DYNAMICS OF MACHINERY

INTRODUCTION ABOUT THEORY OF MACHINES AND

FUNDAMENTALS

UNIT –I BASICS OF MECHANISMS

UNIT I FORCE ANALYSIS 9Dynamic force analysis – Inertia force and Inertia torque– D Alembert’s principle –Dynamic Analysis in reciprocating engines – Gas forces – Inertia effect of connecting rod– Bearing loads – Crank shaft torque – Turning moment diagrams –Fly Wheels – Flywheels of punching presses- Dynamics of Cam follower mechanism.

THEORY OF MACHINES1. INTRODUCTION:

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 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.

Theory of machines and mechanisms is an applied science which is used to understand the relationship between the geometry and motions of the parts of the machine or mechanism and the forces which produces these motions.1.1 SUB- DIVISIONS OF THEORY OF MACHINES:

1.1.1 Kinematics: is that branch of theory of machines which is responsible to study the motion of bodies without reference to the forces which are cause this motion, i.e it’s relate the motion variables (displacement, velocity, acceleration) with the time.

1.1.2 Kinetics: is that branch of theory of machines which is responsible to relate the action of forces on bodies to their resulting motion.

1.1.3 Dynamics: is that branch of theory of machines which deals with the forces and their effects, while acting upon the machine parts in motion.

1.1.4 Statics: is that branch of theory of machines which deals with the forces and their effects, while the machine parts are rest.

1.1.5 Mechanics: is an area of science concerned with the behavior of physical bodies when subjected to forces or displacements, and the subsequent effects of the bodies on their environment.

1.2 FUNDAMENTAL CONCEPTS:

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), and3. Time (t).1.2.1 Derived Units:Some units are expressed in terms of fundamental units known as derived units, e.g., the units of area, velocity, acceleration, pressure, etc.1.2.2 Systems of Units:There are only four systems of units, which are commonly used and universally recognized.These are known as:1. C.G.S. units, 2. F.P.S units, 3. M.K.S. units and 4. S.I. units.1.2.2.1 C.G.S. Units:In this system, the fundamental units of length, mass and time are centimeter, gram and second respectively. The C.G.S. units are known as absolute units or physicist's units.1.2.2.2 F.P.S. Units:In this system, the fundamental units of length, mass and time are foot, pound and second respectively.1.2.2.3 M.K.S. Units:In this system, the fundamental units of length, mass and time are meter, kilogram and second respectively. The M.K.S. units are known as gravitational units or engineer's units.1.2.2.4 International System of Units (S.I. Units):In this system of units, the fundamental units are meter (m), kilogram (kg) and second (s) respectively. But there is a slight variation in their derived units.

1.3.1 Resultant Force:

If a number of forces P,Q,R etc. are acting simultaneously on a particle, then a single force, which will produce the same effect as that of all the given forces, is known as a resultant force. The forces P,Q,R etc. are called component forces. The process of finding out the resultant force of the given component forces, is known as composition of forces.

A resultant force may be found out analytically, graphically or by the following three laws:

Parallelogram law of forces. It states, “If two forces acting simultaneously on a particle be represented in magnitude and direction by the two adjacent sides of a parallelogram taken in order, their resultant may be represented in magnitude and direction by the diagonal of the parallelogram passing through the point.”

Triangle law of forces. It states, “If two forces acting simultaneously on a particle be represented in magnitude and direction by the two sides of a triangle taken in order, their resultant may be represented in magnitude and direction by the third side of the triangle taken in opposite order.”

Polygon law of forces. It states, “If a number of forces acting simultaneously on a particle be represented in magnitude and direction by the sides of a polygon taken in order, their resultant may be represented in magnitude and direction by the closing side of the polygon taken in opposite order.”

1.3.2 Scalars and Vectors: Scalar quantities are those quantities, which have magnitude only, e.g. mass, time, volume,

density etc. Vector quantities are those quantities which have magnitude as well as direction e.g. velocity,

acceleration, force etc. Since the vector quantities have both magnitude and direction, therefore, while adding or

subtracting vector quantities, their directions are also taken into account.1.3.2.1 Representation of Vector Quantities:The vector quantities are represented by vectors. A vector is a straight line of a certain length possessing a starting point and a terminal point at which it carries an arrow head. This vector is cut off along the vector quantity or drawn parallel to the line of action of the vector quantity, so that the length of the vector represents the magnitude to some scale. The arrow head of the vector represents the direction of the vector quantity.1.3.2.2 Addition of Vectors: Consider two vector quantities P and Q, which are required to be added, as shown in Fig.(a). Take a point A and draw a line AB parallel and equal in magnitude to the vector P. Through B, draw BC parallel

and equal in magnitude to the vector Q. Join AC, which will give the required sum of the two vectors P and Q, as shown in Fig.(b).

1.3.2.3 Subtraction of Vector Quantities:

Consider two vector quantities P and Q whose difference is required to be found out as shown in Fig.(a). Take a point A and draw a line AB parallel and equal in magnitude to the vector P. Through B, draw BC parallel and equal in magnitude to the vector Q, but in opposite direction. Join AC, which gives the required difference of the vectors P and Q, as shown in Fig.(b).

1.1.1 FORCE:

A force is a push or pull upon an object resulting from the object's interaction with another object. Whenever there is an interaction between two objects, there is a force upon each of the objects. When the interaction ceases, the two objects no longer experience the force.

1.1.2 TYPES OF FORCES:

In the design of mechanisms, the following forces are generally considered: Applied forces

Force is a vector quantity. Vector is a physical quantity described by magnitude (meaning the strength of the force) and direction. Applied force means the force with which an object has been pushed or pulled by another object.

Inertia forces A force opposite in direction to an accelerating force acting on a body and equal to

the product of the accelerating force and the mass of the body. Frictional forces.

Frictional force is force that acts between two surfaces that are moving past another.

The applied forces act from outside on the mechanism. The inertia forces arise due to the mass of the links of the mechanism and their acceleration. Frictional forces are the outcome of friction in the joints. A pair of action and reaction forces acting on a body is called constraint forces.

1.2 TYPES OF FORCE ANALYSIS: Static force analysis Dynamic force analysis

1.2.1 NEWTON’S LAWS OF MOTION:FIRST LAW:

An every body continuous in its state of rest or of uniform motion in a straight line unless an external forces acts on it.

SECOND LAW:

The rate of change of momentum of a body is directly proportional to the force acting on it and takes place in the direction of force.

THIRD LAW:

To every action there is an equal and opposite reaction.

KINEMATICS OF MOTION:

Kinematics of motion is the relative motion of bodies without consideration of the forces causing the motion. Types:

Plane Motion Rectilinear Motion Curvilinear Motion

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 translator motion.Curvilinear Motion:

It is the motion along a curved path. Such a motion, when confined to one plane, is called plane

curvilinear motion.Linear Displacement:It may be defined as the distance moved by a body with respect to a certain fixed point. The displacement may be along a straight or a curved path.Linear Velocity:It may be defined as the rate of change of linear displacement of a body with respect to the time.Linear AccelerationIt 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.