Very varied. Some of them are a combination of only solid bodies, others contain hydraulic, pneumatic bodies or electrical, magnetic and other devices. Accordingly, such mechanisms are called hydraulic, pneumatic, electric, etc.
From the point of view of their functional purpose, mechanisms are usually divided into the following types:
Engine mechanisms convert various types of energy into mechanical work (for example, mechanisms of internal combustion engines, steam engines, electric motors, turbines, etc.).
Mechanisms of converters (generators) convert mechanical work into other types of energy (for example, mechanisms of pumps, compressors, hydraulic drives, etc.).
The transmission mechanism (drive) has as its task the transmission of motion from the engine to the technological machine or actuator, converting this movement into that necessary for the operation of this technological machine or actuator.
An actuator is a mechanism that directly affects the processed environment or object. Its task is to change the shape, condition, position and properties of the processed environment or object (for example, the mechanisms of metalworking machines, presses, conveyors, rolling mills, excavators, lifting machines, etc.).
Control, monitoring and regulation mechanisms are various mechanisms and devices for ensuring and monitoring the dimensions of processed objects (for example, measuring mechanisms for monitoring dimensions, pressure, liquid levels; regulators that respond to the deviation of the angular speed of the main shaft of the machine and set the specified speed of this shaft; mechanism, regulating the constancy of the distance between the rolls of the rolling mill, etc.).
Mechanisms for feeding, transporting, feeding and sorting processed media and objects include mechanisms for screw augers, scraper and bucket elevators for transporting and feeding bulk materials, mechanisms for loading hoppers for piece workpieces, mechanisms for sorting finished products by size, weight, configuration, etc.
Mechanisms for automatic counting, weighing and packaging of finished products are used in many machines, mainly producing mass piece products. It must be borne in mind that these mechanisms can also be actuators if they are included in special machines designed for these purposes.
This classification shows only the variety of functional applications of mechanisms, which can still be significantly expanded. However, to perform various functions, mechanisms that have the same structure, kinematics and dynamics are often used. Therefore, for studying in the theory of mechanisms and machines, mechanisms are identified that have common methods for their synthesis and analysis of work, regardless of their functional purpose. From this point of view, the following types of mechanisms are distinguished.
1.1. Structure of machines and mechanisms
Most modern cars are created according to the following scheme:
Car- a device that carries out mechanical movements necessary to perform the work process in order to replace or facilitate human physical and mental labor.
Mechanism is an integral part of the machine and is a set of interconnected parts and assemblies that ensure the performance of specified functions.
Drive unit consists of a motor and a transmission mechanism. It is designed to provide kinematic and power characteristics of the actuator.
Transmission mechanism designed to transfer energy from the engine to the actuator with transformation of the type and direction of movement, as well as changes in kinematic and power characteristics.
Actuating mechanism designed to perform the direct work process (processing, transportation, mixing, etc.).
1.2. Simple transfers. Main characteristics
and calculated dependencies
The need to introduce a transmission mechanism is due to its ability to perform various functions:
Energy (power) transmission;
Transformation (decrease or increase) of forces or moments of forces;
Conversion (decrease or increase) of the speed of movement of links;
Converting the type of movement (rotational to translational or vice versa) and changing the direction of movement;
Separation of motion flows from the engine to several executive bodies of the working machine.
Among transmission mechanisms, widely used rotational motion transmission , which can be divided into two main groups:
Transmissions based on the use of friction forces (friction, belt);
Transmissions based on the use of gears (gear, worm, screw, chain).
Let's consider simple gear transmissions, each of which contains two moving links (shafts with gears attached to them) performing rotational motion, and one fixed link (shaft supports). In Fig. 1.1 shows the appearance of the gears and the options for depicting them on block diagrams.
| Bevel gear |
| Worm-gear |
Helical gears are characterized parallel arrangement of gear axes A And b and differ in the arrangement of the gearing: with external gearing and with internal gearing. IN conical gear axis transmission A And b intersect . IN worm worm axis transmission A and worm wheel b cross .
The main kinematic characteristic of transmission mechanisms is gear ratio U, which is the ratio of angular velocities w or rotational frequencies n input (leading) A and output (slave) b links In this case, the designation of the gear ratio has two indices indicating the direction of transmission of movement from the link A to the link b:
.
