Theoretical Mechanics | M. Movnin, A. Izrayelit

The new international system of units (SI) is used through­ out the text. However, taking into account that the engi­neers’ system (mkgfs) still finds wide use, the units of this system are also given. Moreover, wherever necessary the rela­ tions are indicated between the units of the international and engineers’ systems. Normative and design data are given in both systems of units.

In the presentation of the material primary emphasis is placed on the practical significance of conclusions.

To gain a better understanding of theoretical propositions, the solutions of sample problems are given. All solutions are first carried out in algebraic form and then numerical data are substituted.

Although the book is mainly intended for full-time vocatio­nal schools, the large number of detailed and specially selec­ted examples makes it handy for their evening and correspon­dence departments as well.

Translated from the Russian by M. Konyaeva

From the Authors 5

Notation 12

Introduction 15

Chapter I. Basic Definitions and Axioms of Statics 17 

1. Fundamentals 17 

2. Axioms of Statics 22 

3. Constraints and Their Reactions. Axioms of Constraints 25 

Chapter II. Systems of Concurrent Forces in a Plane 28 

4. Analytic Determination of the Resultant of Two Forces Applied at the Same Point 28 

5. Resolution of a Force into Two Components Ap­plied at the Same Point 30 

6. Point Addition of Concurrent Forces in a Plane. Force Polygon 32 

7. Projection of a Force on an Axis 33

8. Projection of a Vector Sumon an Axis 36

9. Analytic Determination of the Resultant of a Sys­tem of Concurrent Forces (Method of Projections)  37 

10. Conditions and Equations of Equilibrium for a Sys­tem of Concurrent Forces 39 

11. Procedure for Solving Equilibrium Problems 40 

12. Theorem of Concurrence of Three Mutually Balanced Non-Parallel Forces 49

Chapter III. Couple 52

13. Addition of Two Parallel Forces of the Same Sense 52 

14. Addition of Two Parallel Forces of OppositeSense 53 

15. Moment of a Couple 56 

16. Equivalence of Couples. Translation of a Couple in Its Plane of Action 58 

17. Theorem of Equivalent Couples 60 

18. Addition of Couples Acting in the Same Plane 61

Chapter IV. Two-Dimensional Systems of Arbitrarily Located Forces 65

19. Moment of a Force About a Point 65 

20. Equilibrium of a Lever 67 

21. Reduction of a Force to a Given Point 69 

22. Reduction of a Two-Dimensional Force System to a Given Point 70 

23. Resultant of a Two-Dimensional Force System 72 

24. Theorem of the Moment of a Resultant (Varignon’s Theorem) 73 

25. A Case of the Reduction of a Two-Dimensional Force System to a Couple 79  

26. Conditions and Equations of Equilibrium for a Two-Dimensional Force System 80  

27. Three Forms of Equilibrium Equations 82

28. Supporting Devices of Beam Systems 85 

29. Classification of Loads 88 

30. Practical Solution of Equilibrium Problems for Two-Dimensional Force Systems 89 

31. Equilibrium of a System of Connected Bodies 101

Chapter V. Friction 106

32. Types of Friction 106 

33. The Laws of Sliding Friction 107 

34. Angle and Cone of Friction 109 

35. Experimental Determination of Coefficients of Friction 114

36. The Laws of Rolling Friction 116

Chapter VI. Three-Dimensional Force Systems 120

37. Force Parallelepiped 120

38. Equilibrium of a System of Concurrent Forces in Space 121

39. Moment of a Force About an Axis 123

40. Equilibrium of an Arbitrary Three-Dimensional Force System 128

Chapter VII Centroids and Centres of Gravity 134

41. Centre of Parallel Forces 134

42. Co-ordinates of the Centre of ParallelForces 135

43. Centroid of a Volume 139

44. Centroid of an Area. Static Moments of an Area 141

45. Centroid of a Line 147

46. Stability of Equilibrium 147

PART 2. KINEMATICS

Chapter VIII. Fundamentals 154

