Robot kollarında enerji akış yönünün motor momentleri üzerine etkileri
Modelling of a manipulatör drive mechanism
Yazar: TAMER ÇELEBİ
Danışman: DOÇ. DR. SAİT YÜCENİR
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü
Derece: Yüksek Lisans, 1995
Konu: Makine Mühendisliği = Mechanical Engineering
Dizin: Güç iletimi = Power transmission ; Robot kolu = Robot arm

Özet:
ÖZET Endrüstriyel robotlarda, motor ile hareketli robot uzvu arasındaki tahrik sisteminde bazı durumlarda güç iletimini sağlayan mekanizmalar mevcuttur. Bu mekanizmalar genellikle hız düşürme Credüksiyon) amacıyla kullanılır ve tercihen yüksek çevrim oranlarına sahiptir. Bu çalışmada, Tübitak Marmara Araştırma Merkezi Robotik Bölümü'nde geliştirilen "Antropomorfik" tipte bir robotun ilk Uç uzvuna ait C Gövde ile arka ve önkol> tahrik sistemleri incelenmektedir. Kütlesel özelliklerin yaklaşık olarak alındığı bu uzuvlara ait tahrik sistemle rinde, elektrik motorları ve bunlara bağlı Harmonic Drive mekanizmaları mevcuttur. Robot hareketi sırasında, tahrik sistemlerinde meydana gelen enerji kayıpları ve bunların her Uç motora ait moment değişimleri üzerine etkilerinin belirlenmesi için, örnek olarak robot uç noktasının yatay ve düşey düzlemlerde basit hareketleri seçilmiştir. Hesaplamada özellikle Harmonic Drive mekanizmalarındaki enerji kayıpları da dikkate alınmış ve bu mekanizmalara ait kayıpların sonuçları ne ölçüde etkilediği belirlenmiştir.

Abstract:
There are three major types of drive in use today : hydraulic, pneumatic and electric motors. For any appli cation of robots, we must decide which of the available drive methods is most suitable. Positional accuracy, reliability, speed of operation, cost and other factors must be considered. Pneumatic drives are the simplest of all drives. These are much like hydraulic systems in principle, but vary considerably in detail. The working fluid is compressed air, but the valve is simpler and pressures are much smaller. High precision is difficult to achieve using pneumatic servo drives, but where the precision is adequate, pneumatic drives are the lightest, in weight and lowest in cost of all available robots. Hydraulic drives can generate greater power in a compact volume than can electric motor drives. Rotary hdraulic motors can be made smaller for a given power output than electric motors. However, electrohydraulic servo valves used to control oil flow are quite expensive and require the use of filtered, high-purity oil to pre vent jamming of the servo valve. Because of the high pressure, there is always a potantial for oil leaks. Electric motors are inherently clean and capable of high precision if operated properly. They are more reli able and require less maintenance. The newer designs of electric motors are beginning to be competitive in size and weight because the use of new magnetic materials. As their capabilities improve electric motors are becoming more and more the actuator of choice in the design of robots. To analyze the dynamic behaviour of a robot, the appropriate joint torques necessary for producing desired outputs must be obtained. This inverse problem is impor tant to robot control and programming. For a given de sired end point velocity and acceleration, the joint an gular velocities and angular accelerations can be found by the inverse kinematics. In the inverse dynamics, the inputs are these kinematic variables described as time functions and the outputs are the joint torques to be applied at each instant by the actuators in order to xafollow the specified trajectories. Two methods can be used in order to obtain the dyna mic equations of motion : The Newton-Euler formulation and the Lagrangian formulation. The Newton-Euler for mulation is derived by the direct interpretation of Newton's second law of motion, which describes dynamic system in terms of force and momentum. The equations in corporate all the forces and moments acting on the indi vidual arm links, including the coupling forces and mo ments between the links. Since the linear endpoint force and moment specified along with trajectories to follow are known, the recursive algorithm based on Newton-Euler formulation can be applied to find joint torques. In many cases it is not possible to find an actuator with the ' speed -fore e or speed-torque characteristics to perform the desired tasks. In other cases it is neces sary to locate the actuator away from the intended joint of the manipulator. For these reasons, it becomes neces sary to use some type of power transmission. Power transmissions perform two functions : transmit power at a distance and act as a power transformer. There are num ber of ways to perform mechanical power transmission. The use of gears is very common. They transmit rotary motion from one shaft to another. The desired speed of a manipulator link is usually much less than the motor which drives it. So, a power transmission with high re duction ratio Ce.g. Harmonic drives, Cyclo gear boxes!) is necessary. Although harmonic drives have been around for a long time, they have not been used extensively until recently. With only three basic elements, the single-stage reduc tion ratios range 50:1 to 320:1 within the same enve lope. Harmonic drive gears are available with position ing accuracy of beter than one minute of arc and repeat ability within a few seconds of arc. They may operate with esentially zero backlash between mating teeth beca use of natural gear pre-load. They also have improved torsional