Use of crank mechanism as mechanical integrator

Abstract

The invention relates to a mechanical integrator for integrating different functions. A crank mechanism comprises a rotating crank having pivotally connected thereto at least two elastic links, the other ends of which are pivotally connected to fixed points of attachment, wherein each link takes on the same or different forms of functions. The axes of the directrices of said links or the distances between the axis of rotation of the crank and the fixed pivot points of attachment of the elastic links are disposed with an angle ψ therebetween. The point of pivotal attachment of the crank to the elastic links traces a curve proportional to the integral of the curve itself, the angle of rotation φ of the crank of the mechanism being proportional to the difference of the integrals of the upper and lower parts of the curve over their absolute value. This makes it possible to use crank mechanisms with an elastic link as integrators and to expand the reliable functional capabilities thereof in the case of converting the translational elastic motion of a point depending on different functions of graphs into rotational motion.

Description

[0001] Description of the invention.

[0002] "Application of a crank mechanism as a mechanical integrator."

[0003] "The field of technology to which the invention relates."

[0004] A mechanical integrator is related to mechanical engineering in various areas of the production of machines, devices, units and mechanisms; it can be used in industry, in agriculture, forestry and housing and communal services, in transport and in everyday life, including in design strength calculations, and as a mechanical integrator of various functions for educational and scientific and technical purposes.

[0005] "Prior Art".

[0006] From the state of the art (1) "I.I. Artobolevsky "Mechanisms in Modern Technology" in 7 volumes, a reference manual for engineers, designers and inventors, Moscow, Nauka, second revised edition, chief editor FML, 1970", volume I, p. 239 mechanism No. 470 "Lever integrator", where through a slider along a fixed guide, a lever has a wheel on an axle at one end, and a pin at the other, where a curve is outlined by a point. The angle of rotation of the wheel is proportional to the integral of this curve. The angle of rotation of the wheel of the counting mechanism is proportional to the difference between the integrals of the upper and lower parts of the curve.

[0007] In the same source of information in the prior art (2) "Volume III 'Lever mechanism with flexible and elastic links for converting rotary motion into reciprocating motion,'" for example, on page 155, mechanism No. 1770, and on page 154, mechanism No. 1768, where it performs rotary motion at the point of attachment to the crank, are listed. However, the technical capabilities of such mechanisms are unknown, and the integral of functions described by the curve of the articulated point of the crank and the elastic link is unknown.

[0008] In the same source of information in the level of technology (3) “Vol. II p. 385, No. 1338 “Crank-link mechanism of a swinging cylinder”, where it is possible to implement the principle of action of elastic links on one common crank, with different nonlinear feed functions on each of the individual, at least two elastic links and with offset angles between the rolling axes of the links.

[0009] According to the state of the art (4) “Volume II “Crank-lever and crank-slider mechanisms”, for example, on page 486 mechanism No. 1494 “Crank-slider mechanism of a two-cylinder engine. where the fixed axes of movement of the sliders form a certain angle of their arrangement, as an example of the arrangement, in particular, at least at least two elastic links, while the technical and functional capabilities of the mechanisms are unknown and the integral of the functions of the curve described by the point of the hinge connection of the crank and the elastic links is unknown.

[0010] In the prior art (5). "M.O. Yarimov, patent for invention No. 2267672 "Yarimov's deaxial crank-slider mechanism" with priority dated October 18, 2002," which demonstrates a mathematical and geometric analogy of the approach when describing the point of the hinge connection of the crank with a link that perceives the same functions y = f(x) = 1.

[0011] According to the source of information (6), I. Newton, "Mathematical Principles of Natural Philosophy", translated from Latin with notes and explanations by A.N. Krylov, L., Publishing House of the USSR Academy of Sciences, 1936", where Newton's words are cited on page 2 of the first edition. From the source of information (6), it is known that the most accurate and reliable solution to problems and issues in physics, especially in mechanics, is the geometric method. Moreover, Newton in the preface to the first edition, on page 2, emphasizes, verbatim: "Thus, geometry is based on mechanical practice, and is nothing other than that part of general mechanics in which the art of accurate measurement is expounded and demonstrated. But since in crafts and industries one has to deal for the most part with the motion of bodies, then usually everything that concerns only quantities is attributed to geometry, everything that concerns motion - to mechanics."

[0012] From the previously available level of technology, no integrators of crank mechanisms with an elastic link and with the difference of integrals of functions of curves from points, the articulated connection of the crank with these links, when feeding or receiving various functions from the elastic links, have been identified.

