesting robot consists of a vehicle, a 4-DOF articulated manipulator, an end-effector, an upper monitor, a vision system and four DC servo drive systems. The Kinematics of the cucumber harvesting robot manipulator was constructed using D-H coordinate frame model. And the inverse kinematics which provides a foundation for trajectory planning has been solved with inverse transform technique. The cycloidal motion, which has properties of continuity and zero velocity and acceleration at the ports of the bounded interval, was adopted as a feasible approach to plan trajectory in joint space of the cucumber harvesting robot manipulator. Moreover, hardware and software based on CAN-bus communication between the upper monitor and the joint controllers have been designed. Experimental results show that the upper monitor communicates with the four joint controllers efficiently by CAN-bus,and the integrated errors of four joint angles do not exceed four degrees. Probable factors resulting in the errors were analyse and the corresponding solutions for improving precision are proposed.Keyword:cucumber harvesting robot, articulated manipulator, trajectory planning, cycloidal motion, CAN-busDOI:10.3965/j.issn.1934-6344.2009.01.001-007Citation:Zhang Libin, Wang Y an, Yang Qinghua, Bao Guanjun, Gao Feng, Xun Yi. Kinematics and trajectory planning of a cucumber harvesting robot manipulator. Int J Agric & Biol Eng, 2009; 2(1): 1－7.1 IntroductionFruit and vegetable harvesting is a labor-intensive job,and the harvesting cost by human labor is about 33%～50% of the total production cost[1]. Therefore, it isurgent to mechanize and automate fruit and vegetable harvesting. Currently, many countries are studying.Received date: 2008-11-20 Accepted date: 2009-03-28Biographies:Zhang Libin, professor, Ph.D, mainly engaged in agricultural robot, mechatronics and control. Wang Y an, Ph.D candidate of Zhejiang University of Technology, ma inly engaged in robotics, intelligent instruments. Y ang Qinghua, professor, Ph.D, mainly engaged in robotics, mechatronics and control. Baoguanjun, lecturer, Ph.D, mainly engaged in robotics, control and machine vision. Gao Feng, associate professor, Ph.D, mainly engaged in electromechanical engineering. Xun Yi, Ph.D, mainly engaged in vision system and image processing. Corresponding author:Zhang Libin, MOE Key Laboratory of Mechanical Manufacture and Automation, Zhejiang University of Technology, Hangzhou 310012, China. Tel & fax: +86-571-88320007. Email: **************.cnharvesting robot, especially Netherlands and Japan. Some of the harvesting robots, such as cucumber, tomato, grape harvesting robots have been applied in greenhousesand others on farms[2,3]. In China, though research on harvesting robot is later than that in developed countries,some favorable achievements have been made through efforts in many universities and research institutes, such as the eggplant picking robot designed by China Agricultural University and the tomato harvesting robot developed by Zhejiang University.Under the support of the National High-Tech Research and Development (863) Program of China(2007AA04Z222), the first systematical cucumber harvesting robot in China was jointly developed by China Agricultural University and Zhejiang University of Technology. It consists of a vehicle, a 4-degree of freedom (DOF for short) articulated manipulator, an end-effector, an upper monitor, a vision system and four DC servo drive systems. Instead of utilizing an industrial manipulator, the 4-DOF articulated manipulator was designed by Zhejiang University of Technology to reduce the cost and adapt to the harvesting environment.This paper mainly investigates the 4-DOF articulated manipulator kinematics and trajectory planning, and it is outlined as follows. In Section 1, the structure of cucumber harvesting robot manipulator is described. The kinematics of manipulator is constructed in Section 2 and the inverse kinematics is solved in Section 3. Section 4 presents the trajectory planning algorithm of cycloidal motion. The hardware and software design of trajectory planning based on CAN-bus is introduced in Section 5. Experiments measuring actual position of four joints are carried out and possible causes for errors are analyzed in Section 6. Finally, conclusions are drawn in Section 7.2 Cucumber harvesting robot manipulator structureThis paper describes in detail the kinematics of the robot manipulator and realization oftrajectory planning control based on CAN-bus. The line diagram and photograph of the articulated manipulator is shown in Figure 1. It is composed of four rotation joints: waist joint (J1), shoulder joint (J2), elbow joint (J3) and wrist joint (J4). One end is fixed on the base, and the other end is connected to an end-effector which contains two parts: a gripper to grasp the fruit and a cutting device to separate the fruit from the plant.Figure 1 Line diagram and photograph of the cucumber harvesting robot manipulator The cucumber harvesting robot system employs multi-CPU, distributed control structure of upper monitor and joint servo controllers. Moreover, the four joints are driven to work in perfect harmony by CAN-bus communication which efficiently supports the distributed real-time control system. The communication system ofthe cucumber harvesting robot is shown in Figure 2. The Upper monitor is used to monitor and manage the whole robot system, locate cucumber target, and plantrajectory. The CAN-bus is the transmission bridge between upper monitor and joint controllers. The servo controllers are distributed in each joint to drive torquemotors and they can realize close-loop control by receiving feed back signals from angle encoders.Figure 2 Communication system of the cucumber harvesting robot3 Coordinate frames of kinematics modelsCoordinate frames of kinematics models are constructed by Denavit-Hartenberg model (D-H for short), which has been widely adopted in robotics due to its explicit physical interpretation of mechanisms and relatively easy implementation in the programming of the robot manipulator. D-H coordinate frame model is based on assignment of Cartesian coordinate frames fixed relative to each link of robot manipulator. And it describes spatial transformation between two consecutive links by 4×4 transformation matrix i-1A i, so the transformation of link n coordinate frame into the basecoordinate frame can be written as[4,5]:where a is the vector of approaching direction; 0 is orientation vector,n = a×0 is thenormal vector;P is the position vector of end-effector relative to thebase coordinate frame.The D-H transformation matrix i-1A i r elating to a number of rotations and translations between two consecutive coordinate frames is expressed as[6,7]:Where θi is joint angle;αi is twist angle;d i is joint offset;a i is the length of link.Figure 3 illustrates the D-H coordinate frames of the robot manipulator and Table 1 summarizes its D-H parameters.Figure 3 D-H coordinate frames of the cucumber harvesting robot manipulatorTable 1 D-H parameters of the robot manipulator4 Inverse kinematics of the cucumber harvesting robot manipulatorThe inverse kinematics problem for a robot manipulator is to find a vector of joint variables that produces a desired end-effector position and orientation.The inverse transform technique is used to solve the problem[8,9]. In order to pick cucumbers conveniently, the wrist joint has to be parallel to X axis of the base coordinate frame, so it can be obtained:θ2 + θ3 +θ4 = 0°For equation (1), it can be rewritten as:WhereFirst, let element (3,4) of matrix (4) and (5) be equal,θ1 can be given by:Then let element (1, 4) and (2, 4) of matrix (4) and (5) be equal, the following equations can be obtained:By simplifying equation (7):From equation (7), θ2, θ3 can be expressed as:5 Trajectory planning in joint space based oncycloidal motionTrajectory planning of the robot manipulator is defined in this way: find temporal motion laws for joint position, velocity and acceleration according to a given operation of the end-effector. The motion laws generated by trajectory planner have to use some particular strategies to eliminate extra movements such as chattering and resonance. They have to be smooth enough, and continuous for their first and second derivatives[10,11]. Within a number of planning algorithms, cycloidal motion is especially suitable to apply in point-to-point trajectory planning because of its smaller amount of calculation, smoothness and continuity,and features of zero velocity and acceleration at the initial and end points of the bounded interval[12]. Its motion curve can be described as[13]:Then its first and second derivatives can be expressed as:Whereis normalized time；T is a single harvest operation time.Figure 4 shows the curves of the cycloidal motion andits first and second derivatives in canonical interval (-1,1). From Figure 4, it can be clearly seen that the cycloidal motion is adequately smooth; also, the velocity and acceleration motions are continuous and the values atFigure 4 Cycloidal motion and its first and second derivatives the initial and end points of interval 0≤τ ≤1 are zeros.This demonstrates that the motion of the end-effector of robot manipulator won’t result chattering, so it can ensure motion stability of the robot system.For joint i , trajectory planning relies on position and orientation of end-effector. So, the first step of trajectory planning is acquiring the three dimensional space description of the target cucumber. This description is based on sensory information such as machine vision as well as priori knowledge aboutkinematics structure of robot manipulator. Then the goal angles q i(f) of the four joints can be obtained from the target position of the end-effector with inverse kinematics (Eqs 6, 10, 12, 13). After the start joint angles q i(0) i q being sent from joint controllers through CAN-bus, the position, velocity, acceleration equations based on cycloidal motion can be expressed as:6 Hardware and software design of trajectory planning based on CAN-bus6.1 Interface circuit of CAN-busController Area Network (CAN) is an advanced serial communication protocol for distributed real-time control system. Different devices such as processors, sensors and actuators can be connected to CAN-bus via twisted-pair wires and can communicate with each other by exchanging messages. The maximum transmissionrate can reach up to 1Mbps in a noisy environment. And it utilizes Carrier Sense MultipleAccess with Collision Detection (CSMA/CD) as the arbitration mechanism to enable its attached nodes to have access to the bus[14-16].The cucumber harvesting robot system employs the point to multi-points communication of CAN-bus. The upper monitor and four joint controllers are composed of dsPIC30f4012 digital signal processor which contains standard CAN controller and MCP2551 transceiver. And a 4-wire interface is designed based on CAN-bus protocol(CAN2.0A), which provides power, ground and two data lines(CAN High and CAN Low). The interface circuit of CAN-bus is shown in Figure 5. And the upper monitor circuit board is shown in Figure 6. The Baudrate of CAN-bus communication is adopted 1Mbps, and the messages transmitted consist of 2-byte identifier, 1-byte data length and 8-byte data. Messages are transmitted with a time internal of 10 ms according to the harvesting requirements. CAN-bus communication exhibits good real-time performance in practical application.Figure 5 Interface circuit of CAN-busFigure 6 Upper monitor circuit board6.2 Software design for trajectory planning of the cucumber harvesting robotThe upper monitor has functions of management and supervision for the robot system, location of cucumber target and trajectory planning. The program designemploys the modularization idea which is composed of several subprograms. Figure 7 illustrates the process of the trajectory planning for the cucumber harvesting robot. It consists of subprograms such as CAN-bus sending and receiving, acquisition of cucumber target, inverse kinematics and trajectory planning.Figure 7 Flow chart for the trajectory planning7 Experiments and analysisIn order to verify the accuracy of the trajectory planning algorithm and CAN-bus communication, experiments to measure the actual position of the fourjoints of the cucumber harvesting robot manipulator were performed with the coordinate measurement machine(CMM) Platinum FaroArm of FARO Technologies Incorporation. As the world’ s best-selling portable measurement arm, Platinum FaroArm is available in sizes ranging from 1.2 m to 3.7 m and has precision of up to 0.013 mm.Experiments were carried out as follows:1) Set the position of the end-effecor:P x = 700mm, P y = 200mm, P z = 668mm . By utilizing the inverse kinematics, the four joint angles can be computed fromequation (6) ～(13):θ1 =15.95°，θ2 =55.82 °，θ3 =-33.48°，θ4 =-22.34°.2)Plan trajectories for each joint with cycloidal motion algorithm and send the planned angle messages to joint controllers by CAN-bus.3)Use Platinum FaroArm to measure the actual angles that torque motors have rotated.4)Set other 9 positions of end-effector, repeat (1)～(3) steps. Experimental results are presented in Table 2.Experimental results in dicate that the integrated errors of four joint angles didn’ t exceed four degrees. The possible reasons for experimental errors are: (1) controlling precision of single joint is 0°～1°；(2) mechanical structure error including installation and deformation error；(3) the end-effector hadn’ t realized closed-loop position control. The corresponding solutions are:(1) add some compensation algorithm to improve control precision of single joint；(2) substitute Aluminum alloy for PVC to manufacture the manipulator to decreasemechanical error；(3)mount a mini camera on the end-effector to realize the close-loop control of manipulator. Table 2 Experimental results on measuring actual position of the four joints of robot manipulator8 Conclusions1)Kinematics of the cucumber harvesting robot manipulator was constructed using D-H coordinate frame model. The inverse kinematics, which provides a foundation for trajectory planning, has been solved with inverse transform technique.2)The cycloidal motion, which has properties of continuity, small amount of calculation, and zero velocity and acceleration at the ports of the bounded interval, is proposed as a feasible approach to plan trajectory in joint space of the robot manipulator.3)Software and hardware of CAN-bus communication between the upper monitor and the joint controllers have been designed.4) Experimental results show that the upper monitor communicated with four joint controllers efficiently by the CAN-bus, and the integrated errors of four jointangles were less than four degrees.AcknowledgmentThis work is supported by the Natural Science Foundation of China (50575206) and the National High-Tech Research and Development (863) Program of China (2007AA04Z222).[References][1] Tang Xiuying, Zhang Tiezhong. Robotics for fruit and vegetable harvesting: a review. Robot, 2005; 27(1): 90－96.[2] E. J. Van Henten, J. Hemming, B.J.A Van Tuijl so on. Collision-free motion planning for a cucumber picking robot. Biosystems Engineering, 2003; 86(2): 135－144.[3] Arima S, Kondo N. Cucumber harvesting robot and plant training system. Journal of Robotics and Mechatronics,1999; 11(3): 208－212.[4] Xiong Youlun. Robotic technology. Wuhan: Huazhong University of Science and Technology Press, 1996; pp. 18－22.[5] M.Abderrahim, A.R.Whittaker. Kinematic model identification of industrial manipulator. Robotics and Computer Integrated Manufacturing, 2000; 16: 1－8.[6] Chen Ning, Jiao Enzhang. A new scheme for solving the inverse kinematics equations of PUMA robot manipulator. Journal of Nanjing Forestry University. 2003; 27(4): 23－26.[7] Fu Jingxun. Robotics. Beijing: China Science and Technology Press, 1989; pp.26－36.[8] Wang Ping, Yang Yanping, Deng Xiao. Study on the motion control of mold polishing robot system. China Mechanical Engineering, 2007; 18(20): 2422－2424.[9] Anatoly P. Pashkevich, Alexandre B. Dolgui. Kinematic aspects of a robot-positioner system in an arc welding application. Control Engineering Practice, 2003; 11: 633－647. [10] Neelam R Prakash, Kamal T S. , Intelligent planning of trajectories for pick-and-place operations. In: Proc. Of International Conference on System, Man and Cybernetics.2000; 55－60.[11] A. Gasparetto, V. Zanotto. A new method for smooth trajectory planning of robot manipulators. Mechanism and Machine Theory, 2007; (42): 455－471.[12] Zhuang Peng, Yao Zhengqiu. Trajectory planning of suspended-cable parallel robot based on law of cycloidal motion. Mechanical Design, 2006; (9): 21－24.[13] Jorge Angeles. The principle of robotic mechanic system. Beijing: Mechanical Industry Press, 2004; 141－148.[14] Hofstee J W, Goense D. Simulation of a CAN-based tractor implement field bus according to DIN 9684. Journal of Agricultural Engineering Research, 1999; 73(4):383—394.[15] Yang Xianghui. Industrial communication and control network. Beijing: Tsinghua University Press, 2003. pp. 84－85.[16] Navet N, Song Y Q. Reliability improvement of the dual-priority protocol under unreliable transmission.Control Engineering Practice, 1999; (7): 975－981.运动学和轨迹规划的黄瓜采摘机器人机械手张利兵、王雁、杨庆华、宝冠君、高锋、薰易(教育部重点实验室的机械制造及自动化、浙江理工大学、中国杭州310012)摘要：为了降低成本，提高黄瓜收获经济效益，黄瓜收获机器人得以发展。