stiffness, compact size, light weight, simple construction and co-axial input -output. Finally, harmo nic drive transmissions are successfully used in indrust- rial robots. When the reduction is used in a robot drive mecha nism, it should be noted that the joint torque obtained by the inverse dynamics is not equal to the torque gene rated by the motor. So, a drive mechanism model must be formed to find the motor torque. The drive mechanism can be seperately examined as two levels : the high speed mo tor level and the low speed load level. The basic dyna mic equation of "Torque = Inertia x Angular acceleration" Xllcan be applied to both levels. For the motor level : CJ + J ) 6+B Ö+Tc sign 0 - T - T C1D m i m rn m m m m t n where J : Rotor inertia of the motor, fixed m J : Inertia of high speed parts in the r educti on, f i xed 0 : Angular displacement of the motor m shaft B : Viskoz friction coefficient for the motor level, fixed Tc : Coulomb friction torque C absolute!} for the motor level, fixed T : Torque developed by the motor, time var yi ng T. : Input torque to the reduction, time in, var yi ng and for 1 oad 1 evel, CJ + JO & + B, O + Tc, sign S = T - T C20 21111 lMl out I where J : Inertia of low speed parts in the reduction, fixed J : Inertia of the robot link being driven, time varying Ö : Angular displacement of the robot link obtained by the inverse kinematics B : Viskoz friction coefficient for the load level, fixed Tc : Coulomb friction torque C absolute} for the load level, fixed T : The joint torque, obtained by the inverse dynamics, time varying T : Output torque from the reduction, out f,, time varying If the reduction ratio is N, it can be written that 9 = N & C33 But the problem is to find the relationship between T. and T. Generally, l,n out T = f N T C42> out in by using this relationship, motor and load level equati ons can be reduced into one. For load level xiii[ N2fCJ +J 3+CJ +J D 1 B + CN2f B +B,] 0, + mi 21 I mil CN Tc +Tc, 3 sign 0 = N f T - T CSD mil ml In most applications it is assumed that the coefficient f equals to one Cf=lD. This means that there are no power loses in the reduction. In other words, the reduction efficiency 77 = % 100. However» there are always power loses in this power transmission system. Then f becomes efficiency : f = 77. One important aspect of the drive is " the direction of power transmission " concept. While the robot end effector follow the specified trajectories, in some cases of the motion, one or more actuators C motor sD may act as a brake. For example, when the end effector moves down ward but the desired acceleration is upward for a PUMA robot, the gravitational effects of the second and third arms C especially when these arms are fully extended ~> cause themselves to accelerate. In that case, the motors in the drive mechanisms must decelerate the angular velo cities of the links. The direction of the power trans mission in that instant is inverse : From load to the mo tor level. The torque relationship is than given by T =7>CT / N } C6D 1 r» * (rill t m ' öut or T = CI/ 7p N T. C73> out ' t n By comparing this equation with equation C4D one can ea sily find f = I/77. The second aspect of the power transmission is the change of efficiency during the motion. The efficiency of the Harmonic Drive mechanism depends on temperature, working speed, torque and the direction of power trans mission. I The temperature effect is negligible, because the working temperature does not change too much C about 30-40 C D. But the efficiency slightly changes with the input speed. For the same speed and torque conditions, the efficiencies in the different directions of power transmission have different values. In the low torque working regions, the difference is too much. So, the ef ficiency changes must be taken into account. Finally, three approaches are possible for the power transmission loses : 1. There is no lose in the reduction. Always 77 - v XIV100. There is no need to determine the direction of po wer transmission. Always f = 1. 2. There is a power lose. But always tj is a cons tant value. To calculate motor torque by using equation C5D, the j direction of power transmission must be deter- mi ned to obtai n f val ue C f = 7? or f = 1 /t? 5. 3. The efficiency is variable. It changes with not only the speed and torque but also the direction of the power transmission. In this study, the drive mechanisms of the first three links of a PUMA robot have been examined. All the se mechanisms is assumed to have a power transmission system C Harmonic Drive 3. Although the robot has 6 deg rees of freedom, 3 wrist rotations have been neglected since their loads are relatively small. So, it was assu med that mass of the wrist and an object held by the ro bot belong to the third link. In the first example, a simple horizontal rotation of the endpoint has been exa mined to find the motor torque of the base link. As a second example, the vertical motion of the second and third link under the gravity has been studied to find the appropriate motor torques by using the inverse dynamics and the equation C4D. To determine the motor torques, three approaches C which have been mentioned above 3 were seperately used and finally, three motor torque varia tions have been found for the same link. Thus, it has been obtained how much differ the motor torques Cfound by three different efficiency approaches^ from each other. The results have been calculated by using computer prog ramming language. x