Rotation frequency n is related to the angular velocity w by the relation:
, rpm
Gears that reduce rotation speed are called gearboxes . In them, the gear ratio is realized due to the ratio of diameters d or number of teeth Z slave b and presenter A gears in mesh:
.
Thus, gearboxes reduce the rotation speed by a factor of the gear ratio due to the ratio of the numbers of teeth of the meshed wheels:
.
In this case, the drive gear in cylindrical and bevel gears, which has a smaller number of teeth, is called gear , and the slave – wheel .
The torque in the gearboxes increases by a factor of the gear ratio, taking into account friction losses estimated by the efficiency coefficient η :
.
Efficiency (h) is the ratio of useful power P n on the output link, spent on the implementation of useful work in a production or technological process, to the power on the input link, expended by the engine:
.
Efficiency takes into account power losses to overcome friction forces in kinematic pairs and is an important criterion for assessing the efficiency of energy use and the technical perfection of the mechanism.
When solving problems, you can use the following efficiency values for various gears: cylindrical - η = 0.97; conical – η = 0.96; worm - η = 0.95 (1 – U / 200), where U– gear ratio in the worm gear.
1.3. Multi-stage transmission mechanisms
If it is necessary to implement a gear ratio whose value exceeds the recommended limits for individual gears, use a sequential arrangement of gears (stages) in the transmission mechanism.
In this case, the overall gear ratio ( U total) and the overall efficiency (h total) of a multi-stage transmission mechanism are defined as the product of gear ratios and the efficiency of all its stages (gears):
,
Where m– the number of stages in the mechanism.
Gear ratio of one or group of stages m– a step mechanism is characterized by the ability to change the speed of rotation n and torque T when transferring movement between the leader i and slave k links of the considered part of the mechanism:
.
Net power on the output shaft of the mechanism ( P out, W) are calculated according to the dependence:
,
Where T out, Nm and n out, rpm – respectively the torque and speed of the output shaft of the mechanism.
The required (calculated) engine power () is determined taking into account losses in the friction units of the mechanism:
Based on the design power and rotational speed, a standard electric motor with the nearest higher power value is selected from the catalogue.
1.4. Examples of problem solving
Task 1. Carry out a structural, kinematic and force analysis of what is shown in Fig. 1.2 drive containing an electric motor and gearbox.
Parameters set:
– number of teeth , , , , , ;
– engine shaft rotation speed rpm;
– torque on the output shaft of the gearbox Nm.
Solution
Structural analysis. The three-stage transmission mechanism is formed by connecting three separate gears in series.
The first stage is a cylindrical gear with external gearing; gear axis 1 and wheels 2 parallel.
The second stage is a bevel gear; gear axis 3 and wheels 4 intersect.
The third stage is a worm gear; worm axes 5 and worm wheel 6 cross.
The axes of the input I and output IV shafts intersect.
Kinematic analysis.
– first stage: 
;
– second stage: 
;
– third stage: 
;
– mechanism: .
We determine the rotation frequency of each shaft of the mechanism, taking into account that the gears are fixed to the shafts and have the same speeds with them:
RPM (according to the problem conditions);
rpm;
rpm;
rpm
Force analysis. We determine the torques on each shaft:
Nm (according to the problem conditions);
Nm.
The efficiency of a worm gear is determined by the dependence:
Nm;
Nm.
Thus, the rotational speed of the shafts decreases stepwise by the gear ratio times ( rpm; rpm; rpm; rpm), and the torques increase (taking into account efficiency) by the gear ratio times ( Nm; Nm; Nm; Nm).
We calculate the useful power based on the output shaft of the gearbox:
W = 2.5 kW.
Required (calculated) engine power:
kW,
From the catalog we select a standard 4A100S4 electric motor with a rotation speed of rpm and a power of kW.
Task 2. Carry out a kinematic analysis of the drive (see Fig. 1.2 in task 1), using other initial data.
Parameters set:
– number of teeth: , , , ;
– engine shaft rotation speed: rpm;
– rotation speed of the gearbox III shaft: rpm.