武汉纺织大学外文文献翻译文献名称：齿轮和轴的介绍name of document: Gear And Shaft Introduction姓名：张涛院系：机械工程与自动化专业：机械设计制造及其自动化班级：机械类11109班指导教师:肖晓峰武汉纺织大学WUHAN TEXTILE UNIVERSITYGEAR AND SHAFT INTRODUCTIONJIN Xin, ZHANG Zhi-jing, YE Xin, LI Zhong-xin(School of Mechanical and Vehicular Engineering, Beijing Institute of Technology,Beijing 100081, China)Abstract:The important position of the wheel gear and shaft can't falter in tradition al machine and modern machines.The wheel gear and shafts mainly install the directio n that delivers the dint at the principal axisbox.The passing to process to make them can is divided into many model numbers, us eding for many situations respectively.So we must be the multilayers to the understan ding of the wheel gear and shaft in many ways .Key words:Wheel; gear; ShaftIn the force analysis of spur gears, the forces are assumed to act in a single plane. We shall study gears in which the forces have three dimensions. The reason for this, in the case of helical gears, is that the teeth are not parallel to the axis of rotation. And i n the case of bevel gears, the rotational axes are not parallel to each other. There are al so other reasons, as we shall learn.Helical gears are used to transmit motion between parallel shafts. The helix angle is the same on each gear, but one gear must have a right-hand helix and the other a left -hand helix. The shape of the tooth is an involute helicoid. If a piece of paper cut in th e shape of a parallelogram is wrapped around a cylinder, the angular edge of the paper becomes a helix. If we unwind this paper, each point on the angular edge generates a n involute curve. The surface obtained when every point on the edge generates an inv1olute is called an involute helicoid.The initial contact of spur-gear teeth is a line extending all the way across the face of the tooth. The initial contact of helical gear teeth is a point, which changes into a li ne as the teeth come into more engagement. In spur gears the line of contact is parallel to the axis of the rotation; in helical gears, the line is diagonal across the face of the t ooth. It is this gradual of the teeth and the smooth transfer of load from one tooth to a nother, which give helical gears the ability to transmit heavy loads at high speeds. Helical gears subject the shaft bearings to both radial and thrust loads. When t he thrust loads become high or are objectionable for other reasons, it may be desirable to use double helical gears. A double helical gear (herringbone) is equivalent to two h elical gears of opposite hand, mounted side by side on the same shaft. They develop o pposite thrust reactions and thus cancel out the thrust load. When two or more single h elical gears are mounted on the same shaft, the hand of the gears should be selected so as to produce the minimum thrust load.Crossed-helical, or spiral, gears are those in which the shaft centerlines are neither parallel nor intersecting. The teeth of crossed-helical fears have point contact with ea ch other, which changes to line contact as the gears wear in. For this reason they will c arry out very small loads and are mainly for instrumental applications, and are definite ly not recommended for use in the transmission of power. There is on difference betw een a crossed helical gear and a helical gear until they are mounted in mesh with each other. They are manufactured in the same way. A pair of meshed crossed helical gears usually have the same hand; that is a right-hand driver goes with a right-hand driven. I n the design of crossed-helical gears, the minimum sliding velocity is obtained when t he helix angle are equal. However, when the helix angle are not equal, the gear with th e larger helix angle should be used as the driver if both gears have the same hand.Worm gears are similar to crossed helical gears. The pinion or worm has a small n umber of teeth, usually one to four, and since they completely wrap around the pitch c2ylinder they are called threads. Its mating gear is called a worm gear, which is not a tr ue helical gear. A worm and worm gear are used to provide a high angular-velocity re duction between nonintersecting shafts which are usually at right angle. The worm ge ar is not a helical gear because its face is made concave to fit the curvature of the wor m in order to provide line contact instead of point contact. However, a disadvantage o f worm gearing is the high sliding velocities across the teeth, the same as with crossed helical gears.Worm gearing are either single or double enveloping. A single-enveloping gearing is one in which the gear wraps around or partially encloses the worm.. A gearing in w hich each element partially encloses the other is, of course, a double-enveloping worm gearing. The important difference between the two is that area contact exists between the teeth of double-enveloping gears while only line contact between those of single-e nveloping gears. The worm and worm gear of a set have the same hand of helix as for crossed helical gears, but the helix angles are usually quite different. The helix angle o n the worm is generally quite large, and that on the gear very small. Because of this, it is usual to specify the lead angle on the worm, which is the complement of the worm helix angle, and the helix angle on the gear; the two angles are equal for a 90-deg. Sha ft angle.When gears are to be used to transmit motion between intersecting shaft, some of bevel gear is required. Although bevel gear are usually made for a shaft angle of 90 de g. They may be produced for almost any shaft angle. The teeth may be cast, milled, or generated. Only the generated teeth may be classed as accurate. In a typical bevel gea r mounting, one of the gear is often mounted outboard of the bearing. This means that shaft deflection can be more pronounced and have a greater effect on the contact of te eth. Another difficulty, which occurs in predicting the stress in bevel-gear teeth, is the fact the teeth are tapered.Straight bevel gears are easy to design and simple to manufacture and give very g3ood results in service if they are mounted accurately and positively. As in the case of s qur gears, however, they become noisy at higher values of the pitch-line velocity. In th ese cases it is often good design practice to go to the spiral bevel gear, which is the be vel counterpart of the helical gear. As in the case of helical gears, spiral bevel gears gi ve a much smoother tooth action than straight bevel gears, and hence are useful where high speed are encountered.It is frequently desirable, as in the case of automotive differential applications, to have gearing similar to bevel gears but with the shaft offset. Such gears are called hyp oid gears because their pitch surfaces are hyperboloids of revolution. The tooth action between such gears is a combination of rolling and sliding along a straight line and ha s much in common with that of worm gears.A shaft is a rotating or stationary member, usually of circular cross section, having mounted upon it such elementsas gears, pulleys, flywheels, cranks, sprockets, and oth er power-transmission elements. Shaft may be subjected to bending, tension, compres sion, or torsional loads, acting singly or in combination with one another. When they a re combined, one may expect to find both static and fatigue strength to be important d esign considerations, since a single shaft may be subjected to static stresses, completel y reversed, and repeated stresses, all acting at the same time.The word “shaft” covers numerous variations, such as axles and spindles. Anaxle i s a shaft, wither stationary or rotating, nor subjected to torsion load. A shirt rotating sh aft is often called a spindle.When either the lateral or the torsional deflection of a shaft must be held to close l imits, the shaft must be sized on the basis of deflection before analyzing the stresses. The reason for this is that, if the shaft is made stiff enough so that the deflection is not too large, it is probable that the resulting stresses will be safe. But by no means shoul d the designer assume that they are safe; it is almost always necessary to calculate the m so that he knows they are within acceptable limits. Whenever possible, the power-tr4ansmission elements, such as gears or pullets, should be located close to the supportin g bearings, This reduces the bending moment, and hence the deflection and bending st ress.Although the von Mises-Hencky-Goodman method is difficult to use in design of shaft, it probably comes closest to predicting actual failure. Thus it is a good way of c hecking a shaft that has already been designed or of discovering why a particular shaft has failed in service. Furthermore, there are a considerable number of shaft-design pr oblems in which the dimension are pretty well limited by other considerations, such as rigidity, and it is only necessary for the designer to discover something about the fille t sizes, heat-treatment, and surface finish and whether or not shot peening is necessary in order to achieve the required life and reliability.Because of the similarity of their functions, clutches and brakes are treated togeth er. In a simplified dynamic representation of a friction clutch, or brake, two inertias I1 and I2 traveling at the respective angular velocities W1 and W2, one of which may be zero in the case of brake, are to be brought to the same speed by engaging the clutch or brake. Slippage occurs because the two elements are running at different speeds and energy is dissipated during actuation, resulting in a temperature rise. In analyzing the performance of these devices we shall be interested in the actuating force, the torque transmitted, the energy loss and the temperature rise. The torque transmitted is related to the actuating force, the coefficient of friction, and the geometry of the clutch or bra ke. This is problem in static, which will have to be studied separately for eath geometr ic configuration. However, temperature rise is related to energy loss and can be studie d without regard to the type of brake or clutch because the geometry of interest is the heat-dissipating surfaces. The various types of clutches and brakes may be classified a s fllows:1. Rim type with internally expanding shoes2. Rim type with externally contracting shoes53. Band type4. Disk or axial type5. Cone type6. Miscellaneous typeThe analysis of all type of friction clutches and brakes use the same general proce dure. The following step are necessary:1. Assume or determine the distribution of pressure on the frictional surfaces.2. Find a relation between the maximum pressure and the pressure at any point3. Apply the condition of statical equilibrium to find (a) the actuating force, (b) the torque, and (c) the support reactions.Miscellaneous clutches include several types, such as the positive-contact clutches, overload-release clutches, overrunning clutches, magnetic fluid clutches, and others.A positive-contact clutch consists of a shift lever and two jaws. The greatest differe nces between the various types of positive clutches are concerned with the design of t he jaws. To provide a longer period of time for shift action during engagement, the ja ws may be ratchet-shaped, or gear-tooth-shaped. Sometimes a great many teeth or jaw s are used, and they may be cut either circumferentially, so that they engage by cylind rical mating, or on the faces of the mating elements.Although positive clutches are not used to the extent of the frictional-contact type , they do have important applications where synchronous operation is required.Devices such as linear drives or motor-operated screw drivers must run to definit e limit and then come to a stop. An overload-release type of clutch is required for thes e applications. These clutches are usually spring-loaded so as to release at a predeterm ined toque. The clicking sound which is heard when the overload point is reached is c onsidered to be a desirable signal.An overrunning clutch or coupling permits the driven member of a machine to “fr eewheel” or “overrun” because the driver is stopped or because another source of pow er increase the speed of the driven. This type of clutch usually uses rollers or balls mo6unted between an outer sleeve and an inner member having flats machined around the periphery. Driving action is obtained by wedging the rollers between the sleeve and th e flats. The clutch is therefore equivalent to a pawl and ratchet with an infinite number of teeth.Magnetic fluid clutch or brake is a relatively new development which has two par allel magnetic plates. Between these plates is a lubricated magnetic powder mixture. An electromagnetic coil is inserted somewhere in the magnetic circuit. By varying the excitation to this coil, the shearing strength of the magnetic fluid mixture may be acc urately controlled. Thus any condition from a full slip to a frozen lockup may be obtai ned.7中文翻译齿轮和轴的介绍金鑫；张之敬；叶鑫；李忠新；(机械与车辆工程学院，北京理工大学，北京100081，中国）摘要:在传统机械和现代机械中齿轮和轴的重要地位是不可动摇的。

