Methods of design and calculation of machines and mechanisms

The study of modern methods for designing and calculating machines and mechanisms is very important for students of engineering specialities. Due to the rapid development of computer technologies, it is now possible to use computer-aided design (CAD) systems for optimal design in mechanical engineering. Therefore, students need to learn both theoretical fundamentals and numerical calculation methods that can be implemented using modern CAD systems, in particular Mathcad, which is often used by engineers to solve problems in various fields.

This textbook discusses the structure and classification of mechanisms, the methodology of their kinematic and dynamic analysis, and optimal design methods common to mechanisms and machines of various purposes. This knowledge is necessary for engineers to create modern machines using different design criteria, as well as to correctly formulate a problem, solve it, analyse the results and, when necessary, choose the optimal solution.

The available literature in this field [2, 3, 6, 8, 10–12, 14, 15] helps students study the theory, formulate problems and choose methods for solving typical tasks in mechanical engineering. However, this knowledge and these skills do not exempt students from routine and sometimes complex calculations, which may obscure the essence of mechanical processes. In other words, it is necessary not only to learn methods for solving problems of various complexity, but also to be able to analyse them so that the solutions do not conceal the mechanical meaning of the processes and phenomena.

The textbook may also be considered an introduction to one of the most widely used mathematical computer-aided design systems — Mathcad — for solving problems in different fields of engineering. The use of Mathcad makes it possible to analyse the behaviour of mechanical systems according to a given task, enabling students who are not yet familiar with numerical methods and programming to solve real engineering problems.

The Mathcad package [5, 9, 13] is an effective tool for analytical transformations and numerical solutions of engineering and physical problems. Its applications range from simple calculations to complex problems in various fields of knowledge. With Mathcad, students and engineers can successfully solve many problems in mechanical engineering. The package has a user-friendly, mathematically oriented interface and convenient graphical tools.

The most effective way to learn calculation and design methods in mechanical engineering is not only to study rules and techniques formally, but to see them in action. Therefore, the textbook focuses mainly on solving practical problems selected for two purposes: first, to serve as a self-study manual for learning how to solve mathematically complex engineering problems; and second, to demonstrate the capabilities of Mathcad and increase students’ and specialists’ interest in using it to solve problems in mechanical engineering.

The textbook consists of eight chapters and an appendix. The first seven chapters are devoted to solving specific problems in the design of machines and mechanisms. Each chapter includes a brief theoretical overview, examples of solving relevant problems and calculation programs in Mathcad. The final chapter provides basic information about Mathcad and a brief overview of its methods used in mechanics, including mathematical, graphical and programming methods.

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