Machines and Mechanisms, Theory of

the general methods of studying and designing machines and mechanisms. The most highly developed part of the science is called the theory of mechanisms; it deals primarily with characteristics that are common to all mechanisms (or to particular groups), regardless of the specific purpose of the machine, instrument, or device. For example, the same mechanism in the form of gears for converting rotary motion may be used in motor vehicles, clocks, or mixing equipment for the chemical industry. In all of these cases the same conversion of motion is required; therefore, the methods of studying and designing such mechanisms have a great deal in common and belong to the theory of mechanisms. The other part of the science is the theory of machines, which deals with methods of research and development that are common to machines in various areas of technology. The two parts of the science are inseparably interrelated, since mechanisms are the basis of virtually all machines.

The tasks of the theory of machines and mechanisms are varied. The most important of them may be grouped in three areas: synthesis of mechanisms, dynamics of machines and mechanisms, and theory of automatons. Synthesis of mechanisms is understood to mean that part of their design that involves selection of a layout and determination of the parameters of such a layout that ensure performance of the required motions. The problems of the dynamics of mechanisms are the study of the motion of particular parts or links of the mechanism that are influenced by external forces. The theory of automatons deals with methods of constructing layouts according to the conditions of coordination of the operation of individual elements and the achievement of optimum productivity, precision, and reliability.

To some extent the division of the problems of the theory of machines and mechanisms into three areas is arbitrary. For example, the synthesis of mechanisms considers not only kinematic but also dynamic conditions; in the dynamics of mechanisms, recommendations for selection of the mechanism’s parameters to produce optimum dynamic characteristics are made based on study of the movement of the mechanism’s elements—that is, dynamic synthesis is performed; and in the theory of automatons, selection of actuating mechanisms and their parameters is based on the methods of synthesis of mechanisms, whereas the optimization for the design of the automaton (specifically, the control layout) is often determined by dynamic indicators. However, a review of the problems of the science of machines and mechanisms on the basis of these divisions gives a sufficiently complete idea of its content.

The foundations of the synthesis of mechanisms in its analytic form were laid in the 19th century in the work of the Russian mathematician and mechanical engineer P. L. Chebyshev. In studying his work, the entire sequence of solving the problems of synthesizing mechanisms may be seen as consisting of three stages.

The first stage is selection of the primary criterion of synthesis and the constraints. Each mechanism must meet a number of requirements that differ in form and content, depending on its purpose and operating conditions. Some of the requirements may even be contradictory, but it is always possible to determine which requirement is decisive for the correct functioning of the mechanism and to select the primary criterion according to which the quality of the mechanism is judged. The primary criterion of synthesis is a function of the parameters of the mechanism (also called the criterion function or target function); the other requirements for the mechanism are formulated as constraints on the parameters. In other words, the first stage in the solution of any problem of synthesis isthe formalization of requirements. In this stage technological and design problems are transformed into mathematical problems.

The second stage is the determination of an analytic expression of the function that describes the magnitude of the primary criterion of synthesis. Selection of the primary criterion is determined by the purpose of the mechanism. For some mechanisms the analytic expression may be highly complex. However, functions exist that are simpler and at the same time characterize the magnitude of the primary criterion with sufficient precision for practical purposes. In this case it is necessary only that the error in replacing the criterion function with its approximate function be less than the error in the actual mechanism caused by imprecision in manufacturing its parts, elasticity of the links, and similar factors.

The third stage is the computation of the permanent parameters of the mechanism for optimization of the primary criterion, taking into account the constraints (limiting conditions). In some cases the conditions are expressed in the form of one or more equations and a system of inequalities from which the unknown parameters are found directly (precision synthesis). In other cases values of the parameters are found for which the deviation of the criterion function from the optimum value is sufficiently small to satisfy the conditions of practical useof the mechanism (approximate synthesis). Chebyshev proposed an original method of computing the desired parameters of the mechanism for approximate synthesis; this later led to the creation of the mathematical theory of the approximation of functions.

The three stages in the synthesis of mechanisms constitute the chief task in the design of mechanisms, since all subsequent operations in calculating the strength of parts and determining design forms cannot substantially change its kinematic and dynamic characteristics. The subsequent development of the methods of synthesizing mechanisms in the work of the Russian scientists A. P. Kotel’nikov (1865-1944) and V. V. Dobrovol’-skii (1880-1956), as well as foreign scientists, consisted in the search for the most expedient methods of carrying out the separate stages of synthesis and applying them to different types of mechanisms (mechanisms with hydraulic and electrical devices, three-dimensional mechanisms with complex motion of the working member, and self-adjusting mechanisms). In this process it became clear that in simple cases the requirements for the primary criterion and constraints may be satisfied using simple graphic methods. However, the use of these methods does not eliminate the need for solving the problem of synthesis in several versions to produce results approaching the optimum. Only the appearance of electronic computers made possible quick and efficient performance of determining the optimum combinations of parameters and even solving problems of synthesis that previously could not be solved because of the complex and cumbersome nature of the computations. In 1965-72, computer programs were written for standard problems of synthesis of mechanisms; such methods make possible optimization of various criteria and consideration of a great number of kinematic, dynamic, and design constraints.