Friction , Lubrication of BearingIn many of the problem thus far , the student has been asked to disregard or neglect friction . A ctually , friction is present to some degree whenever two parts are in contact and move on each other. The term friction refers to the resistance of two or more parts to movement.Friction is harmful or valuable depending upon where it occurs. friction is necessary for fastening devices such as screws and rivets which depend upon friction to hold the fastener and the parts together. Belt drivers, brakes, and tires are additional applications where friction is necessary.The friction of moving parts in a machine is harmful because it reduces the mechanical advantage of the device. The heat produced by friction is lost energy because no work takes place. A lso , greater power is required to overcome the increased friction. Heat is destructive in that it causes expansion. Expansion may cause a bearing or sliding surface to fit tighter. If a great enough pressure builds up because made from low temperature materials may melt.There are three types of friction which must be overcome in moving parts: (1)starting, (2)sliding,and(3)rolling. Starting friction is the friction between two solids that tend to resist movement. When two parts are at a state of rest, the surface irregularities of both parts tend to interlock and form a wedging action. T o produce motion in these parts, the wedge-shaped peaks and valleys of the stationary surfaces must be made to slide out and over each other. The rougher the two surfaces, the greater is starting friction resulting from their movement .Since there is usually no fixed pattern between the peaks and valleys of two mating parts, the irregularities do not interlock once the parts are in motion but slide over each other. The friction of the two surfaces is known as sliding friction. A s shown in figure ,starting friction is always greater than sliding friction .Rolling friction occurs when roller devces are subjected to tremendous stress which cause the parts to change shape or deform. Under these conditions, the material in front of a roller tends to pile up and forces the object to roll slightly uphill. This changing of shape , known as deformation, causes a movement of molecules. As a result ,heat is produced from the added energy required to keep the parts turning and overcome friction.The friction caused by the wedging action of surface irregularities can be overcome partly by the precision machining of the surfaces. However, even these smooth surfaces may require the use of a substance between them to reduce the friction still more. This substance is usually a lubricant which provides a fine, thin oil film. The film keeps the surfaces apart and prevents the cohesive forces of the surfaces from coming in close contact and producing heat .Another way to reduce friction is to use different materials for the bearing surfaces and rotating parts. This explains why bronze bearings, soft alloy s, and copper and tin iolite bearings are used with both soft andhardened steel shaft. The iolite bearing is porous. Thus, when the bearing is dipped in oil, capillary action carries the oil through the spaces of the bearing. This type of bearing carries its own lubricant to the points where the pressures are the greatest.Moving parts are lubricated to reduce friction, wear, and heat. The most commonly used lubricants are oils, greases, and graphite compounds. Each lubricant serves a different purpose. The conditions under which two moving surfaces are to work determine the type of lubricant to be used and the system selected for distributing the lubricant.On slow moving parts with a minimum of pressure, an oil groove is usually sufficient to distribute the required quantity of lubricant to the surfaces moving on each other .A second common method of lubrication is the splash system in which parts moving in a reservoir of lubricant pick up sufficient oil which is then distributed to all moving parts during each cycle. This system is used in the crankcase of lawn-mower engines to lubricate the crankshaft, connecting rod ,and parts of the piston.A lubrication system commonly used in industrial plants is the pressure system. In this system, a pump on a machine carries the lubricant to all of the bearing surfaces at a constant rate and quantity.There are numerous other sy stems of lubrication and a considerable number of lubricants available for any given set of operating conditions. Modern industry pays greater attention to the use of the proper lubricants than at previous time because of the increased speeds, pressures, and operating demands placed on equipment and devices.Although one of the main purposes of lubrication is reduce friction, any substance-liquid , solid , or gaseous-capable of controlling friction and wear between sliding surfaces can be classed as a lubricant.V arieties of lubricationUnlubricated sliding. Metals that have been carefully treated to remove all foreign materials seize and weld to one another when slid together. In the absence of such a high degree of cleanliness, adsorbed gases, water vapor ,oxides, and contaminants reduce frictio9n and the tendency to seize but usually result in severe wear。