47. Subject of Kinematics 154

48. Space and Time 154

49. Basic Definitions 156

Chapter IX. Kinematics of Particles 160

50. Methods of Specifying the Motion of a Particle 160 

51. Velocity of a Particle 162 

52. Acceleration of a Particle 167 

53. Types of Motion of a Particle as Related to Acce­leration 174 

54. Uniformly Variable Motion of a Particle 176 

55. Kinematic Graphs and Relationship Between Them 180

Chapter X. Simple Motions of Rigid Bodies 185

56. Translation of a Rigid Body 185

57. Rotation of a Rigid Body About a Fixed Axis 186

58. Velocities and Accelerations of Points of a Rotating Body 191 

Chapter XI. Methods of Transmission of Rotary Motion 198

59. Classification of Transmission Mechanisms 198 

60. Gear Ratio 198 

61. Cylinder Friction Drives 200 

62. Face Friction Drives 202

63. Cone Friction Drives 203 

64. Belt Drives: Fundamental Concepts 205 

65. Gear Drives: General Considerations 206 

66. Gear Ratio of a Spur Gear Drive 207

67. Gear Trains 208

68. Worm Gearing 212

Chapter XII Complex Motion of Particles 216

69. Base, Relative and Absolute Motions 216 

70. Theorems on Addition of the Velocities and Accelerations of a Particle in Complex Motion 219

Chapter XIII. Plane Motion. 225

71. Concept of Plane Motion of a Rigid Body 225

72. Determination of the Velocity of Any Point of a Body in Plane Motion 226

73. Instantaneous Centre of Zero Velocity 228

74. Determination of the Acceleration of Any Point of a Body in Plane Motion 240

75. Planetary Gearing 244

76. Differential Gearing 247

PART 3. DYNAMICS

Chapter XIV Basic Concepts and Axioms of Dynamics 251

77. Subject of Dynamics 251 

78. Principle of Inertia 252

79. Fundamental Law of Dynamics of Particles 252 80. Systems of Units 254 

81. Axiom of Superposition 256 

82. Axiom of Interaction 258 

83. Two Basic Problems of Dynamics 259

Chapter XV. Motion of Particles. Method of Kinetostatics 268

84. Ideal and Real Constraints 268 

85. D ’Alembert’s Principle 269 

86. Inertia Force for a Particlein Rectilinear Motion 271  

87. Inertia Force for a Particle in Curvilinear Motion 271

88. Inertia Force for a Rigid Body 274

89. Solution of Problems by the Method of Kineto­statics 275

Chapter XVI Work and Power 280

90. Work of a Constant Force in Rectilinear Motion 280 

91. Work of a Variable Force in Curvilinear Motion 282 

92. Work of a Resultant Force 283 

93. Work of a Force of Gravity 285 

94. Work of an Elastic Force 286

95. Concept of Mechanical Efficiency 289

96. Efficiency of a System of Mechanisms Connected in Series 290 

97. Efficiency of a System of Mechanisms Connected in Parallel 291

98. Power 296

99. Work and Efficiency for Bodies Sliding Along an Inclined Plane 298

100. Work and Power in Rotation 306

101. Work in Rolling Motion 308

Chapter XVII The Laws of Dynamics 315

102. Concept of a System of Particles 315 

103. Law of Momentum for a Particle 317 

104. Law of Momentum for a System of Particles 322 

105. Potential and Kinetic Energy 324 

106. Kinetic Energy of a Body in Various Types of Motion 325 

107. Moments of Inertia of Homogeneous Bodies of Simple Shape 327 

108. Law of Kinetic Energy for a Particle 330 

109. Law of Kinetic Energy for a System of Particles 333 

110. Fundamental Equation of Dynamics for a Rigid Body in Rotation 338

Chapter XVIII. Application of the Laws of Kinematics and Dynamics to the Analysis to Mechanisms 345

111. Principles and Definitions 345 

112. Fundamentals of Kinematics of Mechanisms 350

113. Examples of Constructing Velocity Diagrams 359

114. Distribution of Accelerations in a Body in Plane Motion 363

115. Examples of Constructing Acceleration Diagrams 367

116. Cam Gears 374

117. Introduction to the Dynamics of Machinery 381

118. Fundamentals of the Dynamic Analysis of Mecha­nisms 387

119. Fundamentals of Regulation. 395

Subject Index 406