Optimization synthesis of flat lever mechanisms by pressure angle

Authors: Kotov A.V., Krol D. G., Ph. D. in Phys. And Math., Assoc. Prof.

This article is a translation of the original work of the same name, which was written in Russian and published in a peer-reviewed journal. I decided to prepare and publish its English version for several reasons. First, science and engineering thinking have no language barriers. Publishing a translation is a step towards drawing attention to my research from a wider audience, including foreign colleagues, engineers and researchers who may find the proposed method useful. Second, publishing the article in English helps increase the visibility of the blog itself in foreign search engines. This means that my developments and findings are more likely to reach those who truly need them. I am open to discussion, feedback and professional dialogue with anyone who finds the topic of my research relevant. I will be glad if this material proves useful beyond the Russian-speaking audience.

Introduction. The problem of ensuring high efficiency and reliability of lever mechanisms is directly related to minimizing losses in their kinematic pairs, which, in turn, depend on the pressure angle [1, 2]. Exceeding the pressure angle beyond the recommended optimal value leads to an increase in friction losses and radial loads in the joints of the lever mechanism, which results in increased wear, jamming, and a decrease in the overall efficiency of the mechanism [3].

Traditionally, the synthesis of mechanisms based on the pressure angle is classified as a kinematic design task and is solved using graphical or analytical methods, which include constructing position and velocity plans [4 – 6]. Such synthesis can precede force analysis and provide additional qualitative and quantitative assessment of the potential force loading of the mechanism under study. However, formulating and solving this problem often requires cumbersome calculations and graphical constructions, which complicates the possibility of algorithmization and optimization [7].

The application of vector analysis or complex number theory for describing the kinematics of planar lever mechanisms is a well-established and effective approach [8, 9]. It allows for uniform, compact, and minimal analytical expressions to calculate the positions and velocities of all characteristic points and links of the mechanism. At the same time, the potential of vector analysis and complex numbers for solving kinematic synthesis problems, in particular optimization of pressure angles in joints, has not been fully explored. In this regard, the development of a methodology for the rapid assessment of pressure angles at the stage of mathematical modeling, based on this apparatus, retains its scientific and practical relevance.

Evaluation of the possibility of applying the deformable polyhedron method to the problem of optimization kinematic synthesis of a flat lever mechanism

Authors: Kotov A.V., Krol D. G., Ph. D. in Phys. And Math., Assoc. Prof.

This article is a translation of the original work of the same name, which was written in Russian and published in a peer-reviewed journal. I decided to prepare and publish its English version for several reasons. First, science and engineering thinking have no language barriers. Publishing a translation is a step towards drawing attention to my research from a wider audience, including foreign colleagues, engineers and researchers who may find the proposed method useful. Second, publishing the article in English helps increase the visibility of the blog itself in foreign search engines. This means that my developments and findings are more likely to reach those who truly need them. I am open to discussion, feedback and professional dialogue with anyone who finds the topic of my research relevant. I will be glad if this material proves useful beyond the Russian-speaking audience.

Introduction. In modern mechanical engineering, four-bar linkages are widely used due to their unique combination of design and functional advantages. These mechanisms, with a minimum number of links, make it possible to realize complex trajectories of the working parts of machines through the rational selection of their geometric parameters [1]. However, due to increased requirements for the efficiency, accuracy and reliability of lever mechanisms, traditional design methods based on experience and intuition are no longer sufficient to achieve the required kinematic parameters. Therefore, optimization kinematic synthesis of lever mechanisms is becoming a key factor ensuring the competitiveness of the equipment being developed.

In educational practice, the main focus is on geometric methods of synthesis of lever mechanisms, which are clear and relatively simple, but inferior in accuracy to the solution of the problem [2]. Recently, due to the widespread introduction of mathematical packages and programming languages, there has been a significant leap in the application of numerical optimization algorithms for kinematic synthesis of lever mechanisms [3 - 7]. As a result, geometric synthesis methods are gradually receding into the background, giving way to more accurate and efficient machine algorithms.

To date, there is no universal numerical algorithm capable of effectively solving the entire spectrum of optimization problems [8]. The application of popular gradient algorithms to the problems of optimization kinematic synthesis of lever mechanisms requires large computational resources and is not always effective. At the same time, the potential of gradient-free algorithms for solving this class of problems is not fully covered in the scientific literature, which, given their high adaptability for software implementation [9], requires additional research.

Aim of the research. To evaluate the possibility of applying a multi-parameter gradient-free optimization algorithm based on the deformed polyhedron method to solve the problem of optimization kinematic synthesis of a flat lever mechanism. To provide a qualitative assessment of the use of this method when it is implemented in the mathematical package PTC MathCAD.

Possibility of application of the theory of complex numbers to the solution of engineering problems of kinetic analysis of flat lever mechanisms

Authors: Kotov A.V.

This article is an English translation of a original article posted on the blog in Russian. The translation was done using Google Translate, so do not judge strictly. There will certainly be literary errors, but I think the general meaning of the information that I tried to put into this work will be clear to the English-speaking audience. The purpose of this article is to expand the circle of readers of the blog among the English-speaking audience, to tell about the original analytical method of calculating flat lever mechanisms by the method of transforming coordinates in an invariable basis using the theory of complex numbers.

Despite the fact that the foundations of the course «Theory of Mechanisms and Machines» can be said to go back centuries, but if we have to turn to the analytical calculation of lever mechanisms, we will find that no significant shifts in helping to solve these problems have appeared in educational literature so far. It seems that the methods of calculating lever mechanisms have remained at the same level, and science has exhausted itself in this direction and cannot offer anything new, modern and effective.

But what should mechanical engineering do in this case, in which real lever mechanisms have found wide application, and for their rational projection it is necessary to carry out the corresponding calculations? Unfortunately, the well-known principle works here: the drowning man will save himself. Therefore, if science cannot come to the aid of mechanical engineering in terms of developing modern methods for calculating lever mechanisms, then engineers have to solve this problem on their own, by developing their own methods and algorithms.