# Mechanics of Machines-II

#### Course Topics

• INTRODUCTION
• Balancing of Rotating Masses
• Introduction - Balancing of Rotating Masses
• Balancing of a Single Rotating Mass By a Single Mass Rotating in the Same Plane
• Balancing of a Single Rotating Mass By Two Masses Rotating in Different Planes
• Balancing of Several Masses Rotating in the Same Plane
• Balancing of Several Masses Rotating in Different Planes
• Balancing of Reciprocating Masses
• Primary and Secondary Unbalanced Forces of Reciprocating Masses
• Partial Balancing of Unbalanced Primary Force in a Reciprocating Engine
• Partial Balancing of Locomotives
• Effect of Partial Balancing of Reciprocating Parts of Two Cylinder Locomotives
• Variation of Tractive Force
• Swaying Couple
• Hammer Blow
• Balancing of Coupled Locomotives
• Balancing of Primary Forces of Multi-cylinder In-line Engines
• Balancing of Secondary Forces of Multi-cylinder In-line Engines
• Balancing of Radial Engines (Direct and Reverse Cranks Method )
• Balancing of V-engines
• Torsional Vibrations
• Natural Frequency of Free Torsional Vibrations
• Effect of Inertia of the Constraint on Torsional Vibrations
• Free Torsional Vibrations of a Single Rotor System
• Free Torsional Vibrations of a Two Rotor System
• Free Torsional Vibrations of a Three Rotor System
• Torsionally Equivalent Shaft
• Free Torsional Vibrations of a Geared System
• Transverse Vibrations
• Effect of Inertia of the Constraint in Transverse Vibrations
• Natural Frequency of Free Transverse Vibrations Due to a Point Load Acting Over a Simply Supported Shaft
• Values of static deflection () for the various types of beams and under various load conditions
• Natural Frequency of Free Transverse Vibrations Due to Uniformly Distributed Load Acting Over a Simply Supported Shaft
• Natural Frequency of Free Transverse Vibrations of a Shaft Fixed at Both Ends Carrying a Uniformly Distributed Load
• Natural Frequency of Free Transverse Vibrations For a Shaft Subjected to a Number of Point Loads
• Critical or Whirling Speed of a Shaft
• Longitudinal Vibrations
• Natural Frequency of Free Longitudinal Vibrations
• Effect of Inertia of the Constraint in Longitudinal Vibrations
• Frequency of Free Damped Vibrations (Viscous Damping)
• Damping Factor or Damping Ratio
• Logarithmic Decrement
• Frequency of Under Damped Forced Vibrations
• Magnification Factor or Dynamic Magnifier
• Vibration Isolation and Transmissibility

#### INTRODUCTION

Simply speaking, “A machine is a device which received energy in some available form and utilizes it to do some particular type of work” or “A machine may be regarded as an agent for transmitting or modifying energy”.

A machine is a combination of components which can transmit power in a controlled manner and which is capable of performing useful work. A machine consists of a number of kinematically related links.A machine is a combination of resistant bodies (links or elements) with successfully constrained relative motions, which is used for transmitting other forms of energy into mechanical energy or transmitting and modifying available energy to do some particular kind of work.

Every machine will be found to consist of a system of parts (links or elements) connected together in such a manner that, if one be made to move, they all receive a motion, the relation of which to that of the first depends upon the nature of connections (i.e. joints).

The links may be rigid, rigid-hydraulic, or rigid-pneumatic. The power input may be mechanical, electrical, hydraulic, chemical, or nuclear. The power output may be mechanical, electrical hydraulic or thermal.

Examples of machines:

Heat engine- Receives heat energy and transformers it into mechanical energy.

Electric motor- Changes electric energy into mechanical energy.

A pump- Input electric power and output hydraulic power.

The majority of machines receives mechanical energy, and modify it so that the energy can be used for doing some specific task, for which it is designed, common examples of such machines being hoist, lathe, screw jack, etc.

Note:-It should be noted that machine must be capable of doing useful work. A series of kinematically related links put into motion with no output link, and which simply converts input energy to friction heat, is not a machine, unless the original purpose was only to generate heat.

CLASSIFICATION OF MACHINES

1. Machines for generating mechanical energy

- Converts other forms of energy into mechanical work

Examples: Steam engines, Steam turbines, I. C. engines, gas turbines, water turbines etc

2. Machines for transmitting mechanical energy into other form of energy

- Known as converting machines

Examples: Electric generators, air or hydraulic pumps, etc.

3. Machines for utilizing mechanical energy in the performance of useful work.

Examples: Lathe, and other machine tools, etc.

The transmission and modification of energy within the machine require the inclusion of a number of parts (links or elements), which are so selected that they will produce the desired motion and carry with safety the forces to which they are subjected so that the machine can perform its task successfully.

The study of relative motion between the various parts of a machine, and the forces which act on them, is covered under they field of “Theory of machines”, or “The Theory of Machines may be defined as that branch of engineering science which deals with the study of relative motion between various elements of a machine and the forces which act on them.

DIFFERENCE BETWEEN MACHINE AND MECHANISM

In kinematics, a mechanism is a mean of transmitting, controlling, or constraining relative movement. The central theme for mechanisms is rigid bodies connected together by joints. It can also be defined as a combination of resistant bodies that are shaped and connected in such a way that they move with definite relative motion with respect to each other.

A machine is a combination of rigid or resistant bodies, formed and connected in such a way th