Guide to solving problems in theoretical mechanics. Arkusha A.I.

5th ed., rev. - M.: 2002. - 336 p.

For students of mechanical engineering specialties of secondary specialized educational institutions. May be useful for students of technical universities.

Format: djvu (2002 , 5th ed., revised, 336 pp.)

Size: 6.2 MB

Download: yandex.disk

Format: pdf(1976 , 3rd ed., revised, 288 pp.)

Size: 20.5 MB

Download: yandex.disk

Content
Preface
Chapter I. Operations on vectors
§ 1-1. Vector addition. Rules for parallelogram, triangle and polygon
§ 2-1. Decomposition of a vector into two components. Vector difference
§ 3-1. Addition and decomposition of vectors in a graphic-analytical way
§ 4-1. Projection method. Projection of a vector onto an axis. Projections of a vector onto two mutually perpendicular axes. Determination of a vector sum by the projection method
Section one Statics
Chapter II. Flat system converging forces.
§ 5-2. Addition of two forces
§ 7-2. Polygon of forces. Determination of the resultant of converging forces
§ 8-2. Equilibrium of Converging Forces
§ 9-2. Equilibrium of three non-parallel forces
Chapter III. Arbitrary flat system of forces
§ 10-3. Moment of a couple of forces. Addition of force pairs. Equilibrium of force pairs
§ 11-3. Moment of force about a point
§ 12-3. Determination of the resultant arbitrary plane system of forces
§ 13-3. Varignon's theorem
§ 14-3. Equilibrium of an arbitrary plane system of forces
§ 15-3. Equilibrium taking into account friction forces
§ 16-3. Articulated systems
§ 17-3. Statically definable trusses. Methods for cutting nodes and through sections
Chapter IV. Spatial system of forces
§ 18-4. Force parallelepiped rule
§ 19-4. Projection of force onto three mutually perpendicular axes. Determination of the resultant system of spatial forces applied to a point
§ 20-4. Equilibrium of a spatial system of converging forces
§ 21-4. Moment of force about the axis
§ 22-4. Equilibrium of an arbitrary spatial system of forces
Chapter V. Center of gravity........................
§ 23-5. Determining the position of the center of gravity of a body composed of thin homogeneous rods
§ 24-5. Determining the position of the center of gravity of figures composed of plates
§ 25-5. Determination of the position of the center of gravity of sections composed of standard rolled profiles
§ 26-5. Determining the position of the center of gravity of a body composed of parts having a simple geometric shape
Section two Kinematics
Chapter VI. Kinematics of a point
§ 27-6. Uniform rectilinear movement points
§ 28-6. Uniform curvilinear movement of a point
§ 29-6. Uniform motion of a point
§ 30-6. Uneven movement points along any trajectory
§ 31-6. Determination of the trajectory, speed and acceleration of a point if the law of its motion is given in coordinate form
§ 32-6. Kinematic method for determining the radius of curvature of a trajectory
Chapter VII. Rotational movement solid
§ 33-7. Uniform rotational movement
§ 34-7. Equally alternating rotational motion
§ 35-7. Uneven rotational movement
Chapter VIII. Complex movement of point and body
§ 36-8. Addition of the movements of a point when the portable and relative movements are directed along the same straight line
§ 37-8. Addition of the movements of a point when the portable and relative movements are directed at an angle to each other
§ 38-8. Plane-parallel body motion
Chapter IX. Elements of kinematics of mechanisms
§ 39-9. Determination of gear ratios of various gears
§ 40-9. Determination of gear ratios of the simplest planetary and differential gears
Section three Dynamics
Chapter X. Movement material point
§ 41-10. Basic law of point dynamics
§ 42-10. Application of d'Alembert's principle to solving problems involving the rectilinear motion of a point
§ 43-10. Application of d'Alembert's principle to solving problems involving the curvilinear motion of a point
Chapter XI. Work and power. Efficiency
§ 44-11. Work and power in forward motion
§ 45-11. Rotational work and power
Chapter XII. Basic theorems of dynamics
§ 46-12. Problems involving translational movement of the body
§ 47-12. Problems involving rotational movement of the body

The manual contains systematically selected typical problems throughout the course, general guidelines and tips for solving problems. Problem solving is accompanied by detailed explanations. Many problems are solved in several ways.
For students of mechanical engineering specialties of secondary specialized educational institutions. May be useful for students of technical universities.

