Üç serbestlik dereceli manipulatör mekanizmasının prototipinin kurulması ve kinematiğinin incelenmesi
Contruction and kinematic analysis of three degrees of freedom parallel manipulator
- Tez No: 98484
- Danışmanlar: DOÇ.DR. RAMAZAN TAŞALTIN
- Tez Türü: Yüksek Lisans
- Konular: Uçak Mühendisliği, Aircraft Engineering
- Anahtar Kelimeler: Belirtilmemiş.
- Yıl: 1999
- Dil: Türkçe
- Üniversite: İstanbul Teknik Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Belirtilmemiş.
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: 116
Özet
ÖZET Paralel platform mekanizmaları, paralel hareket eden prizmatik bağlantılara sahip üç ya da daha fazla bacak ile birbirine bağlanmış ve paralel eyleyicilerle hareket ettirilen iki adet platformdan oluşan mekanizmalar olup bu konu ile ilgili son yıllarda daha yüksek rij itlik ve yüksek yük taşıma kapasiteleri ve diğer avantaj lan dolayısıyla yoğun olarak araştırılmaya başlanmıştır. Karmaşık kinematik zincire sahip paralel platform mekanizmaları robot uç organlarında, uçuş simülatörlerinde kullanılmıştır. Biz bu çalışmada üç serbestlik dereceli paralel manipülatör mekanizmasını incelemiş, deneysel amaçlı kullanılmak üzere bir prototipini dizayn ederek uçuş simülatörlerinde, tank ve gemilerin namlu sistemlerinde ve robotlarda kullanılabilecek bir mekanizma için öncülük etmiş bulunmaktayız. Tez konusu olarak kurduğumuz sistemin kinematiği detaylı olarak incelenmiş, ters ve düz kinematik denklemleri elde edilmiştir. Elde edilen sonuçların çeşitli hareket durumları için bilgisayar programları yardımıyla simülasyonları yapılmış, sistemin simülasyona uygun olduğu görülmüştür. Ayrıca elde edilen ters ve düz kinematik denklemler MATLAB programıyla birbirine uygulanmış ve denklemlerin doğruluğu görülmüştür. Analitik çözüm elde edebilmek için sembolik çözüm yapabilen MAPLE programı kullanılmış ancak sonuç elde edilememiştir. xı
Özet (Çeviri)
SUMMARY CONSTRUCTION and KINEMATIC ANALYSIS of THREE DEGREES of FREEDOM PARALLEL MANIPULATOR This thesis investigates an experimental manipulator which is designed for real time simulation purpose. An experimental manipulator is designed and constructed at trisonic laboratory of Istanbul Technical University Aeronautical and Astronautical Faculty. The manipulator has three degrees of freedom, angular movement around X and Y direction and longitudinal movement in Z direction in cartesian axes system. Chapter 2 examines basic concepts of parallel and serial mechanisms that are used for simulation and automation purposes. Different types of simulators, currently used for various purposes are briefly introduced. Industrial applications of parallel and serial mechanisms are also examined in this chapter. i Chapter 3 is devoted to literature surveys about the parallel manipulators. Works of different researches are briefly examined in this chapter. Stewart platform, widely used parallel manipulator in industry, is studied in this chapter. Kinematic and dynamic analysis of Stewart platform are briefly introduced. Chapter 4 introduces pneumatic elements used for industrial purposes. Working principles and peripheral devices for pneumatic elements are investigated. Advantages and difficulties of using pneumatic elements are examined. Control organs such as solenoid valves, flow control valves etc. are introduced. Working principles of electro-pneumatic valves which is the basic control element in any pneumatic control system, is studied. xnPneumatic control systems are briefly surveyed in Chapter 5. PLC which is widely used in pneumatic control systems is described in this chapter. PLC is suitable for on-off control purposes. In this type of control strategy the system i controlled by the pneumatic devices have certain reassigned static positions. The system is designed in such a way that no control action needed between these static positions. Contrary to the on-off control strategy, dynamic controller is needed if the controlled process elements should follow a reference trajectory. In this type of control strategy dynamic controller compares the desired reference trajectory with that of the actual system output, and produces the control action to reduce the error between them. Thus dynamic control needed to satisfy this criteria. Dynamic control strategies such as time domain analysis and frequency domain analysis are briefly introduced in this chapter. Pneumatic control elements are also examined in this chapter. Experimental manipulator is described in Chapter 6. The photograph and the schematic diagram of the experimental manipulator is shown in Fig. (1.1). The manipulator consists of two plates and three legs connecting these two plates. The legs can be extended and shortened by pneumatic control elements. Each leg's bottom positions are fixed and can have a movement in the direction shown in Fig (LI). The top positions of the legs can not slide but they can rotate in any direction. The manipulator is designed to simulate yaw and pitch rate of movement of a simple flight simulator. The experimental manipulator can be divided into four parts. The bottom and top plates, pneumatic pistons between these plates, a constant pressure valve and a voltage controlled pressure valve, electrical and mechanic accessories. Details of each part are described in Chapter 6. xiu* Tİ *. o o 1./ '1-* I s*?" - ? I ı TKB*»JÛ Fig 1.1 The schematic diagram and the photograph of the experimental manipulator xivChapter 7 examines kinematics behavior of the experimental parallel manipulator system. In this chapter direct kinematics and inverse kinematics problems are stated. The main purpose of the experimental manipulator is to bring the top plate position to a prescribed orientation, i.e. to bring the manipulator to given angles ^, 0 and height p. There is a nonlinear relationship between angles tf>, 0 and height p (top plate orientation) and k, I, m (lengths of the manipulator legs). Calculation of k, I, m values when angles ^, 0 and height p are known is described as an inverse kinematics problem, Whereas calculation of ^, 0 and p values when k, I, m are known is described as a direct kinematics problem. As stated above the relationship between 0, 0 and p and k, I, m are nonlinear. In fact there are three strongly coupled nonlinear equations that represent this relationship. Direct analytical formula does not exist to solve the inverse kinematics or direct kinematics problem. Therefore numerical procedures have to be used. Numerical nonlinear equation solver routines from MATLAB were used to solve the above nonlinear equation set. The routines need an initial guess and find a solution. If the initial guess is too far from the solution the iteration may not converge. For this reason an approximate solution is developed to solve to the inverse and direct kinematics problem. The approximate case assumes that the center of the top plate does not move in X and Y directions. Of course this is not true when the top plate rotates about X and Y axes, i.e 0 and ^ angles are different from zero. However this is a good approximation in most cases. The advantage of the approximate case is that it has an explicit analytical solution for direct and inverse kinematics problem. Therefore the calculation is straightforward. For this reason approximate case is xvused to be an initial guess for the nonlinear equation solver to find the numeric solution. Since there are many routes to take the manipulator from one position to another the difference between these roots are examined for some eminent initial and final positions. One purpose of the manipulator is to keep ^, 6 and p values in a pre-assigned trajectory. For this reason possible scenarios such as to compress a high amplitude vibration are also given in Chapter 8. Conclusions and future work are given in Chapter 9. Software written in MATLAB to calculate the direct and inverse kinematic are given in the appendices. xvi
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