Solution
We determine the gear ratios:
– first stage: 
;
– third stage: 
;
– general gear ratio of the first and second stages:
;
– the gear ratio of the second stage is determined, taking into account that 
:
;
– the entire mechanism: .
We determine the rotation frequency of each shaft of the mechanism:
RPM (according to the problem conditions);
rpm;
rpm (according to the problem conditions);
rpm
Thus, the gearbox reduces the engine shaft rotation speed by 120 times (from 3000 rpm to 25 rpm), changing it stepwise: in the first stage by 3 times (from 3000 rpm to 1000 rpm), in the second stages 2 times (from 1000 rpm to 500 rpm) and in the third stage 20 times (from 500 rpm to 25 rpm).
Control questions
1. What is a drive, transmission mechanism, actuator? What are they for?
2. What functions can the transmission mechanism perform?
3. Name simple gears as gears and draw their structural diagrams. What relative position of the axes of the driving and driven links is typical for each of the gears?
4. What is gear ratio? How does it characterize the transmission mechanism?
5. What is a gearbox? What functions of a transmission mechanism can it perform? How is the required gear ratio implemented in gearboxes? Draw on the diagram: a helical gearbox with a gear ratio; bevel gear with .
6. Make up all possible dependencies from which the gear ratio can be calculated.
7. What is coefficient of performance (COP)? How does it characterize the transmission mechanism? What operational parameters are calculated taking into account efficiency?
8. What are multi-stage transmission mechanisms used for? How to determine the overall gear ratio and overall efficiency?
9. Solve the problem. Carry out a structural, kinematic and force analysis of what is shown in Fig. 1.3 gearbox.
Parameters set:
– number of teeth , , , ;
– shaft rotation speed
- torque
|
Define:
a) the number of stages in the mechanism;
b) type of transmission in each stage;
c) gear ratio of each stage;
d) rotation speed of shafts I and II;
e) torque on shafts I, III, IV;
f) general gear ratio;
g) overall efficiency;
h) useful and expended power;
i) location of the axes of the input I and output IV shafts.
Answers: a) 3; b) 1-Ch, 2-K, 3-C; c) 15, 2, 4; d) 200 and 100; e) 10, 253, 983; e) 120; g) 0.82; h) 2.57 and 3.14; i) cross.
2. BASIC CONCEPTS OF STATICS
2.1. Force and moment of force.
Couple of forces and moment of a couple of forces
Statics is a branch of mechanics that studies the conditions of equilibrium of the links of a mechanism under the action of forces.
Force (F, N) – a measure of the mechanical interaction of solids. Force is represented as a vector, the action of which is characterized by the point of application (for example, point A), direction along the line of action and magnitude F(Fig. 2.1).
Rice. 2.1 Fig. 2.2
Couple of forces(Fig. 2.2) – a system of parallel forces (), equal in magnitude ( F 1 = F 2) and directed in opposite directions ().
Moment of power( , Nm) relative to a point (for example, t. ABOUT) is the product of the numerical magnitude of the force F on the shoulder h– the shortest distance from a point to the line of action of the force (see Fig. 2.1): 
Moment of a couple of forces (concentrated moment)
(m, Hm) is defined as the product of the magnitude of one of the forces by the arm of the pair h – distance between the lines of action of forces (see Fig. 2.2):
.
|
Torque (T, Nm)– moment of force, the action of which is accompanied by rotation of the link (Fig. 2.4, A).
Bending moment (M, Nm)– moment of force, the action of which is accompanied by bending of the link (Fig. 2.4, b).
2.2. Connections and their reactions
Any structural element or link of a mechanism is a non-free body, the movements of which in space are limited by other bodies, called connections . A constraint that prevents the movement of a non-free body acts on it with a force called communication reaction .
The direction of bond reactions is determined based on the following rules:
1. The coupling reaction is applied at the point of contact of the contacting surfaces and is directed in the direction opposite to the direction in which the movement is limited.
2. If the connection limits movement in several directions simultaneously, then the direction of the reaction is unknown and it is represented in the form of components directed along the axes of the selected coordinate system.
Let's consider the direction of reactions for the main types of bonds (Fig. 2.5).
Smooth surface contact(Fig. 2.5, A). The reaction is directed along the common normal to the contacting surfaces.
