2025

abstract

english

EN The design of a new machine is preceded by an analysis focused on the optimum realisation of the expected utility functions. It is motivated by the desire to obtain the simplest possible solution that minimises power consumption. The most general definition calls synthesis the design of a mechanism involving the selection of the structural scheme and the dimensions of the links in order to obtain the desired motion. When a designer identifies the type of mechanism and searches for its optimal dimensions, such a task is called dimensional synthesis. The earliest methods were developed graphically. They have not only useful but also scientific and didactic qualities. The constructions presented here undoubtedly develop the geometrical imagination needed in an engineer’s work. Despite the obvious limitations of geometric constructions, due to the rather low complexity of the tasks to be solved, such approaches – although historical - are still used today and often form the basis for the development of analytical and computer methods. In this work, the synthesis problem of a mechanism for emptying containers was solved graphically. The method is based on the use of certain geometric-kinematic properties of the four bar linkage mechanism, which constitutes the main kinematic chain of the device. The container that needs to be emptied is attached to the coupler. In order to make optimum use of the kinematics of this mechanism, the coupler moves between two preset extreme positions in which the direction of its rotation changes. At these positions, the instantaneous angular velocity of the container is zero. In the first, simpler approach, it is assumed that the coupler rotates by 90 degrees when the container is emptied and that the active link also rotates by the preset angle. The way the mechanism is designed allows the lengths of some links and the points at which the links are pivoted to the frame to be influenced. Thus the size of the working area can be approximately prescribed. In computer methods, these features are often checked after the dimensions of the mechanism have been found due to the main objective function, and this causes the solution to be rejected in the final stages of the design process. The task was developed to the case in which the rotation angle of the container is given and greater than 90 degrees. the graphical relationship was then described analytically and implemented. Example solutions were presented.

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Book of Abstracts of the 95th Annual Meeting of the Association of Applied Mathematics and Mechanics, April 7th – April 11th, 2025, Poznań (Poland)

95th Annual Meeting of the Association of Applied Mathematics and Mechanics GAMM 2025, 7-11.04.2025, Poznań, Polska