Kinematics of Machines

Kinematics of Machines is a fundamental course of mechanisms and machines. It is intended to introduce-essential elements of machines and their functionality and engenders skills for kinematics analysis of machine elements like linkages, cams, and gears, within the general machine design context.

The subject Kinematics of Machines also known as KOM is one of the important subjects for the Mechanical Engineers. This course tells us about the distinctive features of the machines. This tells us how the machine works. In this course, we will study about the working of the machines. How they work? What would be the speed of output is some input speed is given. What would be the acceleration and so on.

Also check out these subjects

Theory of Machines

Design of Machine Element


So there are two parts, one is kinematics and the other part is machines. First we tell about the kinematics.


Kinematics is the branch of mechanics which tells us about the motion without considering the cause of motion. In this portion, we study the displacement, speed and acceleration without bothering about the input force or torque.

In this, we study about the effect of force and torque on an object. We study about the output velocity, acceleration, when the input torque or force is given.
Prerequisite for the course:
You should have the knowledge of following items before starting this course:

  1. Vectors
  2. Concepts of displacement, velocity and acceleration
  3. Basic mechanics.
  4. And some part of engineering graphics.


The main part of this course is the study of machines. A machine is a tool which converts one form of energy to some useful work. For example an engine converts thermal energy into mechanical energy. So the engine would be a machine. A lathe machine converts electrical energy into some useful mechanical work, so it is a machine.

Although, we will discuss the machine in detail in later part of the tutorials, but the basic definition is “A machine is a combination of rigid or resistant bodies, formed and connected do that they move with definite relative motions and transmit force from the source of power to the resistance to be overcome. A machine has two functions: transmitting definite relative motion and transmitting force.  These functions require strength and rigidity to transmit the forces.”


Topics for Kinematics of Machines : –

Introduction of Mechanisms and Machines:
Concepts of Kinematics and Dynamics, Mechanisms and Machines, Planar and Spatial Mechanisms, Kinematic Pairs, Kinematic Chains, Kinematic Diagrams, Kinematic Inversion, Four bar chain and Slider Crank Mechanisms and their Inversions, Degrees of Freedom, Mobility and range of movement – Kutzbach and Grubler’s criterion, Number Synthesis, Grashof’s criterion

Synthesis and Analysis of Mechanisms:
Position analysis (Analytical Techniques): Loop closure (Vector Loop) representation of linkages, Position analysis of Four bar, slider crank and inverted slider crank mechanisms, Coupler curves, Toggle and Limit Position, Transmission angle, Mechanical Advantage.
Dimensional Synthesis: Definitions of Type, Number and Dimensional Synthesis, Definitions ofMotion, Path and Function generation, precision position, Chebychev spacing, structural error, Freudenstein’s equation, two and three position synthesis (function generation only) of four bar and slider crank mechanisms by graphical and analytical methods.
Velocity and Acceleration Analysis: Velocity and Acceleration Diagrams, Instantaneous Centre of Velocity, Rubbing Velocity, Velocity and Acceleration Images, Corioli’s component of acceleration.
Special Mechanisms: Straight line mechanism, Indicator diagrams, Hooke’s Joint, Steering Mechanisms.

Gears and Gear Trains:
Gears:Terminology, Law of Gearing, Characteristics of involute and cycloidal action, Interference and undercutting, centre distance variation, minimum number of teeth, contact ratio, spur, helical, spiral bevel and worm gears, problems. Gear Trains: Synthesis of Simple, compound & reverted gear trains, Analysis of epicyclic gear trains.

Cams and Followers:
Introduction: Classification of cams and followers, nomenclature, displacement diagrams of follower motion, kinematic coefficients of follower motion.
Synthesis and Analysis: Determine of basic dimensions and synthesis of cam profiles using graphical methods, cams with specified contours.

Books for Kinematics of Machines : –

Theory of Machines by RS Khurmi

Kinematics and Dynamics of Machinery Norton R L, McGraw-Hill

Theory of Machines, Singh Sadhu, Pearson Education

Theory of Machines, Rattan S S, Tata McGraw-Hill +ebook +Textbook


Objective Questions : –

Theory of Machines MCQ with Answers