شبيه‌سازي پرواز در صفحه‌ي روبات پرنده با بازوهاي انعطاف‌پذير

Flight Simulation of a Robot with Elastic Arms In Plane

مدل ديناميكي ارايه‌شده در اين پژوهش اثر انعطاف‌پذيري بازوهاي يك روبات پرنده را بر پرواز آن شبيه‌سازي مي‌كند. اين روبات متشكل از يك جسم مركزي و دو روتور است كه هركدام از روتورها توسط يك بازوي انعطاف‌پذير به آن متصل‌اند. براي ساده‌سازي مسيله پرواز روبات در صفحه در نظر گرفته شده است. هر بازو و روتور متصل به آن به‌صورت مجموعه‌يي مجزا با دو درجه آزادي كشسان مدل شده و اثر آن‌ به جسم مركزي انتقال مي‌يابد. با تركيب روابط حاكم بر پرواز جسم صلب و كشسان بازوها، دستگاهي از معادلات غيرخطي مرتبه دو به ‌دست آمده كه با حل عددي آن رفتار پرنده‌ي كشسان در اثر اعمال نيروي تراست تعيين مي‌شود. بخشي از نتايج ارايه‌شده در اين مقاله تفاوت پرنده‌ي واقعي انعطاف‌پذير را با مدل ايده‌آل صلب در نحوه‌ي اوج‌گيري و مسير پروازي نشان مي‌دهد، و بخشي ديگر در بررسي تاثير برخي پارامترهاي سازه‌يي بر ارتعاشات روبات كاربرد دارد.

In this study, the flight of a robot with elastic arms is simulated. It is assumed that the robot flies in plane and has three rigid degrees of freedom. Flying robots are considered to have a central body with two rotors connected to it, and two beams that are elastic in bending and inextensible in length. The mass of eachconnecting arm is divided between the corresponding rotor and the central body. Each arm adds two elastic degrees of freedom to the problem. Equations of elastic deformations for each side are derived by considering each rotor and its connecting arm as a clamped beam at the root under a transverse load, with bending moment acting on its tip. Constraint forces and moments from both sides are applied to the central body and then equations of in plane motion of the flying robot are derived. Also, three equations are added to find the pitch angle, flight path and position of the robot, with respect to an inertial frame. Some case studies are added to show the differences between a rigid and an elastic simulation of a flying robot. Since the differential equations are second order and non-linear, a numeric method is used to solve them for specified rotors thrusts. Effects of different structural parameters, like damping coefficient, length to diameter ratio, and installation angle of connecting arms, on elastic deformations and the flight path of the flying robot, are investigated. It is shown that as the length to diameter ratio of the connecting arm increases, frequency of vibration decreases and its amplitude increases. Lowering the installation angle will increase both the amplitude and frequency of vibrations. More importantly, it can be seen that an elastic robot climbs harmonically and that deformations of the connecting arms may change the flight path. Although increasing the damping coefficient of the arms will lower the amplitude of harmonic motion, it is shown that higher damping values may result in higher deviations from the assumed flight path.