Contact of smooth surfaces with corner points and cusps(Fig. 2.5, b). The reaction is directed normal to the smooth surface.
Inextensible thread(Fig. 2.5, V). Reactions and are directed along the threads to the points of suspension.
Articulating support(Fig. 2.5, G). The reaction is perpendicular to the supporting surface.
Articulated-fixed support(Fig. 2.5, d). The direction of the reaction is unknown. Presented in the form of unknown components and .
Hard seal(Fig. 2.5, e). In such a support there can be three components of the reaction: , and the support moment.
2.3. Equilibrium conditions for a plane system of forces
A rigid body is in a state of equilibrium if it is motionless relative to the reference frame under consideration.
For the equilibrium of a rigid body under the action of an arbitrary system of forces, it is necessary and sufficient that the main vector and the main moment of this system relative to any point ABOUT bodies were equal to zero:
Main vector system of forces is equal to the geometric sum of all forces of the system:
Main point system of forces is equal to the sum of the moments of all forces relative to the selected center of reduction 0:
.
As a result, the equilibrium conditions take the form:
.
When solving practical problems, the analytical method of solving vector equations is used, according to which the projection of the sum of vectors onto any axis is equal to the sum of the projections of the summands of the vectors onto the same axis .
In this regard, the above equilibrium conditions for a plane system of forces can be written in the form of three independent equilibrium equations of a rigid body relative to a rectangular XY coordinate system:
.
A rigid body is in equilibrium if the algebraic (taking into account the sign) sum of the projections of all forces on each of the coordinate axes is equal to zero and the algebraic sum of the moments of all forces relative to any point O of the XY plane is equal to zero.
To determine the magnitude and direction of the bond reaction, it is necessary to perform the following steps:
1) replace external connections with their reactions, depicting their possible direction on the power diagram;
2) from the equilibrium equations of the system of forces, determine the magnitude of the unknown reactions;
3) if, as a result of calculations, any reaction turns out to be negative, you need to change its direction in the diagram to the opposite;
4) carry out a control check of the correctness of determination of reactions both in magnitude and in direction, using additionally one of the equilibrium equations, for example, the equation of moments about a point on the plane that was not previously considered.
When drawing up equilibrium equations, it is convenient to use the following provisions:
– the projection of the force vector onto the axis is equal to the product of the modulus (magnitude) of the force and the cosine of the angle between the line of action of the force and the axis, taken with a plus sign if the directions of the vector and the axis coincide, or minus if they are opposite:
– the moment of force is taken with a plus sign if it acts in the direction of movement clockwise, and with a minus sign if it acts in the opposite direction.
2.4. Example of problem solving
Task. In Fig. Figure 2.6 shows a beam on two hinged supports A and C, loaded by a flat system of external forces and moments:
N; N; Nm;
Dimensions of beam sections:
It is required to determine the magnitude and direction of the support reaction vectors and .
Solution
Let us depict on the force diagram the estimated direction of the reactions of the supports and - both vectors are directed upward.
Let us determine the magnitude and direction of reactions and using the equilibrium equations of a plane system of forces.
Let's create an equation for the moments of forces relative to the support WITH, considering the effect of the moment in the direction of clockwise movement to be positive (with a plus sign):
Reaction = 400 N,directed downwards.
Let's create an equation for the projections of all forces onto the vertical axis Y, considering the upward direction of the vector to be positive (with a plus sign):
The minus sign indicates the wrong direction. We change the direction of the vector in the diagram to the opposite.
Reaction = 200 N,directed downwards.
We check the correctness of the solution using an additional equation for the moments of forces relative to any non-support point, for example the point IN:
The “zero” obtained as a result of calculations indicates the correctness of the determination of reactions both in magnitude and direction.
Control questions
1. Define force. What characterizes the action of force?
2. How to determine the moment of force about a point?
3. Define a force couple. How to find the moment of a couple of forces? How is it indicated on the diagrams?
4. Define torque and bending moments.
5. What is called a connection, a connection reaction?
6. Formulate rules for determining the direction of bond reactions.
7. What is called the main vector and main moment of a system of forces? How are they determined?
8. Formulate the equilibrium conditions for a plane system of forces; write the equilibrium equations.
9. Solve the problem. In Fig. Figure 2.7 shows a beam on two hinged supports B and D, loaded with forces N, N and a concentrated moment Nm. Size m. Determine the magnitude and direction of the support reactions and check.