[0013] The essence of the invention.

[0014] The objective of the proposed invention is to design a device by using crank mechanisms with an elastic link as mechanical integrators, expanding their reliable functional capabilities when converting the translational elastic motion of a point for functions of graphs fed into rotational motion in scientific and technical fields, as well as in various fields of production of machines, devices, units and assemblies.

[0015] The aim of the invention is the design of a device for using crank mechanisms with an elastic link as mechanical integrators, expanding their reliable functional capabilities, when converting the translational elastic motion of a point depending on various functions of graphs into rotational motion for scientific and technical and in various fields of production of machines, devices, units and assemblies.

[0016] The technical result is achieved by using a crank mechanism containing a rotating crank with at least two elastic links pivotally connected to it, which, with the other ends pivotally connected to fixed points of these elastic links, with each of them receiving the same or different types of functions, with the axes of the guides of these links or the distances between the axis of rotation of the crank and the fixed with hinged attachment points of the other ends of these elastic links, located at a certain angle between them, with the angle φ of rotation of the crank and with its point connected by a hinge with elastic links, drawing a curve proportional to the integral of this curve, with the angle of rotation of the crank of the mechanism proportional to the difference of the integrals of the upper and lower parts of the curve, in absolute value, as a mechanical integrator.

[0017] According to the source of information (7), K.V. Frolov, S.V. Popov et al. “Theory of Mechanisms and Mechanics of Machines”, Moscow, VShD998, on pp. 304-306 “Synthesis of Four-Link Mechanisms Based on Two Positions of Links” is known in the topic “Mechanism with a Reciprocating Rotating (Swinging) Cylinder” the methodology and part of the scientific approach to solving the problems posed by the author with a previously unknown result are known. At the same time

[0018] From the source (8), Editor-in-Chief Yu.V. Prokhorov "Mathematical Encyclopedic Dictionary" Moscow, Scientific Publishing House "Great Russian Encyclopedia", 1995, p. 164 "Graphical calculations" - methods for obtaining numerical solutions to various problems by means of graphical constructions are known. To solve the problem posed in the invention, it is necessary to perform graphical calculations in the form of a product of at least two sinusoidal functions per crank and supplied along each elastic link, for example, for a spring in the form of a linear y = b - ax, and nonlinear forms, etc. At the same time, there is a need perform the addition of each product of these functions, shifted in phase by an angle at one point of rotation of the crank. As a result of mechanical displacement of the points of the links of the crank mechanism, at least two elastic links, various integral curves are obtained according to Fig.2 - Fig.4, which give the difference of the integrals between the upper and lower parts, relative to the axis f of the final graph of rotation of the crank. The disadvantage of graphical calculations in (8) is the low accuracy of the answers obtained. However, by compiling a computer program with the author's code, the goal is achieved with any required accuracy and the results of the stated problem, depending on the specified steps of the numerical calculation in the mathematical expressions given below. The solution of the stated problem is carried out through the compilation of a program for electronic computers, computers. The initial material for solving the stated problem is the mathematical formula [1] of the author, which describes the law of motion of the hinge point, fastening the crank with the elastic link.The author's mathematical expression is as follows: g. where M(k) is the integral of the curve described by the point of the hinge connection of the crank with the elastic link of the mechanism;

[0019] M(cp) is a mathematical formula for the curve described by the point of the hinge joint of the crank with the elastic link of the mechanism depending on the angle of rotation of the crank; is the angle of rotation of the crank of the mechanism; is the angle of the initial position of the crank of the mechanism (0°); - angle of the extreme, limit position of the crank of the mechanism (360°); k - relative value of the distance between the axis of rotation of the crank and the fixed pivot point of the other end of the fastening of this elastic link.

[0020] It is derived by the author from Fig. 1, where the center of rotation of the crank O, the fixed point of the elastic link C and the rotating point A of the connection of the crank with the elastic link form a triangle with an elastic link AC variable in length. There is an angle φ of rotation of the crank, an angle of deviation of the elastic link AC from the distance between the axis O of the crank pa and a fixed point C of attachment of the other end of the elastic link, and the angle between two straight lines OC and OC', designated K. Elastic forces in t Point A is decomposed into two components, along the crank and perpendicular to the crank.

[0021] The component of elastic forces F perpendicular to the crank is always equal to Since the angle between the crank and the auxiliary line through point A, which is parallel to OC, is also equal to the angle φ of rotation of the crank AO, and the angle between the auxiliary line through point A and AC is also equal to the angle 0, as are angles with mutually parallel sides.