The dynamics of mechanisms is sometimes called the dynamics of machines, since consideration of the dynamic phenomena taking place in mechanisms is of paramount importance in the design of machines. In the first works on the dynamics of machines, done by N. E. Zhukovskii and N. I. Mertsalov (1866-1948), only solid-state mechanics as applied to mechanisms with rigid links was used. After the introduction of new mechanisms, first with hydraulic devices and later also with pneumatic devices (1930-50), the dynamics of machines came to rely not only on solid-state mechanics but also on the mechanics of liquids and gases. The problems of machine dynamics changed significantly with the considerable increase in the load capacity and speed of machines and the higher quality requirements; consideration of the elastic characteristics of the links, clearances in moving joints, and variability of mass and moments of inertia became necessary. Primary attention was devoted to the development of methods of the theory of oscillations of mechanical systems as applied to a real mechanism, with elastic and partially elastic elements, clearances, dry friction and lubrication, and complex rules of deformation of materials. The harmful effect of oscillations, which cause an increase in the load on links of the mechanism, loss of stability, fatigue fractures, and unacceptable changes in the prescribed motion, is under study. At the same time, oscillations may be put to use in vibration machines, in which the oscillatory movement of the working member is the main motion determined by the purpose of the machine. Among such machines are vibration conveyors, sorting machines, and pile drivers. The new problems of machine dynamics are being solved through the development of methods of analytic mechanics and the nonlinear theory of oscillations, the mechanics of variable mass, and the theory of elasticity. Methods that make it possible to find dynamic criteria for calculating mechanisms by the frequency and amplitude of set oscillations and for determining the boundaries of stability with adequate efficiency and speed without integrating systems of differential equations are very important in solving such problems.

The theory of automatons came to be considered one of the most important parts of the theory of machines and mechanisms comparatively recently (1945-50). Automatons are distinguished from nonautomated machines primarily by the fact that the sequence of operation of individual mechanisms, including loading and unloading mechanisms, is preset by a control system. Therefore, development of the theory of automatons is associated with improvement in methods of constructing control layouts according to a selected criterion of optimization—for example, according to the condition of producing the minimum number of elements in a layout. Methods based on the use of algebraic logic have become most common, and accordingly, this division of the theory of automatons has come to be called logical synthesis of control systems. In addition to electrical elements, control systems are using pneumatic elements, which are ordinarily more reliable.

The development of methods for the construction of control systems for automatons led to the creation of programmed control systems in which the program of required motions is expressed in the form of numbers (digits), which are the elementary steps. Special types of motors, called step-by-step electric motors, are provided to carry out the steps. Self-adjusting and adapting systems of programmed control, in which the program automatically makes corrections on the basis of experience with the system’s previous work cycles and the conditions under which the system is intended to work, are particularly valuable.

The latest advance in the theory of automatons is the development of methods for the design of robots—that is, automatons that simulate the characteristics and functions of living organisms and, in particular, simulate human actions in moving implements and objects. To a great extent the diagrams of robots are the same as those of manipulators (mechanical arms), which are used for work in a vacuum, under water, and in aggressive mediums. The working members of manipulators are capable of performing the complex three-dimensional movements required for their operation. Modern computer methods and equipment, which make possible the writing and changing of programs of motion during operation, are used to control the actions of manipulators and robots. The use of robots in combination with machine tools and monitoring and assembly automatons equipped with programmed control systems facilitates full automation of production. Their use gives systems of automatons flexibility and adaptability to changing production conditions. The methods of the theory of machines and mechanisms and control theory are used together in the design of robots and manipulators. Both the general methods (structural synthesis of three-dimensional open kinematic chains, the kinematics and dynamics of three-dimensiona mechanisms with multiple degrees of freedom, and the theory of mechanisms with a variable structure that changes in the process of movement) and the methods of solving problems that relate only to manipulators (provision of flexibility and stability of operation, selection of the correct relationship between power and idle strokes, and design of systems in which the operator feels the force generated on the working member or grip) are developing for use in the design of robots and automatic manipulators.

Intensive work is under way in many countries in all three divisions of the theory of machines and mechanisms. National conferences on the problems of this science are held regularly (every two to three years) in the USSR, the USA, the German Democratic Republic, Rumania, Czechoslovakia, and the Federal Republic of Germany. The International Federation for the Theory of Machines and Mechanisms was formed in 1969 to organize and hold international meetings and congresses on the theory of machines and mechanisms and for exchange of knowledge and the conduct of joint projects (above all in terminology, standardization, theory of manipulators, and problems of higher education).