Answer: H, directed upward; H, pointing down.
3. BASIC CONCEPTS
RESISTANCE OF MATERIALS
3.1. Strength, rigidity, stability
The performance of a structure depends on the strength, rigidity and stability of its constituent elements.
Strength– the ability of a structure and its elements to bear a load without destruction.
Rigidity– the ability of a structure and its elements to resist deformation, that is, a change in the original shape and size under the influence of loads.
Sustainability– the ability of a structure and its elements to maintain the initial form of elastic equilibrium.
Most mechanical parts are designed for strength, solving three main problems:
Determination of rational sizes;
Determination of safe loads;
Selection of the most suitable materials.
In this case, the real structure is replaced by a design diagram, and the calculation results are verified experimentally.
3.2. Section method. Internal power factors
External forces
, acting on structural elements, are divided into active (loads) and reactive (reactions of connections). They cause the appearance internal forces
resistance. If the internal forces exceed the adhesive forces of individual particles of the material, the destruction of this structural element will occur. Therefore, to assess the strength of the object being studied, it is necessary to know the internal forces and the law of their distribution throughout the object. To solve these problems use section method
. Let us consider a structural element of arbitrary shape in equilibrium (Fig. 3.1), loaded by a system of external forces 
. In any section of this element there will be internal forces that need to be determined. To do this, let’s mentally dissect the object in question with an arbitrarily selected section into two parts: A and B.
Each of these parts will be acted upon by external forces and internal forces in the section, balancing the action of the cut off part:
; 
.
Consequently, the internal forces arising in the section under consideration are equal to the sum of the external forces acting on one of the cut-off parts.
Lecture 1
Theory of mechanisms and machines - is a science that studies the structure, kinematics and dynamics of machines and mechanisms in connection with their analysis and synthesis.
Analysis– study of structural, kinematic and dynamic properties of mechanisms. There is some ready-made mechanism, the properties of which are being studied.
Synthesis– design of mechanisms with specified structural, kinematic and dynamic properties to carry out the required movements. Thus, when synthesizing a mechanism, we have the opposite task of analysis: to design a mechanism based on given properties.
Theory of mechanisms and machines– the science of the most general methods of studying machines and mechanisms and designing them for given operating conditions.
Let us introduce some basic concepts used in studying the course on the theory of mechanisms and machines.
Car- a device that performs certain movements or operations to perform useful work or convert energy.
A machine is a set of material resources artificially created by man, which reproduces his labor functions. A machine replaces a person not only in his physical, but also in his mental work, facilitates this work and increases labor productivity.
All machines can be divided into the following main types:
energy machines– converting various types of energy (electric motors, generators, pneumatic motors, hydraulic motors, etc.);
technological machines– designed to transform the dimensions, properties, shape or condition of a material (metalworking machines, rolling mills, weaving machines, etc.);
transport vehicles– designed for moving materials (cars, diesel locomotives, airplanes, cranes, lifts);
information machines– designed for receiving and converting information (arithmometers, mechanical integrators, accounting machines). An electronic computer, strictly speaking, is not a machine. The name of the machine was retained in order of historical continuity.
The machine is characterized by three main features:
2) the presence of moving parts;
3) doing useful work.
The kinematic basis of all machines is the mechanism.
Mechanism is a device designed to convert and transmit motion (for example, a gearbox).
Unlike a machine, a mechanism does not directly perform useful work. The mechanism is characterized by two main features:
1) artificial origin;
2) the presence of moving parts.
In all questions of kinematics and calculations of machines, where forces and energy are not taken into account, the concepts of machine and mechanism are identified.
When analyzing a mechanism, they do not use real drawings of the mechanism parts, but its kinematic diagram.
Kinematic diagram of the mechanism– is an abstract (conventional) image of a mechanism, made in the form of interconnected segments of straight lines and other symbols.
Mechanism parts are replaced with their conventional images in accordance with GOST 2770-68. Since the movement of any body can be characterized by the movement of a straight line segment associated with it, the links of the mechanism can be depicted on a kinematic diagram in the form of straight line segments.