[0022] After constructing the auxiliary segments AB and OB, according to Fig. 1, from the well-known sine theorem for triangle AOC or ABC we obtain the necessary ratios of the sides.

[0023] Using the angles (φ - 0), the sum of the moments of elastic forces F on the axis O of the crank r or OA is determined: When F = 1, we find why the angle is expressed through the angle φ by considering the theorems sines of the angles of triangle AOC or ABC. For example, for triangle ABC we have the expression or equality: ((OC + or [3]

[0024] After multiplying both parts of the equality [3] by sinP we obtain the equality: [4]

[0025] From this we have: [5]

[0026] If we square both sides of the first [5] equality we get: [6]

[0027] Since according to the mathematical reference book, we have: [7]

[0028] After taking the square root of both sides of the last equality [7], we obtain: [8] or after accepting the equality r = 1, we have: [9]

[0029] After simplifying the radical expression we have: or angle (ф) ((ф

[0010]

[0030] After substituting and replacing the angle on the right side of the equality we obtain the value of the total points of the curve [1]:

[0031] [AND] After integration, we have the area of ​​the curve described by the point of connection of the crank with the elastic link of a separate mechanism. The second mechanism in Fig. 1, at least of the coupled mechanism of the stated problem of the invention, is located at an angle φ from the first or rotated by an angle in the direction of rotation of the crank, therefore the expression of the integral and has the form according to the expression [2]:

[0032] [1]

[0033] For the second of the paired crank mechanisms with an elastic link we have:

[0034] [2]

[0035] The function y = f(x) of an arbitrary or required form is specified or supplied to the point of the crank hinge along the elastic link of the mechanism, as shown in Fig. 1. Then the equalities [1] and [2] will take the following form:

[0012]

[0036] For the second of the paired crank mechanisms with an elastic link we have:

[0037]

[0013] When the crank rotates, at this point of attachment, for example, from the linear identical functions y = b - ax on the elastic links, according to Fig. 2 and Fig. 3, we always obtain integral curves, with the difference of the integrals of the upper and lower parts, separated by the horizontal axis φ, of the crank rotation angles. There is a special case when at the point of the crank hinge connection, at least two elastic links are each supplied with a function then the integral has curves of mirror-equal area in their upper and lower parts relative to the axis of periodic rotation of the crank or the angle φ of rotation of the crank according to Fig. 4. If at least one of the elastic links supplies or receives the function y = f(x) = 1, and the other link receives a different function y = f(x) different from unity, then at the output at the point of the hinge connection of the crank with the elastic link, a curve is obtained with the difference of the integrals of the upper and lower parts of the curve, separated by the horizontal axis of rotation of the crank φ.

[0038] Below is a fragment of the code of a computer program, with the help of which the stated goal of the invention is proven and practically achieved with high accuracy.

[0039]

[0040] By selecting the necessary commands in a computer program, for example, from Fig. 2, it is possible to obtain a wide variety of values ​​of the difference of integrals for any given functions y = f(x), at least for two elastic links of the author's crank mechanism, under the conditions of the inevitable existence of a rotating crank.

[0041] "Brief description of drawings."

[0042] Fig. 1 shows, in the form of a diagram, the arrangement of elastic links I and II at an angle in the guides with points C and C' fixedly fixed with hinged other ends. Each elastic link transmits functions M1 and M2. The fixed distances between the axis of rotation of the crank and the attachment points C and C' are designated as k, in relative values ​​to the crank, through one common crank r = 1 with the axis of rotation O, and the angles of its rotation. The opposite arrows indicate the directions of movement. elastic links I and II with transmitted M1 and M2 functions. The changing angle is also shown P and depends on the length of the elastic links AC and OC at different angles and different values ​​of the links and their location.

[0043] Fig. 2 shows the command window for working with a computer program for various types of functions y = f(x), for example, linear y = b - ax, and nonlinear ones in the lower right table. The values ​​​​b and a are specified at the top in the right table. Values, for example, k = 7, angle y = 90 o between the fixed links k1 and k2 we set and select in the left table of commands given to the program. These fixed links can be accepted and set as equal in magnitude, as in Fig. 2 for each elastic link, or different. Below, in the left table, the integrals of the upper positive part of the desired curve are shown, and the integral of its lower negative part. The code of the universal program for all the specified functions is the fragment given above. The program can be programmed with any linear or nonlinear function y = f(x), either the same or different for each elastic link of the mechanism, under one condition of the existence of a rotating

[0044] • crank. In Fig. 2, according to the left table of numbers, the fifty-first exact calculated data are reflected, the sought-after integral curve according to Fig. 3, representing the difference between the upper and lower parts of the integrals by absolute value, obtained by the author, the proposed mechanical integrator. The calculation step of the program for the sought-after integral curve is set to 1°. For greater accuracy, any calculation step can be taken.