1.英文文献翻译1.1英文文献原文题目Chapter 2 Research and rotating machinery fault vibration fault diagnosis of common.Rotating machinery are those main function is to be completed by the rotary movement of mechanical equipment, such as steam turbines, gas turbines, generators, motors, centrifugal blowers, centrifugal compressor pumps, vacuum pumps and a variety of slow growth of the gears and other machinery equipment, all belong to the scope of rotating machinery. Rotating machinery is the application of machinery and equipment most widespread, the number of the largest and most representative one of machinery and equipment, especially in electric power, petrochemical, metallurgy, machinery, aviation, nuclear industry and other industries, rotating machinery is a significant share an important position.2.1 Classification of Rotating Machinery VibrationRotating machinery vibration failure was classified as a major form of failure, according to different classification methods, a variety may be as follows1.By vibration frequency classification(1) Vibration frequency;(2) Harmonic vibration, for example, two octave, 3 octave vibration;(3) The entire baseband frequency scores (such as 1 / 2, 1 / 3, etc.)of the vibration;(4) Frequency and baseband into the relationship between a certain percentages (eg 38% ~ 49%) of the vibration;(5) ultra-low-frequency (vibration frequency 5Hz below) vibration;(6) Ultra-high frequency (vibration frequency in 10 kHz and above) Vibration2. Amplitude direction according to classification(1) Diameter (horizontal) to the vibration that is the direction along the shaft diameter of the vibration is generally divided into horizontal vibration straight vibration.(2) Axial vibration, that is, the direction along the axis of vibration cutting;(3) Tensional vibration, that is, the vibration along the shaft rotation direction.3. by vibration of the reasons for classification(1) The vibration caused by rotor imbalance;(2) Shaft misalignment caused by vibration;(3) Sliding bearing and crankshaft vibration caused by eccentricity;(4) The machine parts caused by loose vibration;(5) Friction (such as seal friction, the rotor and the stator friction, etc.) caused by vibration;(6) Bearing damage caused by vibration;(7) Sliding bearing oil whirls and oil whip caused by vibration;(8) Air power and hydraulic vibration caused by factors such as;(9) Bearing stiffness asymmetry caused by vibration;(10) Electrical aspects of the reasons for the vibration caused by4. Vibration occurred by the site classification(1) Rotor or shaft (including the journal, shaft profile vane, etc.)vibration;(2) Bearings (including the film sliding bearings and rolling bearing) vibration;(3) Shell, bearing vibration;(4) Infrastructure (including aircraft seats, table, or bracket, etc.) vibration;(5) Other areas such as valves, pipe stem, and a variety of structural vibration, etc.In addition, if according to the characteristics and forms of vibration, but also separation of synchronous vibrations (forced vibration) and sub-synchronous (self-excited vibration), etc... Due to vibrations caused by the failure of its manifestations are diverse, in order to accurately identified the cause failures cause - generally speaking, have to rely on signal processing techniques and vibration theory, and other modern methods and means to conduct a comprehensive and integrated analysis and in accordance with the gradual accumulation of experience in the specific circumstances, the only way to achieve fault diagnosis success. Failure of rotating machinery and therefore must be characterized by research.2.2 The characteristics of rotating machinery faultThe implementation of fault in the dynamic monitoring of rotating machinery, we must pay attention to other features:2.2.1 Rotor FeaturesThe rotor component is the core of rotating machinery and equipment, which is fixed by the shaft and the installation of various types of circular discoid components (such as coupling, bearings, impeller, gear, balance disk, pulley, wheel, flywheel, etc.), formed. As the entire rotor in high-speedrotation movements, so its manufacture, installation, commissioning, maintenance and management have a very high demand. If you had problems with one of these components, or in connection with a change in part an exception occurred, they immediately drew a strong vibration unit. It can be said of dynamic monitoring rotating machinery monitoring and diagnosis is mainly the rotor state of motion.2.2.2 The frequency characteristics of rotating machinery vibrationMost of rotating machinery vibration signals is periodic signals, quasi-periodic signal, or a stationary random signal. Failure of rotating machinery vibration characteristics have a common point, namely, the failure of their characteristic frequency related with the rotor speed is equal to the rotor rotation frequency (referred to as transfer frequency, also known as frequency) and its octave or sub-frequency. Therefore, the analysis of vibration signals of the frequency and turn the relationship between the frequencies of rotating machinery fault diagnosis of a key.2.2.3 for rotating machinery vibration monitoring the main wayVibration signal analysis is the basic method for monitoring rotating machinery, the main three-pronged approach to obtain monitoring information1. Analysis of rotating machinery vibration frequency of each type of fault has its own characteristic frequency at the scene to make the frequency of the vibration signal analysis is the diagnosis of rotating machinery of the most effective method. Frequency speed of rotating machinery is like a "military demarcation line," the entire band is divided into sub-and super-asynchronous asynchronous vibration frequency of vibration of two sections, to seize this point, helps us to analyze and judge the fault2. Analysis of amplitude and direction of features in some cases(certainly not all occasions) different types of rotating machinery fault vibration on the performance characteristics of a clear direction. Therefore, the vibration of rotating machinery measurements, as long as conditions permit, the general measure of each measuring point should be horizontal, vertical and axial three directions, as in different directions to provide us with a different fault information. Leakage measured in one direction, you may losea message.3. Analysis of the relationship between the amplitude changes with the speed of a considerable portion of rotating machinery fault vibration amplitude and speed changes are closely related, so on-site measurements, when necessary, to create conditions for as much as possible, in the process of changing the speed amplitude measurement of the machine value.2.3 Rotating Machinery Vibration Fault DiagnosisAs mentioned earlier, equipment fault diagnosis is essentially a pattern classification are based on test analysis obtained on the state information, and grouped into a certain type of equipment failure. Therefore, the characteristics of each type of fault must have sufficient understanding. Equipment diagnostics development today, the people through a large number of experimental studies and a wide range of diagnostic practice, for a variety of devices (especially rotating machinery) of the failure mechanism, fault type and its characteristics have a considerable understanding of understanding. Statistics show that, with the production of a different nature, the type of equipment used is also different, so the proportion of various types of failures is also inconsistent. Here are several common fault diagnosis of rotating machinery vibration characteristics, diagnostic methods and examples.2.3.1 ImbalanceAccording to the information that various types of rotating machinery failure due to imbalance of about 30%, we can see that the machine rotor imbalance caused by rotating machinery vibration is a common multiple faults. To fully understand and grasp the characteristics and mechanism of unbalanced fault diagnosis is very important.1. The causes of imbalances caused by rotor imbalance are many reasons, such as:① unreasonable because it is designed geometry caused by different heart, or deviate from the geometric center line of rotary valve shaft;② Manufacture, installation error;③ Rotor material uneven, or heat unevenly;④ Rotor initial bending;⑤ Work medium in the solid impurities in the rotor on the uneven deposition;⑥ Rotor in the course of corrosion, wear and tear;⑦ Rotor parts loose, fall off.2. Rotor imbalance may lead to consequences for the flexible rotor may also generate additional degree of damage due to dynamic inertia of the centrifugal force caused by imbalance. For various reasons caused by rotor unbalance fault is a basically the same pattern. To sum up, the rotor imbalance may lead to the following undesirable consequences:(1) The rotor caused by repeated bending and internal stress, causing the rotor fatigue, even lead to rotor fault;(2) To enable the machine in operation during the excessive vibration and noise, so that it will accelerate the wear of bearings and other componentsto reduce life expectancy and efficiency of the machine;(3) Through the vibration of the rotor bearings, machine transmits to the base blocks and buildings, resulting in deterioration in working conditions.3. Rotor imbalance generally include the following four cases(1) Static unbalance;(2) double-sided imbalances;(3) Static and dynamic imbalance;(4) Dynamic imbalance. for example:2-1:Among them, static imbalance is an imbalance in the cross section, while the remaining three kinds of imbalance is an imbalance on the number of sections, and each inspired by a cross-section due to imbalances in the lateral vibration and static unbalance is the same as the mechanism of. In other words, the cross section generated by the phase and amplitude of vibration and its size may vary, but the vibration frequency is exactly the same, are the first-order rotation frequency (fundamental frequency),2-1f0 - a first-order frequency of the rotor, ie rotor fundamental frequency (Hz); n - rotor speed (r / min).Unbalanced rotor in rotation will produce a cycle of change was the imbalance in power, the cycle just that, as shown in Figure 2-2.With the rotor unbalance vibration signal, its time waveform and frequency spectrum of the typical curves shown in Figure 2-3, and generally has the following characteristics:(1) The vibration signal of the original time waveform of sine wave;(2) The frequency spectrum of vibration signal, its fundamental frequency component and a significant proportion, while other components such as frequency-doubling the proportion of relatively small.(3) In the process of speeding up or down, when (that is, when speed is less than the critical speed), the amplitude increases with the increase in W, both bearing the same direction of the force, while in the later, the amplitude increases with the W, but will decreases, and gradually tends to a smaller valuation.4. The basic method of diagnosis of unbalanced fault diagnosis of unbalanced faults, we must first analyze the signal frequency components, the existence of transponder prominent situation. Second, look at the direction of vibration characteristics, if necessary, further analysis of the changes in amplitude as speed or measuring the phase. Because the latter two tests carried out too much trouble to stop the problem involved, which in general is difficult in the production of the site done, and only to a non-for not only had to do when, but time can not be delayed too long.2.3.2 MisalignmentAs the rotor and turn on the sub-shaft connection between the use of connecting devices install properly, or due to bearing centerline deviation, or offset, or because the rotor bending, rotor and bearing clearance and load transfer in the bearing after the deformation and other reasons, tend to result in between the rotor (shaft) to the poor, resulting in vibration and lead to mechanical failure. It is also one of the very common mechanical failures .1. Shaft misalignment of the shaft does not include the three forms of coupling misalignment and bearing right in both cases, here we only discuss the coupling (shaft) misalignment. Coupling does not usually possesses the following three forms,For example2-4:(1) Parallel misalignment, this time through the rotor axis lines in parallel displacement.(2) The angle misalignment, this time to switch on the two axis lines intersect, or angle displacement.(3) Parallel synthesis misalignment angle, this time two lines intersect the rotor axis of displacement.Figure 2-5 shows the shaft vibration caused by misalignment angle parallel to the simple diagramIn general, the rotor shaft misalignment can cause additional load on the bearings, resulting in the bearing load between the re-allocation would lead to serious bearing damage caused by a strong vibration. On the other hand, with the coupling on both sides of bearing the load changes that may cause the system critical speed of the change in the uneven effects of an increase, giving rise to the coupling fatigue. When the bearing change is large, for the sliding bearing oil film may also cause instability.2. Shaft misalignment of the main features of a typical shaft misalignment radial vibration signal time waveform and frequency spectrum 2-6. And mainly has the following characteristics:(1) The vibration signal of the original time waveform distortion sinewave. (2) The radial vibration frequency spectrum of the signal to a multiplier, and second harmonic components of the main shaft misalignment more serious, and the second harmonic component of the greater proportion, in most cases more than one harmonic component of .(3) The axial vibration of components in the spectrum to octave higheramplitude.(4) Coupling on both sides of the axial vibration is essentially 180 °inverting.(5) A typical trajectory for the banana-shaped axis is precession.(6) Vibration on the more sensitive to changes in load, the generalvibration amplitude increases with the load increase.2.3.3 Rotor CrackIf the rotor rotating machinery are poorly designed (including the improper selection or structure is irrational) or improper processing methods, or the super life of running, it will cause stress concentration leading to cracks. On the other hand, fatigue, creep and stress corrosion can cause micro-cracks in the rotor, plus large change due to the twist and radial loadto form the mechanical stress state, resulting in continuous expansion of these micro-cracks eventually become a macro-crack.1. Three forms of rotor cracks(1) Closed crack. Rotor rotates; the crack was always closed state. When the crack zone in a compressive stress state, would constitute a closed crack, such as the rotor weight is not an unbalanced force smaller or unbalanced force precisely the opposite point to cracks, or uneven quality, moments generated by the rotor is greater than the quality of generated moment and so on. Closed crack little effect on the rotor thrust.(2) Open crack. When the rotor spins, the crack was always open state. Open cracks force the situation is exactly the opposite and closed crack; the crack area is always in tension stress state. Open crack will reduce the stiffness of the rotor, and its stiffness to the different nature of each, so that vibration increased.(3) The opening and closing crack. With the rotation of the rotor movement, crack was open and close alternately state, and generally turn the rotor of each week, the crack will be the corresponding open and closed each time. Crack opening and closing part of the open crack and the crack in the middle of a closed transition state, which is the most complex forms. Figure 2-7 shows the rotor with the opening and closing crack deflection curve diagram.Despite the change in the crack will affect the rotor vibration characteristics, but in most cases is not very sensitive, even the cracks in the rotor has a deep, sometimes hard to find significant changes in the vibration condition. For example, according to theoretical calculations, if there is a change in central depth is equal to 1 / 4 turn on the diameter of the crack, its stiffness is only about 10%, while the changes in critical speed is smaller, only 5%. Therefore, these changes will likely be completely submerged into the other signal, that is, from the observed changes in the natural frequency of the rotor, or when the normal operation of the vibration changes according to the early detection of cracks is very difficult. At present more effective way is to stop the process of measurement and analysis open the rate of change in amplitude.Generally speaking, when there open crack rotor, the rotor will become of all the stiffness of the differences. As a result, the vibration of the rotor with a non-linear nature of the spectrum, in addition to a harmonic component, there are twice, three times to five times the high-harmoniccomponents. Toward the crack, the stiffness of the rotor will be further reduced; a multiplier component, as well as twice or three times or five times, and other first-order harmonic components of the amplitude will be even greater.2. Be passed on to crack the monitoring and diagnosis is divided into three areas(1) Open, stopping when the variation of amplitude versus speed.(2) The impact of crack depth on the amplitude.Under normal circumstances, the vibration spectrum and the second harmonic component of twice the amplitude will increase with the depth of the monotonic crack growth, while the corresponding phase decreased with the increase of crack depth irregular fluctuations. It just can be used to distinguish between normal vibrations caused by imbalance.(3) The crack growth rate.But the crack propagation speed increases as the crack depth to accelerate, with a corresponding rate of increase in amplitude occurs phenomenon. In particular the rapid increase in second harmonic amplitude can often provide crack diagnostic information, so can take advantage of two trends in the changes in the harmonic components to diagnose the rotor cracks.3. Rotor cracks after the general characteristics of(1) The first-order critical speed is smaller than normal, especially when the crack worsens.(2) As the crack and stiffness caused by rotor asymmetry, the rotor speed of the formation of multiple resonance.(3) The crack rotor vibration response, one harmonic component of the degree of dispersion when compared with large crack-free.(4) A constant speed, the doubled, tripled the third harmonic and other components of the amplitude and the phase-order instability, and in particular to highlight the second harmonic component.(5) Due to the stiffness of cracked rotor asymmetry, so that pairs of rotor balancing difficulty.1.2中文翻译第2章旋转机械故障的研究及常见故障的振动诊断旋转机械是指那些主要功能是由旋转运动来完成的机械设备，如汽轮机、燃气轮机、发电机、电动机、离心式鼓风机、离心式压缩机泵、真空泵以及各种减速增速的齿轮传动装置等机械设备，都属于旋转机械范围。