ACTIONS ON VECTORS.
When solving problems in theoretical mechanics, they usually produce various actions over scalar quantities (quantities without direction - length, area, mass, time, etc.) and over vector quantities(quantities with direction - force, speed, acceleration, etc.).

Due to the fact that vectors have a direction, mathematical operations on them differ significantly from similar operations on scalars.

For addition scalar quantities It is enough to know arithmetic or algebra. For example, if you need to add two numbers expressing lengths of 5 and 8 m, then the total length of 13 m is obtained as arithmetic sum numbers: 5 + 8=13.

If the algebraic values -5 and 4-8 or + 5 and - 8 are added, then the result is achieved using the algebraic sum - 5 + 8 = 4- 3 or + 5 - 8 = - 3.

When adding and subtracting vectors, the final result depends, firstly, on the numerical value (modulus) of the vectors and, secondly, on their direction. Therefore, these actions on vectors are performed using the construction of geometric figures.
The result of adding vectors is called a geometric sum.
Accordingly, the result of subtracting two vectors is called the geometric difference.

Content
Preface
Chapter I. Operations on vectors
§ 1-1. Vector addition. Rules for parallelogram, triangle and polygon
§ 2-1. Decomposition of a vector into two components. Vector difference
§ 3-1. Addition and decomposition of vectors in a graphic-analytical way
§ 4-1. Projection method. Projection of a vector onto an axis. Projections of a vector onto two mutually perpendicular axes. Determination of a vector sum by the projection method
Section one Statics
Chapter II. Plane system of converging forces
§ 5-2. Addition of two forces
§ 7-2. Polygon of forces. Determination of the resultant of converging forces
§ 8-2. Equilibrium of Converging Forces
§ 9-2. Equilibrium of three non-parallel forces
Chapter III. Arbitrary flat system of forces
§ 10-3. Moment of a couple of forces. Addition of force pairs. Equilibrium of force pairs
§ 11-3. Moment of force about a point
§ 12-3. Determination of the resultant arbitrary plane system of forces
§ 13-3. Varignon's theorem
§ 14-3. Equilibrium of an arbitrary plane system of forces
§ 15-3. Equilibrium taking into account friction forces
§ 16-3. Articulated systems
§ 17-3. Statically definable trusses. Methods for cutting nodes and through sections
Chapter IV. Spatial system of forces
§ 18-4. Force parallelepiped rule
§ 19-4. Projection of force onto three mutually perpendicular axes. Determination of the resultant system of spatial forces applied to a point
§ 20-4. Equilibrium of a spatial system of converging forces
§ 21-4. Moment of force about the axis
§ 22-4. Equilibrium of an arbitrary spatial system of forces
Chapter V. Center of gravity
§ 23-5. Determining the position of the center of gravity of a body composed of thin homogeneous rods
§ 24-5. Determining the position of the center of gravity of figures composed of plates
§ 25-5. Determination of the position of the center of gravity of sections composed of standard rolled profiles
§ 26-5. Determining the position of the center of gravity of a body composed of parts having a simple geometric shape
Section two Kinematics
Chapter VI. Kinematics of a point
§ 27-6. Uniform linear motion of a point
§ 28-6. Uniform curvilinear movement of a point
§ 29-6. Uniform motion of a point
§ 30-6. Uneven movement of a point along any trajectory
§ 31-6. Determination of the trajectory, speed and acceleration of a point if the law of its motion is given in coordinate form
§ 32-6. Kinematic method for determining the radius of curvature of a trajectory
Chapter VII. Rotational motion of a rigid body
§ 33-7. Uniform rotational movement
§ 34-7. Equally alternating rotational motion
§ 35-7. Uneven rotational movement
Chapter VIII. Complex movement of point and body
§ 36-8. Addition of the movements of a point when the portable and relative movements are directed along the same straight line
§ 37-8. Addition of the movements of a point when the portable and relative movements are directed at an angle to each other
§ 38-8. Plane-parallel body motion
Chapter IX. Elements of kinematics of mechanisms
§ 39-9. Determination of gear ratios of various gears
§ 40-9. Determination of gear ratios of the simplest planetary and differential gears
Section three Dynamics
Chapter X. Motion of a material point
§ 41-10. Basic law of point dynamics
§ 42-10. Application of d'Alembert's principle to solving problems involving the rectilinear motion of a point
§ 43-10. Application of d'Alembert's principle to solving problems involving the curvilinear motion of a point
Chapter XI. Work and power. Efficiency
§ 44-11. Work and power in forward motion
§ 45-11. Rotational work and power
Chapter XII. Basic theorems of dynamics
§ 46-12. Problems involving translational movement of the body
§ 47-12. Problems involving rotational movement of the body.