[0045] In Fig. 3, for example, a graph is shown in the form of a curve and visual proportions of the difference in the integrals of the upper and lower parts of the curve relative to the axis f, obtained by the integrator from the same linear dependence (b - ax) for each elastic link, from two elastic links, with offset distances between the axis of rotation of the crank and the fixed hinge points of attachment of the other ends of these elastic links, in phase by an angle on one common crank, as two functions M = M1 + M2. The vertical axis of the graph shows the integrated function M, in arbitrary units. The horizontal axis shows the angles rotation of the crank, while the limits of integration of the function M include all intervals of angles in the form of segments, when the curve M intersects the horizontal axis of the gr affix f. For example, in this case, the positive, or upper, part consists of a single segment of the horizontal f-axis from point 0 to point 1. The lower part consists of a segment of the horizontal f-axis from point 1 to point 2. The proportions of the difference of the integrals by absolute value are clear and obvious. The upper part is smaller than the lower part of the integrals of the curve M. The program automatically generates the conditional numerical values ​​of each upper and lower part of the integrals, as well as their sum or difference by their absolute value.

[0046] This type of integral difference, for the example of the supplied linear function y - b - ax, was obtained with the initial data b = 3.141593, a = 1, and the computer returned values ​​of the upper part of the integral of the function M +2.369048, and of the lower part -9.55744. The difference of the integrals in absolute values ​​of the conditional values ​​will be equal in absolute value to 1 - 7.1883921. The total sum of the area under the integral curve of the common upper and lower parts is equal to 11.726487 in absolute value of the terms. All necessary required quantities (sum or difference) are output by pressing the keys.

[0047] Fig. 4 shows a graph in the form of a curve and a proportion for the difference of the author's integrals, equal to zero, for conditional equal symmetric functions y = 1, on each of the elastic links of the crank mechanism and the total curve from these functions shifted in phase by an angle between fixed links on one common crank. The positive upper integral of the curve consists of two segments at points 0 to 1 and points 2 to 3 along the horizontal axis f. The negative lower integral of the curve consists of two segments at points 1 to 2 and points 3 to 4 along the axis f. "Implementation of the invention."

[0048] The invention is carried out by using a crank mechanism comprising a rotating crank with at least two elastic links pivotally connected to it, which in turn have other ends pivotally connected to fixed points of these elastic links, with each of them receiving or feeding along these elastic links the same or different types of linear and nonlinear functions, with the axes of the guides of these links or the distances between the axis of rotation of the crank and the fixed hinge points of attachment of the elastic links, located at a certain angle between them, with an angle q> of rotation of the crank and with its point pivotally connected to the elastic links, drawing a curve proportional to the integral of this curve, with the angle of rotation of the crank of the mechanism proportional to the difference of the integrals of the upper and lower parts of the curve, according to their absolute value, as a mechanical integrator.

[0049] For practical implementation of the invention, the elastic link in the case of a linear function y = b - ax can be represented as springs, rubber or other elastic material, with the same or different mechanical characteristics from each elastic link to one common crank. This rectilinear inclined graph of the function is reflected in the information source (9) on page 89, Fig. 3.2 for an elastic swinging link, as a spring. In the case of a nonlinear function y = 1 / x, according to the information source (10) on page 205, the graph Fig. 3.4 is shown as the work of thermodynamic forces in a swinging cylinder with a piston on a pV diagram, where after introducing the values ​​of the piston area and gas pressure per unit piston area, the function is generalized into a y = 1 / x hyperbola. Hyperbolas are classical thermodynamic processes, vacuum, compressed air, through rocker mechanisms (3), with the same or different mechanical characteristics from each elastic link to one common crank.In the case of a nonlinear function y = 1 / x. 2 , a square hyperbola—these are magnetic or electromagnetic characteristics, through rocker mechanisms (3), for example, with permanent magnets. The author's integrator design, with at least two elastic links, can be implemented by realizing the link values, with the input or actions of specific linear or nonlinear functions from each of at least two elastic links.

[0050] Fig.2 - Fig.4 show the data obtained as a result of precise calculations through the creation of computer programs based on the mathematical functions [1] and [2],

[0012] and

[0013] derived by the author and based on scientific knowledge, and reliably, with high accuracy, confirming the author's ability to obtain the technical result of the integrator. Drawing the final types of graphs according to Fig.2 - Fig.4 without errors is very difficult, and impossible. Moreover, the program code excludes human errors.