诊断名词术语基本术语(1)状态监测(condition monitoring)－对机械设备的工作状态（静的和动的）进行监视和测量（实时的或非实时的），以了解其正常与不正常。

(2)故障诊断(fault diagnosis)又称为技术诊断(technical diagnosis)－采用一定的诊断方法和手段，确定机械设备功能失常的原因、部位、性质、程度和类别，明确故障的存在和发展。

(3)简易诊断(simple diagnosis)－使用简易仪器和方法进行诊断。

(4)精密诊断(meticulous diagnosis)－使用精密仪器进行的诊断（优于精确诊断或精度诊断术语）。

(5)故障征兆(symptom of fault)（或称故障症状）－能反映机械设备功能失常，存在故障的各种状态量。

(6)征兆参数(symptom of parameter)－能有效识别机械设备故障源故障的各种特征量，包括：原始量和处理量。

(7)状态识别(condition recognition/identification)－为判断机械设备工作状态的正常与不正常和通过故障状态量的区别，诊断其故障的方法。

(8)特征提取(feature extraction)－为了正确识别和诊断机械设备故障的存在与否，对征兆参数进行特别的处理。

(9)故障类别(fault classification)－反映机械设备功能失常、结构受损、工作实效的专用分类、名称。

(10)故障性质(nature of fault)－描述故障发生速度、危险程度、发生规律、发生原因等问题。

(11)突发故障(sudden fault)－突然发生的故障。

在故障发生瞬间，必须采用实时监控、保安装置、紧急停机等措施。

(12)渐发故障(slow fault)－故障的形成和发展比较缓慢，能够提供监测与诊断的条件。

(13)破坏性故障(damaging fault)或称灾难性故障(catastrophic fault)－故障的发生影响机械设备功能的全部失去，并造成局部或整体的毁坏，难以修复重新使用。