Modern technology uses a wide variety of devices, instruments and machines that are designed to transmit energy and motion using special mechanisms. It is for this reason that those engineers whose specialization is the design, operation and development of manufacturing technologies for technical products must have all the necessary knowledge regarding their energy and mechanics. This means that they need to have a complete understanding of what mechanisms are, by what methods their power, kinematic and metric calculations are made, as well as the dynamic processes that occur during their operation. The general theory of mechanisms and machines combines all these issues.
Interesting machines and mechanisms
In technology cars are called such mechanical devices that perform some useful work associated with various energy conversions or the implementation of the production process. Each machine has in its design a working (executive) body, driven through a system of mechanisms by a machine-engine.
Mechanism, this is a certain set of fixed and moving parts, due to which the transformation and transmission of forces and movements is ensured, as a result of which useful work is performed.
All mechanisms consist of separate bodies, which are called links. Each of them consists of one or more parts that are fixedly connected to each other. Any mechanism consists of moving links and at least one fixed link. Of these, the leading one is the one to which motion is imparted as a result of the application of torques and external forces. Slave The links to which the movement is transmitted are named. For example, in a device such as a machine vice, leading the link is the handle, slave– movable sponge. The body and the fixed jaw attached to it constitute fixed link. In most cases, mechanisms are components of kinematic circuits of machines, but they can also have independent applications (such, for example, are the mechanisms of tachometers, adding machines, clocks, etc.).
The main feature that distinguishes mechanism or car from the structure is that their individual components are in motion. As for the difference between a mechanism and a machine, it lies in the fact that the mechanism itself neither converts various energies nor performs any independent useful work.
In theory machines and mechanisms Mainly the provisions of theoretical mechanics and its laws are used. In addition, the subject of its study is methods for studying various mechanisms and machines, as well as the strict scientific foundations of their construction. It should also be noted that the theory of machines and mechanisms is an application to mechanical engineering issues, and at the same time a direct continuation of theoretical mechanics, since it actively uses methods of dynamic, kinematic and structural analysis and synthesis.
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One of the tasks of the modern theory of mechanisms is the study and systematization of the enormous heritage accumulated by practical mechanical engineering in the form of various mechanisms used in a wide variety of machines, instruments and devices. Analysis of this material by type of mechanism showed that all work on their systematization should be divided into several stages. The first stage is collections, including mechanisms used in a wide variety of branches of mechanical engineering. The next stage is collections devoted to individual branches of mechanical engineering, for example, precision mechanics mechanisms, metal-cutting machine mechanisms, aircraft engine mechanisms, etc.
When selecting mechanisms, the author mainly provided diagrams and descriptions of general-purpose mechanisms, or mechanisms used in a wide variety of branches of mechanical engineering. But individual mechanisms of the target, industry direction were also included in the directory as being of interest not only for this narrow industry, but also for other branches of mechanical engineering. These mechanisms are separated into a separate subgroup - target device mechanisms. Kinematic pairs and movable connections are given by the author not in a schematic, but in a constructive representation, in order to facilitate the designer’s process of designing the mechanism. The author used extensive material in Russian and foreign languages.
For the purpose of greater clarity and ease of use of this reference manual when depicting mechanisms, the basis was not the conventional images of links and elements of kinematic pairs established by the relevant standards, but schematic symbols that are of a constructive nature, i.e. links and elements of kinematic pairs were depicted in the form of conventional rods, sliders, scenes, etc., having only approximately the size ratios that they could have had in their design.
Further, in the process of processing the material, in most cases it was necessary to abandon the accurate representation of individual parts of mechanisms, as is customary in structural drawings, since this would require the introduction into the drawing of a number of additional details that have important design significance, but obscure the basic perception of that form of movement, which can be reproduced by this mechanism. This especially applies to parts of frames, bearings, struts, thrust rings, bushings, etc. Moreover, some conventions used in modern structural drawings in terms of sections, projections, shading, images of threads, dotted lines, etc. were not always taken into account, since strict adherence to them would damage the clarity of readers’ perception of the kinematics and structure of the mechanisms.
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An example of calculating a spur gear. The choice of material, calculation of permissible stresses, calculation of contact and bending strength have been carried out.
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