بهينه‌سازي سينماتيكي و ديناميكي مكانيزم چهارميله‌اي صفحه‌ي داراي لقي مفصل

Kinematic and Dynamic Optimization of a Planar Four-Bar Linkage with Joint Clearance

در اين نوشتار الگوريتم جديدي براي بهينه‌سازي سينماتيكي و ديناميكي سازوكار چهارميله‌يي صفحه‌يي كه داراي مفصل لق است، ارايه مي شود. بديهي است كه در صورت وجود لقي در يك مفصل، يك درجه آزادي غيرقابل كنترل به سازوكار افزوده مي شود. اين امر مي تواند منبع ايجاد خطا در پيمايش مسير مطلوب و توليد ارتعاش و صدا در طول حركت ‌شود. با فرض تماس دايم بين دو عضو مفصل، لقي را مي توان به‌صورت يك عضو مجازي بدون جرم در نظر گرفت. در اين نوشتار يك سازوكار چهارميله‌يي طراحي مي شود به‌گونه‌يي كه بتواند به‌طور همزمان مسير مطلوب را با كم‌ترين خطا طي كند (بهينه‌سازي سينماتيكي). همچنين با تغيير توزيع جرم در عضوها، زاويه‌ي عضو مجازي لقي به‌گونه‌يي كنترل مي شود كه بتوان خطاي ناشي از آن را جبران ‌كرد (بهينه‌سازي ديناميكي). براي بهينه‌سازي اين مسيله‌ي غيرخطي از الگوريتم اجتماع پرندگان استفاده مي شود.

Geometrical perfection is usually assumed in the synthesis of linkages; i.e. they are treated without clearance at the joints. But, in practice, clearance in the joints is inevitable due to tolerances and defects arising from design and manufacturing or wearing after a certain working period. Moreover, it provides allowance for the connecting links to move relative to each other. On the other hand, joint clearances affect the performance of linkages tremendously. Here, we design a planar four-bar linkage to follow the desired trajectory, in the presence of clearance at the joint between the crank and the coupler. Firstly, the kinematical synthesis is performed. It is noteworthy that in the presence of clearance at a joint, the linkage gains an additional, uncontrollable, degree of freedom (DOF). Therefore, one has to solve the optimization problem only if this unwanted mobility can be controlled. At this step, a time history of the second DOF is assumed to be known. Thus, the optimization problem can be solved. At the second step, the assumed time history of the second DOF of the mechanism has to be satisfied. This can be performed by mass re-distribution of the links. This highly nonlinear optimization problem can be solved numerically. Recently, evolutionary algorithms have become increasingly popular for solving nonlinear problems in various fields, especially on mechanism design; Particle Swarm Optimization (PSO), Differential Evolution, Genetic Algorithms and the Ant Colony Optimization Technique are among the most popular. Here, we present an algorithm based on PSO to solve, simultaneously, these highly nonlinear optimization problems with some constraints. This dual optimization problem is solved for planar four-bar linkage using a continuous contact model, based on the assumption that the pin is always in contact with the socket. Finally, an example is included to demonstrate the efficiency of the algorithm. The results clearly show that the linear and angular accelerations of the links for the optimal design are very smooth and bounded.