英文原文A Practical Approach to Vibration Detection and Measurement——Physical Principles and Detection TechniquesBy: John Wilson, the Dynamic Consultant, LLCThis tutorial addresses the physics of vibration; dynamics of a spring mass system; damping; displacement, velocity, and acceleration; and the operating principles of the sensors that detect and measure these properties. Vibration is oscillatory motion resulting from the application of oscillatory or varying forces to a structure. Oscillatory motion reverses direction. As we shall see, the oscillation may be continuous during some time period of interest or it may be intermittent. It may be periodic or nonperiodic, i.e., it may or may not exhibit a regular period of repetition. The nature of the oscillation depends on the nature of the force driving it and on the structure being driven.Motion is a vector quantity, exhibiting a direction as well as a magnitude. The direction of vibration is usually described in terms of some arbitrary coordinate system (typically Cartesian or orthogonal) whose directions are called axes. The origin for the orthogonal coordinate system of axes is arbitrarily defined at some convenient location.Most vibratory responses of structures can be modeled as single-degree-of-freedom spring mass systems, and many vibration sensors use a spring mass system as the mechanical part of their transduction mechanism. In addition to physical dimensions, a spring mass system can be characterized by the stiffness of the spring, K, and the mass, M, or weight, W, of the mass. These characteristics determine not only the static behavior (static deflection, d) of the structure, but also its dynamic characteristics. If g is the acceleration of gravity:F = MAW = MgK = F/d = W/dd = F/K = W/K = Mg/KDynamics of a Spring Mass SystemThe dynamics of a spring mass system can be expressed by the system's behavior in free vibration and/or in forced vibration.Free Vibration. Free vibration is the case where the spring is deflected and then released and allowed to vibrate freely. Examples include a diving board, a bungee jumper, and a pendulum or swing deflected and left to freely oscillate.Two characteristic behaviors should be noted. First, damping in the system causes the amplitude of the oscillations to decrease over time. The greater the damping, the faster the amplitude decreases. Second, thefrequency or period of the oscillation is independent of the magnitude of the original deflection (as long as elastic limits are not exceeded). The naturally occurring frequency of the free oscillations is called the natural frequency, f n:(1)Forced Vibration. Forced vibration is the case when energy is continuously added to the spring mass system by applying oscillatory force at some forcing frequency, f f. Two examples are continuously pushing a child on a swing and an unbalanced rotating machine element. If enough energy to overcome the damping is applid, the motion will continue as long as the excitation continues. Forced vibration may take the form of self-excited or externally excited vibration. Self-excited vibration occurs when the excitation force is generated in or on the suspended mass; externally excited vibration occurs when the excitation force is applied to the spring. This is the case, for example, when the foundation to which the spring is attached is moving.Transmissibility. When the foundation is oscillating, and force is transmitted through the spring to the suspended mass, the motion of the mass will be different from the motion of the foundation. We will call the motion of the foundation the input, I, and the motion of the mass the response, R. The ratio R/I is defined as the transmissibility, Tr:Tr = R/IResonance. At forcing frequencies well below the system's natural frequency, R I, and Tr 1. As the forcing frequency approaches the natural frequency, transmissibility increases due to resonance. Resonance is the storage of energy in the mechanical system. At forcing frequencies near the natural frequency, energy is stored and builds up, resulting in increasing response amplitude. Damping also increases with increasing response amplitude, however, and eventually the energy absorbed by damping, per cycle, equals the energy added by the exciting force, and equilibrium is reached. We find the peak transmissibility occurring when f f f n. This condition is called resonance.Isolation. If the forcing frequency is increased above f n, R decreases. When f f = 1.414 fn, R = I and Tr = 1; at higher frequencies R <I and Tr <1. At frequencies when R <I, the system is said to be in isolation. That is, someof the vibratory motion input is isolated from the suspended mass.Effects of Mass and Stiffness Variations. From Equation (1) it can be seen that natural frequency is proportional to the square root of stiffness, K, and inversely proportional to the square root of weight, W, or mass, M. Therefore, increasing the stiffness of the spring or decreasing the weight of the mass increases natural frequency.DampingDamping is any effect that removes kinetic and/or potential energy from the spring mass system. It is usually theresult of viscous (fluid) or frictional effects. All materials and structures have some degree of internal damping. In addition, movement through air, water, or other fluids absorbs energy and converts it to heat. Internal intermolecular or intercrystalline friction also converts material strain to heat. And, of course, external friction provides damping.Damping causes the amplitude of free vibration to decrease over time, and also limits the peak transmissibility in forced vibration. It is normally characterized by the Greek letter zeta () , or by the ratio C/C c, where c is the amount of damping in the structure or material and C c is "critical damping." Mathematically, critical damping is expressed as C c = 2(KM)1/2. Conceptually, critical damping is that amount of damping which allows the deflected spring mass system to just return to its equilibrium position with no overshoot and no oscillation. An underdamped system will overshoot and oscillate when deflected and released. An overdamped system will never return to its equilibrium position; it approaches equilibrium asymptotically. Displacement, Velocity, and AccelerationSince vibration is defined as oscillatory motion, it involves a change of position, or displacement (see Figure 1).Figure 1.Phase relationships among displacement, velocity, and acceleration are shown on these time history plots.Velocity is defined as the time rate of change of displacement; acceleration is the time rate of change of velocity. Some technical disciplines use the term jerk to denote the time rate of change of acceleration.Sinusoidal Motion Equation. The single-degree-of-freedom spring mass system, in forced vibration, maintained at a constant displacement amplitude, exhibits simple harmonic motion, or sinusoidal motion. That is, its displacement amplitude vs. time traces out a sinusoidal curve. Given a peak displacement of X, frequency f, and instantaneous displacement x:(2)at any time, t.Velocity Equation. Velocity is the time rate of change of displacement, which is the derivative of the time function of displacement. For instantaneous velocity, v:(3)Since vibratory displacement is most often measured in terms of peak-to-peak, double amplitude, displacement D = 2X:(4)If we limit our interest to the peak amplitudes and ignore the time variation and phase relationships:(5)where:V = peak velocityAcceleration Equation. Similarly, acceleration is the time rate of change of velocity, the derivative of the velocity expression:(6)and(7)where:A = peak accelerationIt thus can be shown that:V = fDA = 22 f2 DD = V/ fD = A/22 f2From these equations, it can be seen that low-frequency motion is likely to exhibit low-amplitude accelerations even though displacement may be large. It can also be seen that high-frequency motion is likely to exhibit low-amplitude displacements, even though acceleration is large. Consider two examples:• At 1 Hz, 1 in. pk-pk displacement is only ~0.05 g acceleration; 10 in. is ~0.5 g • At 1000 Hz, 1g acceleration is only ~0.00002 in. displacement; 100 g is ~0.002 in.Measuring Vibratory DisplacementOptical Techniques. If displacement is large enough, as at low frequencies, it can be measured with a scale, calipers, or a measuring microscope. At higher frequencies, displacement measurement requires more sophisticated optical techniques.High-speed movies and video can often be used to measure displacements and are especially valuable for visualizing the motion of complex structures and mechanisms. The two methods are limited by resolution to fairly large displacements and low frequencies. Strobe lights and stroboscopic photography are also useful when displacements are large enough, usually >0.1 in., to make them practical.The change in intensity or angle of a light beam directed onto a reflective surface can be used as an indication of its distance from the source. If the detection apparatus is fast enough, changes of distance can be detected as well.The most sensitive, accurate, and precise optical device for measuring distance or displacement is the laser interferometer. With this apparatus, a reflected laser beam is mixed with the original incident beam. The interference patterns formed by the phase differences can measure displacement down to <100 nm. NIST and other national primary calibration agencies use laser interferometers for primary calibration of vibration measurement instruments at frequencies up to 25 kHz.Electromagnetic and Capacitive Sensors. Another important class of noncontact, special-purpose displacement sensors is the general category of proximity sensors. These are probes that are typically built into machinery to detect the motion of shafts inside journal bearings or the relative motion of other machine elements. The sensors measure relative distance or proximity as a function of either electromagnetic or capacitive (electrostatic) coupling between the probe and the target. Because these devices rely on inductive or capacitive effects, they require an electrically conductive target. In most cases, they must be calibrated for a specific target and specific material characteristics in the gap between probe and target.Electromagnetic proximity sensors are often called eddy current probes because one of the most popular types uses eddy currents generated in the target as its measurement mechanism. More accurately, this type of sensor uses the energy dissipated by the eddy currents. The greater the distance from probe to target, the less electromagnetic coupling, the lower the magnitude of the eddy currents, and the less energy they drain from theprobe. Other electromagnetic probes sense the distortion of an electromagnetic field generated by the probe and use that measurement to indicate the distance from probe to target.Capacitive proximity sensor systems measure the capacitance between the probe and the target and are calibrated to convert the capacitance to distance. Capacitance is affected by the dielectric properties of the material in the gap as well as by distance, so calibration can be affected by a change of lubricant or contamination of the lubricant in a machine environment.Contact Techniques. A variety of relative motion sensors use direct contact with two objects to measure relative motion or distance between them. These include LVDTs, cable position transducers (stringpots), and linear potentiometers. All of these devices depend on mechanical linkages and electromechanical transducers.Seismic Displacement Transducers. These devices, discussed in detail later, were once popular but now are seldom used. They tend to be large, heavy, and short lived.Double Integration of Acceleration. With the increasing availability and decreasing cost of digital signal processing, more applications are using the more rugged and more versatile accelerometers as sensors, then double integrating the acceleration signal to derive displacements. While older analog integration techniques tended to be noisy and inaccurate, digital processing can provide quite high-quality, high-accuracy results.Measuring Vibratory VelocityTransducers. Some of the earliest "high-frequency" vibration measurements were made with electrodynamic velocity sensors. These are a type of seismic transducer that incorporates a magnet supported on a soft spring suspension system to form the seismic (spring mass) system. The magnetic member is suspended in a housing that contains one or more multiturn coils of wire. When the housing is vibrated at frequencies well above the natural frequency of the spring mass system, the mass (magnet) is isolated from the housing vibration. Thus, the magnet is essentially stationary and the housing, with the coils, moves past it at the velocity of the structure to which it is attached. Electrical output is generated proportional to the velocity of the coil moving through the magnetic field. Velocity transducers are used from ~10 Hz up to a few hundred Hz. They tend to be large and heavy, and eventually wear and produce erratic outputs.Laser Vibrometers. Laser vibrometers or laser velocimeters are relatively new instruments capable of providing high sensitivity and accuracy. They use a frequency-modulated (typically around 44 MHz) laser beam reflected from a vibrating surface. The reflected beam is compared with the original beam and the Doppler frequency shift is used to calculate the velocity of the vibrating surface. Alignment and standoff distance are critical. Because of the geometric constraints on location, alignment, and distances, they are limited to laboratory applications. One version of laser vibrometer scans the laser beam across a field of vision, measuring velocity at each point. The composite can then be displayed as a contour map or a colorized display. The vibration map can be superimposed on a video image to provide the maximum amount of information about velocity variations on a large surface.Integration of Acceleration. As with displacement measurements, low-cost digital signal processing makes it practical to use rugged, reliable, versatile accelerometers as sensors and integrate their output to derive a velocity signal.Measuring Vibratory AccelerationMost modern vibration measurements are made by measuring acceleration. If velocity or displacement data are required, the acceleration data can be integrated (velocity) or double integrated (displacement). Some accelerometer signal conditioners have built-in integrators for that purpose. Accelerometers (acceleration sensors, pickups, or transducers) are available in a wide variety of sizes, shapes, performance characteristics, and prices. The five basic transducer types are servo force balance; crystal-type or piezoelectric; piezoresistive or silicon strain gauge type; integral electronics piezoelectric; and variable capacitance. Despite the different electromechanical transduction mechanisms, all use a variation of the spring mass system, and are classified as seismic transducers.Seismic Accelerometer Principle. All seismic accelerometers use some variation of a seismic or proof mass suspended by a spring structure in a case (see Figure 3). When the case is accelerated, the