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CONTENTS
1. Introduction
2. Kinematics of Motion
3. Kinetics of Motion
4. Simple Harmonic Motion
5. Simple Mechanisms
6. Velocity in Mechanisms (Instantaneous Centre Method)
7. Velocity in Mechanisms (Relative Velocity Method)
8. Acceleration in Mechanisms
9. Mechanisms with Lower Pairs
10. Friction
11. Belt, Rope and Chain Drives
12. Toothed Gearing
13. Gear Trains
14. Gyroscopic Couple and Precessional Motion
15. Inertia Forces in Reciprocating Parts
16. Turning Moment Diagrams and Flywheel
17. Steam Engine Valves and Reversing Gears
18. Governors
19. Brakes and Dynamometers
20. Cams
21. Balancing of Rotating Masses
22. Longitudinal and Transverse Vibrations
23. Torsional Vibrations
24. Computer Aided Analysis and Synthesis of Mechanisms
25. Automatic Control

BRIEF INTRODUCTION TO THEORY OF MACHINES BY RS KHURMI AND JK GUPTA

Definition

The subject Theory of Machines may be defined as that branch of Engineering-science, which deals with the study of relative motion between the various parts of a machine, and forces which act on them. The knowledge of this subject is very essential for an engineer in designing the various parts of a machine.
A machine is a device which receives energy in some available form and utilises it to do some particular type of work.

Sub-divisions of Theory of Machines

The Theory of Machines may be sub-divided into the following four branches :
1. Kinematics. It is that branch of Theory of Machines which deals with the relative motion between the various parts of the machines.
2. Dynamics. It is that branch of Theory of Machines which deals with the forces and their effects, while acting upon the machine parts in motion.
3. Kinetics. It is that branch of Theory of Machines which deals with the inertia forces which arise from the combined effect of the mass and motion of the machine parts.
4. Statics. It is that branch of Theory of Machines which deals with the forces and their effects while the machine parts are at rest. The mass of the parts is assumed to be negligible.

The measurement of physical quantities is one of the most important operations in engineering. Every quantity is measured in terms of some arbitrary, but internationally accepted units, called fundamental units. All physical quantities, met within this subject, are expressed in terms of the following three fundamental quantities :
1. Length (L or l),
2. Mass (M or m), and
3. Time (t).

Kinematics of Motion

Introduction

We have discussed in the previous Chapter, that the subject of Theory of Machines deals with the motion and forces acting on the parts (or links) of a machine. In this chapter, we shall first discuss the kinematics of motion i.e. the relative motion of bodies without consideration of the forces causing the motion. In other words, kinematics deal with the geometry of motion and concepts like displacement, velocity and acceleration considered as functions of time.

Plane Motion : When the motion of a body is confined to only one plane, the motion is said to be plane motion. The plane motion may be either rectilinear or curvilinear.
Rectilinear Motion : It is the simplest type of motion and is along a straight line path. Such a motion is also known as translatory motion.
Curvilinear Motion :  It is the motion along a curved path. Such a motion,when confined to one plane, is called plane curvilinear motion. When all the particles of a body travel in concentric circular paths of constant radii (about the axis of rotation perpendicular to the plane of motion) such as a pulley rotating about a fixed shaft or a shaft rotating about its own axis, then the motion is said to be a plane rotational motion.

Linear Velocity : It may be defined as the rate of change of linear displacement of a body with respect to the time. Since velocity is always expressed in a particular direction, therefore it is a vector quantity. Mathematically, linear velocity, v = ds/dt

Linear Acceleration : It may be defined as the rate of change of linear velocity of a body with respect to the time. It is also a vector quantity.