[0051] The stated problem is solved, and the aim of the invention is also achieved, by using a crank mechanism containing a rotating crank with at least two elastic links pivotally connected to it, which, in turn, have other ends pivotally connected to fixed points of these elastic links, with each of them receiving or supplying the same or different types of functions along these elastic links, with the axes of the guides of these links or the distances between the axis of rotation of the crank and the fixed hinge points of attachment of the elastic links, located at a certain angle between them, with the angle of rotation of the crank and with its point connected by a hinge with elastic links, drawing a curve proportional to the integral of this curve, with the angle of rotation of the crank of the mechanism proportional to the difference of the integrals of the upper and lower parts of the curve, according to their absolute value, as a mechanical integrator.

[0052] The functionality of crank mechanisms with elastic links has been expanded.

[0053] Thus, the author's mechanical integrator is a solution to many problems in mechanics, through high-precision calculated geometric movements of points of similar crank mechanisms with elastic links, and allows achieving the most complex goals through the simplest application of such mechanisms in industrial and scientific-technical fields.

[0054] The proposed invention, the use of a crank mechanism with an elastic link as an integrator, is disclosed to the skilled person, is novel, involves an inventive step, and is industrially applicable. At the same time, the invention is based on the strict scientific and technical level of modern knowledge, supported and proven by precise mathematical and practical calculations and visual demonstrations of its operation.

[0055] Sources of information.

[0056] 1. I. I. Artobolevsky “Mechanisms in modern technology” in 7 volumes, Reference manual for engineers, designers and inventors, Moscow, Nauka, second revised edition, chief editor FML, 1970”, volume I, p. 239 mechanism No. 470 “Lever integrator”.

[0057] 2. I. I. Artobolevsky “Mechanisms in modern technology” in 7 volumes Volume III “Lever mechanism with flexible and elastic links for converting rotary motion into reciprocating motion”, for example, on page 155 mechanism No. 1770, and on page 154 mechanism No. 1768, where at the point of attachment with the crank it performs rotary motion.

[0058] 3. I. I. Artobolevsky “Mechanisms in modern technology” in 7 volumes, Volume II, p. 385, No. 1338 “Crank-link mechanism of a swinging cylinder”.

[0059] 4. I. I. Artobolevsky “Mechanisms in modern technology” in 7 volumes, “Volume II “Rocker-lever and crank-slider mechanisms”, for example, on page 486 mechanism No. 1494 “Crank-slider mechanism of a two-cylinder engine.

[0060] 5. M. O. Yarimov, patent for invention No. 2267672 “Yarimov’s deaxial crank-slider mechanism” with priority dated 18.10.2002.

[0061] 6. I. Newton, “Mathematical Principles of Natural Philosophy”, translated from Latin with notes and explanations by A.N. Krylov, L., Publishing House of the USSR Academy of Sciences, 1936.”

[0062] 7. K.V. Frolov, S.V. Popov, et al. “Theory of Mechanisms and Mechanics of Machines”, Moscow, VSh, 1998, pp. 304-306.”

[0063] 8. Editor-in-chief Yu.V. Prokhorov “Mathematical Encyclopedic Dictionary” Moscow, Scientific Publishing House “Great Russian Encyclopedia”, 1995, p. 164 “Graphical calculations”.

[0064] 9.I.V. Saveliev, "Course of General Physics" Mechanics, Moscow, ed. Astrel ACT, 2005 p.89.

[0065] 10.A.G. Alenitsy, E.I. Butikov, A.S. Kondratyev "Short physical and mathematical reference book", Moscow, "Science" Main editorial office FML, 1990, p.205.

Claims

Invention formula. "Application of a crank mechanism as a mechanical integrator." The use of a crank mechanism comprising a rotating crank with at least two elastic links pivotally connected to it, which in turn have other ends pivotally connected to fixed points of these elastic links, each of which assumes the same or different types of functions, with the axes of the guides of these links or the distances between the axis of rotation of the crank and the fixed hinge points of attachment of the elastic links, located at a certain angle y between them, with an angle (ρ) of rotation of the crank and with its point pivotally connected to the elastic links, drawing a curve proportional to the integral of this curve, with an angle φ of rotation of the crank of the mechanism proportional to the difference of the integrals of the upper and lower parts of the curve, according to their absolute value, as a mechanical integrator. SUBSTITUTE SHEET (RULE 26)

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