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Guide to solving problems in theoretical mechanics. Arkusha A.I.

5th ed., rev. - M.: 2002. - 336 p.

For students of mechanical engineering specialties of secondary specialized educational institutions. May be useful for students of technical universities.

Format: djvu (2002 , 5th ed., revised, 336 pp.)

Size: 6.2 MB

Download: yandex.disk

Format: pdf(1976 , 3rd ed., revised, 288 pp.)

Size: 20.5 MB

Download: yandex.disk

Content
Preface
Chapter I. Operations on vectors
§ 1-1. Vector addition. Rules for parallelogram, triangle and polygon
§ 2-1. Decomposition of a vector into two components. Vector difference
§ 3-1. Addition and decomposition of vectors in a graphic-analytical way
§ 4-1. Projection method. Projection of a vector onto an axis. Projections of a vector onto two mutually perpendicular axes. Determination of a vector sum by the projection method
Section one Statics
Chapter II. Plane system of converging forces.
§ 5-2. Addition of two forces
§ 7-2. Polygon of forces. Determination of the resultant of converging forces
§ 8-2. Equilibrium of Converging Forces
§ 9-2. Equilibrium of three non-parallel forces
Chapter III. Arbitrary flat system of forces
§ 10-3. Moment of a couple of forces. Addition of force pairs. Equilibrium of force pairs
§ 11-3. Moment of force about a point
§ 12-3. Determination of the resultant arbitrary plane system of forces
§ 13-3. Varignon's theorem
§ 14-3. Equilibrium of an arbitrary plane system of forces
§ 15-3. Equilibrium taking into account friction forces
§ 16-3. Articulated systems
§ 17-3. Statically definable trusses. Methods for cutting nodes and through sections
Chapter IV. Spatial system of forces
§ 18-4. Force parallelepiped rule
§ 19-4. Projection of force onto three mutually perpendicular axes. Determination of the resultant system of spatial forces applied to a point
§ 20-4. Equilibrium of a spatial system of converging forces
§ 21-4. Moment of force about the axis
§ 22-4. Equilibrium of an arbitrary spatial system of forces
Chapter V. Center of gravity........................
§ 23-5. Determining the position of the center of gravity of a body composed of thin homogeneous rods
§ 24-5. Determining the position of the center of gravity of figures composed of plates
§ 25-5. Determination of the position of the center of gravity of sections composed of standard rolled profiles
§ 26-5. Determining the position of the center of gravity of a body composed of parts having a simple geometric shape
Section two Kinematics
Chapter VI. Kinematics of a point
§ 27-6. Uniform linear motion of a point
§ 28-6. Uniform curvilinear movement of a point
§ 29-6. Uniform motion of a point
§ 30-6. Uneven movement of a point along any trajectory
§ 31-6. Determination of the trajectory, speed and acceleration of a point if the law of its motion is given in coordinate form
§ 32-6. Kinematic method for determining the radius of curvature of a trajectory
Chapter VII. Rotational motion of a rigid body
§ 33-7. Uniform rotational movement
§ 34-7. Equally alternating rotational motion
§ 35-7. Uneven rotational movement
Chapter VIII. Complex movement of point and body
§ 36-8. Addition of the movements of a point when the portable and relative movements are directed along the same straight line
§ 37-8. Addition of the movements of a point when the portable and relative movements are directed at an angle to each other
§ 38-8. Plane-parallel body motion
Chapter IX. Elements of kinematics of mechanisms
§ 39-9. Determination of gear ratios of various gears
§ 40-9. Determination of gear ratios of the simplest planetary and differential gears
Section three Dynamics
Chapter X. Motion of a material point
§ 41-10. Basic law of point dynamics
§ 42-10. Application of d'Alembert's principle to solving problems involving the rectilinear motion of a point
§ 43-10. Application of d'Alembert's principle to solving problems involving the curvilinear motion of a point
Chapter XI. Work and power. Efficiency
§ 44-11. Work and power in forward motion
§ 45-11. Rotational work and power
Chapter XII. Basic theorems of dynamics
§ 46-12. Problems involving translational movement of the body
§ 47-12. Problems involving rotational movement of the body