Friction

Introduction

It has been established since long, that the surfaces of the bodies are never perfectly smooth. When, even a very smooth surface is viewed under a microscope, it is found to have roughness and irregularities, which may not be detected by an ordinary touch. If a block of one substance is placed over the level surface of the same or of different material, a certain degree of interlocking of the minutely projecting particles takes place. This does not involve any force, so long as the block does not move or tends to move. But whenever one block moves or tends to move tangentially with respect to the surface, on which it rests, the interlocking property of
the projecting particles opposes the motion. This opposing force, which acts in the opposite direction of the movement of the upper block, is called the force of friction or simply friction. It thus follows, that at every joint in a machine, force of friction arises due to the relative motion between two parts and hence some energy is wasted in overcoming the friction. Though the friction is considered undesirable, yet it plays an important role both in nature and in engineering e.g. walking on a road, motion of locomotive on rails, transmission of power by belts, gears etc. The friction between the wheels and the road is essential for the car to move forward.

Types of Friction : In general, the friction is of the following two types
1. Static friction. It is the friction, experienced by a body, when at rest.
2. Dynamic friction. It is the friction, experienced by a body, when in motion. The dynamic friction is also called kinetic friction and is less than the static friction. It is of the following three
types :
(a) Sliding friction. It is the friction, experienced by a body, when it slides over another body.
(b) Rolling friction. It is the friction, experienced between the surfaces which has balls or rollers interposed between them.
(c) Pivot friction. It is the friction, experienced by a body, due to the motion of rotation as in case of foot step bearings.
The friction may further be classified as :
1. Friction between unlubricated surfaces, and
2. Friction between lubricated surfaces.

Friction Between Lubricated Surfaces :

When lubricant (i.e. oil or grease) is applied between two surfaces in contact, then the friction may be classified into the following two types depending upon the thickness of layer of a lubricant.
1. Boundary friction (or greasy friction or non-viscous friction). It is the friction, experienced between the rubbing surfaces, when the surfaces have a very thin layer of lubricant. The thickness of this very thin layer is of the molecular dimension. In this type of friction, a thin layer of lubricant forms a bond between the two rubbing surfaces. The lubricant is absorbed on the surfaces and forms a thin film. This thin film of the lubricant results in less friction between them. The boundary friction follows the laws of solid friction.
2. Fluid friction (or film friction or viscous friction). It is the friction, experienced between the rubbing surfaces, when the surfaces have a thick layer of the lubrhicant. In this case, the actual surfaces do not come in contact and thus do not rub against each other. It is thus obvious that fluid friction is not due to the surfaces in contact but it is due to the viscosity and oiliness of the lubricant.
Note : The viscosity is a measure of the resistance offered to the sliding one layer of the lubricant over an adjacent layer. The absolute viscosity of a lubricant may be defined as the force required to cause a plate of unit area to slide with unit velocity relative to a parallel plate, when the two plates are separated by a layer of lubricant of unit thickness. The oiliness property of a lubricant may be clearly understood by considering two lubricants of equal viscosities and at equal temperatures. When these lubricants are smeared on two different surfaces, it is found that the force of friction with one lubricant is different than that of the other. This difference is due to the property of the lubricant known as oiliness. The lubricant which gives lower force of friction is said to have
greater oiliness.

Toothed Gearing

Introduction :

We have discussed in the previous chapter, that the slipping of a belt or rope is a common phenomenon, in the transmission of motion or power between two shafts. The
effect of slipping is to reduce the velocity ratio of the system. In precision machines, in which a definite velocity ratio is of importance (as in watch mechanism), the only positive drive is by means of gears or toothed wheels. A gear drive is also provided, when the distance between the driver and the follower is very small.

Friction Wheels :

The motion and power transmitted by gears is kinematically equivalent to that transmitted by friction wheels or discs. In order to understand how the motion can be
transmitted by two toothed wheels, consider two plain circular wheels A and B mounted on shafts, having sufficient rough surfaces and pressing against each other.

Longitudinal and Transverse Vibrations

Introduction

When elastic bodies such as a spring, a beam and a shaft are displaced from the equilibrium position by the application of external forces, and then released, they execute a vibratory motion. This is due to the reason that, when a body is displaced, the internal forces in the form of elastic or strain energy are present in the body. At release, these forces bring the body to its original position. When the body reaches the equilibrium position, the whole of the elastic or strain energy is converted into kinetic energy due to which the body continues to move in the opposite direction. The whole of the kinetic energy is again converted into strain energy due to which the body again returns to the equilibrium position. In this way, the vibratory motion is repeated indefinitely.