Introduction to Kinematics of Machines in Mechanical Engineering

This article/resource deals with the introduction of the kinematics of machines which is base on any real-life mechanism and for a successful mechanism to run, it has to follow Grashoff's law, Kennedy's theorem, etc. Here an attempt is made to highlight all probable basic concepts to start a study of the science of kinematics of machine. This article gives a basic overview of kinematic links, kinematic chains, mechanism and its inversion for getting real-life applications from it.

Introduction to Kinematics

Kinematics is the branch of science which deals with motion without considering the forces which cause the motion. On the other hand, kinetics is the branch of science which also takes forces that causes motion as well as weight and inertia effects in the study.

Kinematic Link and Kinematic Pair

  • Link: It is defined as a machine element having relative motion with respect to other parts of the machine element.

  • Kinematic pair is defined as a joint of two links that permit relative motion between elements or links. Kinematic pair is constituted when there is mechanical contact between them and having an arrangement of mechanism.

  • Lower pair is said to be constituted when two elements have surface contact between them.

  • Higher pair is said to be constituted when two-element has a point of contact between them.

  • Kinematic Chain

    Kinematic chain is one in which number of links are so connected that relative motion of any point on a link with respect to any other point on the other link follows a governing law
  • L = 2/3(J+2) Where, L = Number of links, J = Number of Joints

  • or
  • J = 3/2(L)-2, Where, H = Number of Higher pairs

  • One Higher pair = Two lower pair

  • The criterion for a chain to be constrained:

    J+H/2 = 3/2(L)-2,

    Where, H = Number of Higher pairs and J =Number of binary joints in the chain
    If R.H.S. = L.H.S. , Chain is said to be locked.


    • If the one of the link of constrained kinematic chain is fixed, it results into 'Mechanism'

    • A mechanism with four links is called simple mechanism. Mechanism with single degree of freedom are having only even number of links.

    • Real life example is automobile propelling system which contains links in form of piston, connecting rod and cranks shaft to which flywheel and rear tire is attached.

    • Four bar mechanism and single slider mechanism
    • Mechanism should follow Grashoff's law
      Grashoff's Law "The sum of lengths of shortest and longest link should not be greater than the sum of the remaining link lengths if there is to be continuous relative motion between the links"
    • Example, Linkage mechanism of excavator and its system.

    Excavator_Real life example of linkage and mechanism

    Inversion of kinematic chain

    • The different mechanism obtained by fixing one of the links of kinematic chain is called inversion of kinematic chain.

    • Four bar mechanism and single slider mechanism if inverted; they give following inversion for different application in real world.

    Inversion of Four Bar Chain

    • Beam Engine (Crank & lever mechanism)

    • Connecting rod of locomotive (Double crank mechanism)

    • Watt's Indicator mechanism (Double lever mechanism)

    Inversion of single slider crank chain

    • Pendulum pump (Bull engine)

    • Oscillating cylinder engine

    • Rotary IC Engines (Gnome engine)

    • Crank and solotted lever quick return motion mechanism

    • Whitworth's Quick return motion mechanism

    Double Slider Crank Chain

    • Elliptical trammels

    • Scotch yoke mechanism

    • Oldham's coupling

    Other basic concepts in Kinematics

    • The centre which goes on changing from one instance to another is called instantaneous centre.
    In order to find the location and number of location of instantaneous center of rotation of body, body/mechanism must follow this law/theorem,
    Kennedy's Theorem : If three bodies have plane motions, their instantaneous center lie on a straight line.
    And Number of instantaneous centre = n(n-1)/2; where n=number of links

    Real life applications of Kinematics of Machines

    1. Piston and Cylinder assembly of an automobile
    2. Fuel system combined with the accelerator in automobile
    3. Pantograph
    4. Heavy earthmoving machinery
    5. Railway engine and its supporting flywheel motions
    6. Steering of an automobile
    7. Scissor
    8. Jack


    More articles: Resource Queries Kinematics


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