proof mass is also accelerated by the force transmitted through the spring structure. Then the displacement of the spring, the displacement of the mass within the case, or the forcetransmitted by the spring is transduced into an electrical signal proportional to acceleration.Accelerometers. Transducers designed to measure vibratory acceleration are called accelerometers. There are many varieties including strain gauge, servo force balance, piezoresistive (silicon strain gauge), piezoelectric (crystal-type), variable capacitance, and integral electronic piezoelectric. Each basic type has many variations and trade names. Most manufacturers provide excellent applications engineering assistance to help the user choose the best type for the application, but because most of these sources sell only one or two types, they tend to bias their assistance accordingly.For most applications, my personal bias is toward piezoelectric accelerometers with internal electronics. The primary limitation of these devices is temperature range. Although they exhibit low-frequency roll-off, they are available with extremely low-frequency capabilities. They provide a preamplified low-impedance output, simple cabling, and simple signal conditioning, and generally have the lowest overall system cost.Most important to the user are the performance and environmental specifications and the price. What's inside the box is irrelevant if the instrument meets the requirements of the application, but when adding to existing instrumentation it is important to be sure that the accelerometer is compatible with the signal conditioning. Each type of accelerometer requires a different type of signal conditioning.Accelerometer Types. The most common seismic transducers for shock and vibration measurements are:∙Piezoelectric (PE); high-impedance output∙Integral electronics piezoelectric (IEPE); low-impedance output∙Piezoresistive (PR); silicon strain gauge sensor∙Variable capacitance (VC); low-level, low-frequency∙Servo force balancePiezoelectric (PE) sensors use the piezoelectric effects of the sensing element(s) to produce a charge output. Because a PE sensor does not require an external power source for operation, it is considered self-generating. The "spring" sensing elements provide a given number of electrons proportional to the amount of applied stress (piezein is a Greek word meaning to squeeze). Many natural and man-made materials, mostly crystals or ceramics and a few polymers, display this characteristic. These materials have a regular crystalline molecular structure, with a net charge distribution that changes when strained.Piezoelectric materials may also have a dipole (which is the net separation of positive and negative charge along a particular crystal direction) when unstressed. In these materials, fields can be generated by deformation from stress or temperature, causing piezoelectric or pyroelectric output, respectively. The pyroelectric outputs can be very large unwanted signals, generally occurring over the long time periods associated with most temperature changes. Polymer PE materials have such high pyroelectric output that they were originally used as thermal detectors. There are three pyroelectric effects, which will be discussed later in detail.Charges are actually not "generated," but rather just displaced. (Like energy and momentum, charge is always conserved.) When an electric field is generated along the direction of the dipole, metallic electrodes on faces at the opposite extremes of the gradient produce mobile electrons that move from one face, through the signal conditioning, to the other side of the sensor to cancel the generated field. The quantity of electrons depends on the voltage created and the capacitance between the electrodes. A common unit of charge from a PE accelerometer is the picocoulomb, or 10-12 coulomb, which is something over 6 × 106 electrons.Choosing among the many types of PE materials entails a tradeoff among charge sensitivity, dielectric coefficient (which, with geometry, determines the capacitance), thermal coefficients, maximum temperature, frequency characteristics, and stability. The best S/N ratios generally come from the highest piezoelectric coefficients.Naturally occurring piezoelectric crystals such as tourmaline or quartz generally have low-charge sensitivity, about one-hundredth that of the more commonly used ferroelectric materials. (But these low-charge output materials are typically used in the voltage mode, which will be discussed later.) Allowing smaller size for a given sensitivity, ferroelectric materials are usually man-made ceramics in which the crystalline domains (i.e., regions in which dipoles are naturally aligned) are themselves aligned by a process of artificial polarization.Polarization usually occurs at temperatures considerably higher than operating temperatures to speed the process of alignment of the domains. Depolarization, or relaxation, can occur at lower temperatures, but at very much lower rates, and can also occur with applied voltages and preload pressures. Depolarization always results intemporary or permanent loss of sensitivity. Tourmaline, a natural crystal that does not undergo depolarization, is particularly useful at very high temperatures.Because they are self-generating, PE transducers cannot be used to measure steady-state accelerations or force, which would put a fixed amount of energy into the crystal (a one-way squeeze) and therefore a fixed number of electrons at the electrodes. Conventional voltage measurement would bleed electrons away, as does the sensor's internal resistance. (High temperature or humidity in the transducer would exacerbate the problem by reducing the resistance value.) Energy would be drained and the output would decay, despite the constant input acceleration/force.External measurement of PE transducer voltage output requires special attention to the cable's dynamic behavior as well as the input characteristics of the preamplifier. Since cable capacitance directly affects the signal amplitude, excessive movement of the cable during measurement can cause changes in its capacitance and should be avoided. Close attention should also be paid to the preamp's input impedance; this should be on the order of 1000 M or higher to ensure sufficient low-frequency response.In practice, a charge amplifier is normally used with a PE transducer.Instead of measuring voltage externally, a charge should be measured with a charge converter. It is ahigh-impedance op amp with a capacitor as its feedback. Its output is proportional to the charge at the input and the feedback capacitor, and is nearly unaffected by the input capacitance of the transducer or attached cables. The high-pass corner frequency is set by the feedback capacitor and resistor in a charge converter, and not the transducer characteristics. (The transducer resistance changes noise characteristics, not the frequency.) If time constants are long enough, the AC-coupled transducer will suffice for most vibration measurements.Perhaps the most important limitation of high-impedance output PE transducers is that they must be used with "noise-treated" cables; otherwise, motion in the cable can displace triboelectric charge, which adds to the charge measured by the charge converter. Triboelectric noise is a common source of error found in typical coaxial cables.Most PE transducers are extremely rugged. Each of the various shapes and sizes available comes with its own performance compromises. The most common types of this transducer are compression and shear designs. Shear design offers better isolation from environmental effects such as thermal transient and base strain, and is generally more expensive. Beam-type design, a variation of the compression design, is also quite popular due to its lower manufacturing cost. But beam design is generally more fragile and has limited bandwidth.Integral Electronics Piezoelectric (IEPE). Many piezoelectric accelerometers/force transducers include integral miniature hybrid amplifiers, which, among their other advantages, do not need noise-treated cable. Most require an external constant current power source. Both the input supply current and output signal are carried over the same two-wire cable. The low-impedance output of the IEPE design (see Figure 5) provides relative immunityto the effects of poor cable insulation resistance, triboelectric noise, and stray signal pickup.Output-to-weight ratio of IEPE is higher than with PE transducers. Additional functions can be incorporated into the electronics (see Figure 6), including filters, overload protection, and self-identification.Lower cost cable and conditioning can be used since the conditioning requirements are comparatively lax compared to PE or PR. The sensitivity of IEPE accelerometers/force transducers, in contrast to PR, is not significantly affected by supply changes. Instead, dynamic range, the total possible swing of the output voltage, is affected by bias and compliance voltages. Only with large variations in current supply would there be problems with frequency response when driving high-capacitance loads.A disadvantage of built-in electronics is that it generally limits the transducer to a narrower temperature range. In comparison with an identical transducer design that does not have internal electronics, thehigh-impedance version will always have a higher mean time between failures (MTBF) rating. In addition, the necessarily small size of the amplifier may preclude some of the desirable features offered by a full-blown laboratory amplifier, such as the ability to drive long cable. Slew limiting is therefore a concern with these transducers (some designs have relatively high output impedance) when driving long lines or other capacitive loads. The problem can be remedied by increasing the amount of drive current within the limit specified by the manufacturer.The circuits need not necessarily be charge converters because the capacitance due to leads between the sensor and the amplifier is small and well controlled. Quartz is used in the voltage mode, i.e., with source followers, because its small dielectric coefficient provides comparatively high voltage per unit charge. Voltage conversion also aids ferroelectric ceramics that have the sag in frequency response in charge mode due to their frequency-dependent dielectric coefficient. The amplitude frequency response in the voltage mode is quite flat.Piezoresistive. A PR accelerometer is a Wheatstone bridge of resistors incorporating one or more legs that change value when strained. Because the sensors are externally supplied with energy, the output can be meaningfully DC coupled to respond to steady-state conditions. Data on steady-state accelerations comes at a cost, however. The sensitivity of a bridge varies almost directly with the input excitation voltage, requiring a highly stable and quiet excitation supply .The output of a bridge configuration is the difference between the two output leads. A differential amplifier is required or, alternatively, both leads from the excitation must float to allow one of the output lines to be tied to ground. The differential configuration provides the advantage of common-mode rejection; that is to say, any noise signals picked up on the output lines, if equal, will be canceled by the subtraction in the amplifier.A cautionary note is in order here: With high-output PR transducers, there is a temptation to dispense with an amplifier and simply to connect the output leads directly to an oscilloscope. This will not work if both the scope and the excitation are single ended. Oscilloscopes often have single-ended input (the negative side of the input is ground). If the excitation is also grounded (with the excitation equal to ground), one leg of the bridge is shuntedand the entire excitation voltage is placed across that one leg of the bridge. If you are using AC coupling on the scope, you might misinterpret the reasonably shaped, but small and noisy, output.Most PR sensors use two or four active elements. Voltage output of a two-arm, or half-bridge, sensor is half that of a four-arm, or full bridge.Stability requirements for a PR transducer power supply and its conditioning are considerably tighter than they are for IEPE. Low-impedance PR transducers share the advantages of noise immunity provided by IEPE, although the output impedance of PR is often large enough that it cannot drive large capacitive loads. As is the case with an underdriven IEPE, the result is a low-pass filter on the output, limiting high-frequency response.The sensitivity of a strain gauge comes from both the elastic response of its structure and the resistivity of the material. Wire and thick or thin film resistors have low gauge factors; that is, the ratio of resistance change to the strain is small. Their response is dominated by the elastic response. They are effectively homogeneous blocks of material with resistivity of nearly constant value. As with any resistor, they have a value proportional to length and inversely proportional to cross-sectional area. If a conventional material is stretched, its width reduces while the length increases. Both effects increase resistance.The Poisson ratio defines the amount a lateral dimension is narrowed compared to the amount the longitudinal dimension is stretched. Given a Poisson ratio of 0.3 (a common value), the gauge factor would be 1.6; resistance would change 1.6 × more than it is strained. A typical gauge factor for metal strain gauges is ~2.The response of strain gauges with higher gauge factors is dominated by the piezoresistive effect, which is the change of resistivity with strain. Semiconductor materials exhibit this effect, which, like piezoelectricity, is strongly a function of crystal orientation. Like other semiconductor properties, it is also a strong function of dopant concentration and temperature. Gauge factors near 100 are common for silicon gauges, and, when combined with small size and the stress-concentrating geometries of anisotropically etched silicon, the efficiency of the silicon PR transducer is very impressive. The miniaturization allows natural frequencies >1 MHz in some PR shock accelerometers.Most contemporary PR sensors are manufactured from a single piece of silicon. In general, the advantages of sculpting the whole sensor from one homogeneous block of material are better stability, less thermal mismatch between parts, and higher reliability. Underdamped PR accelerometers tend to be less rugged than PE devices. Single-crystal silicon can have extraordinary yield strength, particularly with high strain rates, but it is a brittle material nonetheless. Internal friction in silicon is very low, so resonance amplification can be higher than for PE transducers. Both these features contribute to its comparative fragility, although if properly designed and installed they are used with regularity to measure shocks well above 100,000 g. They generally have wider bandwidths than PE transducers (comparing models of similar full-scale range), as well as smaller nonlinearities, zero shifting, and hysteresis characteristics. Because they have DC response, they are used when long-duration measurements are to be made.。

