Mathematical Dimensional Synthesis of Four-Bar Linkages Based on Cognate Mechanisms

In the field of mechanical engineering, understanding mechanisms is essential for designing and developing devices and systems. Mechanisms, composed of interconnected elements, transform the energy applied to the input link into motion or force in the output link. Mechanisms are found in a wide variety of machines, from industrial machines to household machines. In this paper, a mechanism synthesis method is developed that can model four-bar linkages and build their cognate mechanisms to be able to select the mechanism that best suits the required work. Studying four-bar mechanisms offers a strong foundation for grasping more complex mechanical systems. The concepts and principles learned from four-bar mechanisms are widely applicable to advanced mechanical systems, making them a crucial starting point in mechanical engineering education and research. The mechanism synthesis method proposed in this article is organized into three main sections. The first section provides a comprehensive overview of the theoretical and mathematical foundations required for modeling mechanisms, laying the groundwork for understanding the subsequent calculations. The second section delves into the process of obtaining and analyzing the initial mechanism and constructing cognate mechanisms, detailing the procedures and algorithms used for modeling and calculating the coupling curve. Finally, the third section discusses the practical implementation of the method, including the graphical representation of mechanisms and a comparative analysis of the solutions obtained, assessing dimensional differences, design and manufacturing efficiency, and their suitability for various practical applications. The proposed four-bar mechanism synthesis method serves as a valuable tool for mechanism design, offering versatile and adaptable solutions that can optimize both technical performance and economic viability across a wide range of engineering applications.