The textbook was created for professions related to metalworking.
The fundamentals of theoretical mechanics, strength of materials, parts and machine mechanisms are outlined; Examples of calculations are given. Provides information about the main ways to increase mechanical properties materials and trends in the development of machine and mechanism designs.

Connections and their reactions.
A body that can make any movement in space is called free; An example of a free body is an airplane or a projectile flying in the air. In various types of structures and structures, we usually encounter bodies whose movements are subject to restrictions. Such bodies are called non-free. A body that limits the freedom of movement of a rigid body is a connection in relation to it. If the forces applied to the body tend to move it in one direction or another, and the connection prevents such movement, then the body will act on the connection with a force of pressure on the connection.

TABLE OF CONTENTS
Basic notations used
Introduction
Section 1. Theoretical mechanics
1.1. Basic concepts and axioms of statics
1.2. Connections and their reactions
1.3. Flat force system
1.4. Elements of friction theory
1.5. Spatial system of forces
1.6. Determining the center of gravity
1.7. Kinematics of a point
1.8. The simplest motions of a rigid body
1.9. Laws of dynamics, equations of motion of a material point, D'Alembert's principle
1.10. Forces acting on points mechanical system
1.11. Theorem on the motion of the center of mass of a mechanical system
1.12. Work of force
1.13. Power
1.14. Efficiency
Section 2. Fundamentals of Strength of Materials
2.1. Basic Concepts
2.2. Tension and compression
2.3. Basic mechanical characteristics of materials
2.4. Tensile and compressive strength calculations
2.5. Shear and crush
2.6. Torsion
2.7. Straight bend
2.8. Determination of displacements during bending using the Vereshchagin method
2.9. Calculation of timber for the combined action of torsion and bending
2.10. Strength under dynamic loads
2.11. Stability under axial loading of the rod
2.12. Revealing the static indetermination of rod systems
Section 3. Machine parts and mechanisms
3.1. Machines and their main elements
3.2. Basic criteria for the performance and calculation of machine parts
3.3 Engineering materials
3.4. Rotational details
3.5 Body parts
3.6 Springs and leaf springs
3.7 Permanent connections of parts
3.8 Detachable connections details
3.9. Plain bearings
3.10. Rolling bearings
3.11. Couplings
3.12. Friction gears
3.13. Belt drives
3.14. Gears
3.15. Worm gears
3.16. Chain transmissions
3.17. Sliding screw-nut transmission
3.18. Screw-nut transmission
3.19. Rack and pinion gears
3.20. Crank mechanisms
3.21. Rocker mechanisms
3.22. Cam mechanisms
3.23. General information about gearboxes
Section 4. Improving the mechanical properties of materials and structures
4.1. Basic ways to improve mechanical properties
4.2. Strengthening treatment by plastic deformation
4.3. Increasing the wear resistance of surface layers
4.4. Surface Coatings
4.5. Strengthening of surface layers by chemical-thermal treatment
4.6. Strengthening the lead screws
Conclusion. Trends in the development of machine and mechanism designs
Applications
1. Hot rolled equal flange steel angles (according to GOST 8509-93)
2. Hot rolled unequal steel angles (according to GOST 8510-86)
3. Hot-rolled steel channels (according to GOST 8240-89)
4. Hot-rolled steel I-beams (according to GOST 8239-89)
5. Conventional graphic symbols in diagrams. Kinematics elements (according to GOST 2.770-68*)
Bibliography.

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