外文原文：Full-Pose Calibration of a Robot Manipulator Using a Coordinate-Measuring MachineThe work reported in this article addresses the kinematic calibration of a robot manipulator using a coordinate measuring m a c h i n e(C M M)w h i c h i s a b l e t o o b t a i n t h e f u l l p o s e o f t h e e n d-e f f e c t o r.A k i n e m a t i c m o d e l i s d e v e l o p e d f o r t h e manipulator, its relationship to the world coordinate frame and the tool. The derivation of the tool pose from experimental measurements is discussed, as is the identification methodolo gy.A complete simulation of the experiment is performed, allowing the observation strategy to be defined. The experimental work is described together with the parameter identification and accuracy verification. The principal conclusion is that the m et ho d is a ble t o calibrate the robot succes sful ly, with a resulting accuracy approaching that of its repeatability.Keywords: Robot calibration; Coordinate measurement; Parameter identification; Simulation study; Accuracy enhancement 1. IntroductionIt is wel l known tha t robo t manip ula tors t ypical ly ha ve reasonable repeatability (0.3 ram), yet exhibit poor accuracy(10.0m m).T h e p r o c e s s b y w h i c h r o b o t s m a y b e c a l i b r a t e di n o r d e r t o a c h i e v e a c c u r a c i e s a p p r o a c h i n g t h a t o f t h e m a n i p u l a t o r i s a l s o w e l l u n d e r s t o o d .I n t h e c a l i b r a t i o n process, several sequential steps enable the precise kinematic p ar am et er s o f th e m an ip u l ato r to b e ide nti fi ed,l ead ing t o improved accuracy. These steps may be described as follows: 1. A kinematic model of the manipulator and the calibration process itself is developed and is usually accomplished with s t a n d a r d k i n e m a t i c m o d e l l i n g t o o l s.T h e r e s u l t i n g m o d e l i s u s e d t o d e f i n e a n e r r o r q u a n t i t y b a s e d o n a n o m i n a l (m a n u f a c t u r e r's)k i n e m a t i c p a r a m e t e r s e t,a n d a n u n k n o w n, actual parameter set which is to be identified.2. Ex pe ri me n ta l m ea su re m e nts o f th e rob ot po se (p art ial o r complete) are taken in order to obtain data relating to the actual parameter set for the robot.3.The actual kinematic parameters are identified by systematicallyc h a n g i n g t h e n o m i n a l p a r a m e t e r s e t s o a s t o r ed u ce t h e e r r o r q u a n t i t y d ef i n e d i n t h e m o d e l l i ng ph a s e.O n e a p p r o a c h t o a c hi e v i n g t h i s i d e n t i f i c a t i o n i s d e t e r m i n i n g t h e a n a l y t i c a l d i f f e r e n t i a l r e l a t i o n s h i p b e t w e e n t h e p o s e v a r i a b l e s P a n d t h e k i n e m a t i c p a r a m e t e r s K i n t h e f o r m of a Jacobian,and then inverting the equation to calculate the deviation of t h e k i n e m a t i c p a r a m e t e r s f r o m t h e i r n o m i n a l v a l u e sAlternatively, the problem can be viewed as a multidimensional o p t i m i s a t i o n t a s k,i n w h i c h t h e k i n e m a t i c p a r a m e t e r set is changed in order to reduce some defined error function t o z e r o.T h i s i s a s t a n d a r d o p t i m i s a t i o n p r o b l e m a n d m a y be solved using well-known methods.4. The final step involves the incorporation of the identified k i n e m a t i c p a r a m e t e r s i n t h e c o n t r o l l e r o f t h e r o b o t a r m, the details of which are rather specific to the hardware of the system under study.This paper addresses the issue of gathering the experimental d a t a u s e d i n t h e c a l i b r a t i o n p r o c e s s.S e v e r a l m e t h o d s a r e available to perform this task, although they vary in complexity, c o s t a n d t h e t i m e t a k e n t o a c q u i r e t h e d a t a.E x a m p l e s o f s u c h t e c h n i q u e s i n c l u d e t h e u s e o f v i s u a l a n d a u t o m a t i c t h e o d o l i t e s,s e r v o c o n t r o l l e d l a s e r i n t e r f e r o m e t e r s, a c o u s t i c s e n s o r s a n d v i d u a l s e n s o r s .A n i d e a l m e a s u r i n g system would acquire the full pose of the manipulator (position and orientation), because this would incorporate the maximum information for each position of the arm. All of the methods m e n t i o n e d a b o v e u s e o n l y t h e p a r t i a l p o s e,r e q u i r i n g m o r ed a t a t o be t a k e nf o r t h e c a l i b r a t i o n p r o c e s s t o p r o c e e d.2. TheoryIn the method described in this paper, for each position in which the manipulator is placed, the full pose is measured, although several intermediate measurements have to be taken in order to arrive at the pose. The device used for the pose m e a s u r e m e n t i s a c o o r d i n a t e-m e a s u r i n g m a c h i n e(C M M), w h i c h i s a t h r e e-a x i s,p r i s m a t i c m e a s u r i n g s y s t e m w i t h a q u o t e d a c c u r a c y o f0.01r a m.T h e r o b o t m a n i p u l a t o r t o b e c a l i b r a t e d,a P U M A560,i s p l a c e d c l o s e t o t h e C M M,a n d a special end-effector is attached to the flange. Fig. 1 shows the arrangement of the various parts of the system. In this s e c t i o n t h e k i n e m a t i c m o d e l w i l l b e d e v e l o p e d,t h e p o s e estimation algorithms explained, and the parameter identification methodology outlined.2.1 Kinematic ParametersIn this section, the basic kinematic structure of the manipulator will be specified, its relation to a user-defined world coordinatesystem discussed, and the end-point toil modelled. From these m o d e l s,t h e k i n e m a t i c p a r a m e t e r s w h i c h m a y b e i d e n t i f i e d using the proposed technique will be specified, and a method f o r d e t e r m i n i n g t h o s e p a r a m e t e r s d e s c r i b e d. The fundamental modelling tool used to describe the spatial relationship between the various objects and locations in the m a n i p u l a t o r w o r k s p a c e i s t h e D e n a v i t-H a r t e n b e r g m e t h o d ,w i t h m o d i f i c a t i o n s p r o p o s e d b y H a y a t i,M o o r i n g a n d W u t o a c c o u n t f o r d i s p r o p o r t i o n a l m o d e l s w he n tw o co n se cu t iv e jo i n t a x e s ar e nom ina ll y p a r all el. A s s h o w n i n F i g.2,t h i s m e t h o d p l a c e s a c o o r d i n a t e f r a m e o neach object or manipulator link of interest, and the kinematics a r e d e f i n e d b y t h e h o m o g e n e o u s t r a n s f o r m a t i o n r e q u i r e d t o change one coordinate frame into the next. This transformation takes the familiar formT h e a b o v e e q u a t i o n m a y b e i n t e r p r e t e d a s a m e a n s t o t r a n s f o r m f r a m e n-1i n t o f r a m e n b y m e a n s o f f o u r o u t o f t h e f i v e o p e r a t i o n s i n d i c a t e d.I t i s k n o w n t h a t o n l y f o u r transformations are needed to locate a coordinate frame with r es pect to the p revious one. Whe n consecutiv e ax es are not parallel, the value of/3. is defined to be zero, while for the case when consecutive axes are parallel, d. is the variable chosen to be zero.W h e n c o o r d i n a t e f r a m e s a r e p l a c e d i n c o n f o r m a n c e w i t h the modified Denavit-Hartenberg method, the transformations given in the above equation will apply to all transforms of o n e f r a m e i n t o t h e n e x t,a n d t h e s e m a y b e w r i t t e n i n a g e n e r i c m a t r i x f o r m,w h e r e t h e e l e m e n t s o f t h e m a t r i x a r e functions of the kinematic parameters. These parameters are simply the variables of the transformations: the joint angle 0., the common normal offset d., the link length a., the angle o f tw is t a., a nd th e an g l e /3.. Th e mat rix f orm i s u suall y expressed as follows:For a serial linkage, such as a robot manipulator, a coordinate frame is attached to each consecutive link so that both the instantaneous position together with the invariant geometry a r e d e s c r i b e d b y t h e p r e v i o u s m a t r i x t r a n s f o r m a t i o n.'T h etransformation from the base link to the nth link will therefore be given byF i g.3s h o w s t h e P U M A m a n i p u l a t o r w i t h t h e D e n a v i t-H a r t e n b e r g f r a m e s a t t a c h e d t o e a c h l i n k,t o g e t h e r with world coordinate frame and a tool frame. The transformation f r o m t h e w o r l d f r a m e t o t h e b a s e f r a m e o f t h e manipulator needs to be considered carefully, since there are potential parameter dependencies if certain types of transforms a r e c h o s e n.C o n s i d e r F i g.4,w h i c h s h o w s t h e w o r l d f r a m e x w,y,,z,,t h e f r a m e X o,Y o,z0w h i c h i s d e f i n e d b y a D H t r a n s f o r m f r o m t h e w o r l d f r a m e t o t h e f i r s t j o i n t a x i s o f t h e m a n i p u l a t o r,f r a m e X b,Y b,Z b,w h i c h i s t h e P U M Amanufacturer's defined base frame, and frame xl, Yl, zl which is the second DH frame of the manipulator. We are interested i n d e t e r m i n i n g t h e m i n i m u m n u m b e r o f p a r a m e t e r s r e q u i r e d to move from the world frame to the frame x~, Yl, z~. There are two transformation paths that will accomplish this goal: P a t h1:A D H t r a n s f o r m f r o m x,,y,,z,,t o x0,Y o,z o i n v o l v i n g f o u r p a r a m e t e r s,f o l l o w e d b y a n o t h e r t r a n s f o r m f r o m x o,Y o,z0t o X b,Y b,Z b w h i c h w i l l i n v o l v e o n l y t w o parameters ~b' and d' in the transformFinally, another DH transform from xb, Yb, Zb to Xt, y~, Z~ w hi ch i nv ol v es f o ur p ar a m ete r s e xc ept t hat A01 a n d 4~' ar e b o t h a b o u t t h e a x i s z o a n d c a n n o t t h e r e f o r e b e i d e n t i f i e d independently, and Adl and d' are both along the axis zo and also cannot be identified independently. It requires, therefore, o nl y ei gh t i nd ep e nd en t k i nem a t ic p arame ter s to g o fr om th e world frame to the first frame of the PUMA using this path. Path 2: As an alternative, a transform may be defined directly from the world frame to the base frame Xb, Yb, Zb. Since this is a frame-to-frame transform it requires six parameters, such as the Euler form:T h e f o l l o w i n g D H t r a n s f o r m f r o m x b,Y b,z b t O X l,Y l,z l would involve four parameters, but A0~ may be resolved into 4~,, 0b, ~, and Ad~ resolved into Pxb, Pyb, Pzb, reducing theparameter count to two. It is seen that this path also requires e i g h t p a r a m e t e r s a s i n p a t h i,b u t a d i f f e r e n t s e t.E i t h e r o f t h e a b o v e m e t h o d s m a y b e u s e d t o m o v e f r o m t h e w o r l d f r a m e t o t h e s e c o n d f r a m e o f t h e P U M A.I n t h i s w o r k,t h e s e c o n d p a t h i s c h o s e n.T h e t o o l t r a n s f o r m i s a n E u l e r t r a n s f o r m w h i c h r e q u i r e s t h e s p e c i f i c a t i o n o f s i x parameters:T he total n umber of paramete rs u sed in the k inem atic model becomes 30, and their nominal values are defined in Table 1.2.2 Identification MethodologyThe kinematic parameter identification will be performed as a multidimensional minimisation process, since this avoids the calculation of the system Jacobian. The process is as follows: 1. Be gi n wi t h a g ue ss s e t of k in em atic par am ete r s, s uch a s the nominal set.2. Select an arbitrary set of joint angles for the PUMA.3. Calculate the pose of the PUMA end-effector.4.M e a s u r e t h e a c t u a l p o s e o f t h e P U M A e n d-e f f e c t o r f o r t he s am e se t o f j oi nt a n g les.In g enera l, th e m e a sur ed an d predicted pose will be different.5. Mo di fy t h e ki n em at ic p ara m e te rs in a n o rd erl y man ner i n o r d e r t o b e s t f i t(i n a l e a s t-s q u a r e s s e n s e)t h e m e a s u r e d pose to the predicted pose.The process is applied not to a single set of joint angles but to a number of joint angles. The total number of joint angles e t s r e q u i r e d,w h i c h a l s o e q u a l s t h e n u m b e r o f p h y s i c a l measurement made, must satisfyK p i s t h e n u m b e r o f k i n e m a t i c p a r a m e t e r s t o b e i d e n t i f i e d N i s t h e n u m b e r o f m e a s u r e m e n t s(p o s e s)t a k e n D r r e p r e s e n t s t h e n u m b e r o f d e g r e e s o f f r e e d o m p r e s e n t i n each measurement.In the system described in this paper, the number of degrees of freedom is given bysince full pose is measured. In practice, many more measurements s h o u l d b e t a k e n t o o f f s e t t h e e f f e c t o f n o i s e i n t h e e xp er im en ta l m ea s ur em en t s. T h e o pt imisa tio n pro c e dur e use d is known as ZXSSO, and is a standard library function in the IMSL package .2.3 Pose MeasurementIt is apparent from the above that a means to determine the f u l l p o s e o f t h e P U M A i s r e q u i r e d i n o r d e r t o p e r f o r m t h e calibration. This method will now be described in detail. The end-effector consists of an arrangement of five precisiontooling b a l l s a s s h o w n i n F i g. 5.C o n s i d e r t h e c o o r d i n a t e s o f the centre of each ball expressed in terms of the tool frame (Fig. 5) and the world coordinate frame, as shown in Fig. 6. T h e r e l a t i o n s h i p b e t w e e n t h e s e c o o r d i n a t e s m a y b e w r i t t e n as:w he re P i' i s t he 4 x 1 c o lum n ve ct or of th e coo r d ina tes o f the ith ball expressed with respect to the world frame, P~ is t he 4 x 1 c o lu mn ve ct or o f t h e c oo rdina tes o f t h e it h bal l expressed with respect to the tool frame, and T is the 4 • 4 h o m o g e n i o u s t r a n s f o r m f r o m t h e w o r l d f r a m e t o t h e t o o l frame.The n may be foun d, a n d use d as th e m easure d pose in t he calibration process. It is not quite that simple, however, since it is not possible to invert equation (11) to obtain T. The a bo ve proce ss is performed f or t he four ball s, A, B, C and D, and the positions ordered as:or in the form:S i n c e P',T a n d P a r e a l l n o w s q u a r e,t h e p o s e m a t r i x m a y be obtained by inversion:I n pr ac ti ce it m a y be d i f fic u l t fo r the CM M to a c ces s fou r b a i l s t o d e t e r m i n e P~w h e n t h e P U M A i s p l a c e d i n c e r t a i n configurations. Three balls are actually measured and a fourth ball is fictitiously located according to the vector cross product:R e g a r d i n g t h e d e t e r m i n a t i o n o f t h e c o o r d i n a t e s o f t h ec e n t r e o f a b a l l b a s ed o n me a s u r e d p o i n t s o n i t s s u rf a c e, n o a n a l y t i c a l p r o c e d u r e s a r e a v a i l a b l e.A n o t h e r n u m e r i c a l optimisation scheme was used for this purpose such that the penalty function:w a s m i n i m i s e d,w h e r e(u,v,w)a r e t h e c o o r d i n a t e s o f t h e c e n t r e o f t h e b a l l t o h e d e t e r m i n e d,(x/,y~,z~)a r e t h e coordinates of the ith point on the surface of the ball and r i s th e ba ll di am e te r. I n the t es ts perf orm ed, i t was foun d sufficient to measure only four points (i = 4) on the surface to determine the ball centre.中文译文：应用坐标测量机的机器人运动学姿态的标定这篇文章报到的是用于机器人运动学标定中能获得全部姿态的操作装置——坐标测量机（CMM）。