The document outlines a seminar on inversions of mechanisms and technical writing, focusing on various kinematic chains and their classifications. It details different mechanisms such as four-bar, single slider crank, and double slider crank mechanisms, explaining their components and operational principles. References are provided for further reading on the theory of machines.

1. Inversions of Mechanism
Seminar and Technical writing (CR7998)
Spring (2020-21)
Course Instructor- Prof. Debasish Sarkar
Presented by
JAKKAMPUDI CHANDRIKA
520CR1002
Ph.D. Research Scholar
Department of Ceramic Engineering,
National Institute of Technology, Rourkela,
Odisha

2. Table of contents
 Introduction
 Inversions of four bar mechanism
 Inversions of single slider crank mechanism
 Inversions of double slider crank mechanism
 References

3. Introduction
 Kinematic link: Kinematic link is also called as an element. Kinematic link is a resistant
body which moves relative to other elements.
 Kinematic pair: Two Kinematic links which has contact between them form a Kinematic
pair. The two links are able to transform motion between them.
 Kinematic chain: Kinematic chain is an assembly of Kinematic pairs.

4.  Mechanism: Whenever one link of Kinematic chain fixed, that type of Kinematic chain
is called as mechanism. Mechanism is used to transmit motion.
 Machine: When a mechanism is used to transmit power or to do work, then it becomes
a machine.
 Mobility for Plane Mechanism (n): The number of independent input parameters
required to get the desired output from mechanism.
 Kutzbach’s criterion for n,
n = 3 (l – 1) – 2 j – h
j = Number of binary joints,
h = Number of higher pairs, and
l = Number of links.

5.  If n = zero, then the mechanism turns into a structure. There is absence of relative
motion among the links.
 If n = 1, then the mechanism needs a single input motion.
 If n = 2, then the mechanism needs two separate input motions
 If n≤-1, then the mechanism becomes statically indeterminate structure and redundant
constraints present in the Kinematic chain.
 Inversion of mechanism: The method of fixing different links in a Kinematic chain to
obtain different mechanisms is known as inversion of mechanism.

6. Inversions of four bar mechanism
 Four bar mechanism:

7.  Crank: The link which makes complete revolution relative to other links is called as crank.
It is also called as a driver.
 Lever: The link which undergoes oscillation or partial rotation is called as lever. It is also
called as rocker, follower.
 Coupler: The link which connects crank and rocker is known as coupler. It acts like a
connecting rod.
 Frame: It is a fixed link.
Crank and lever mechanism:

8.  If the link adjacent to the shortest link fixed, then
the shortest link rotates 360 degrees.
 The link opposite to shortest link oscillates and
forms crank-lever mechanism or crank-rocker
mechanism.
 In this case the sum of the shortest link length and
the longest link length is less than the sum of the
other two link’s length.
 Example: beam engine

9. Beam engine

10. Double crank mechanism:
 When the shortest link is fixed, then the links adjacent to the shortest link rotates 360
degrees and forms double crank mechanism.
 In this case, the sum of the lengths of the shortest link and the longest link is less than the
sum of the other 2 link’s length.

11. Parallelogram linkage mechanism:
Connecting rod of a locomotive
 In this case the sum of the shortest link length and the
longest link length is equal to the sum of the other 2
link’s length.
 Fix link 1 to get this mechanism. Link 2 and link 4
rotate 360 degrees.
 Example: Connecting rod of a locomotive

12. Double rocker mechanism:
 When the link opposite to the shortest
link fixed, then the links adjacent to
shortest link oscillates and forms
double-rocker mechanism.
 Example: Watt’s indicator mechanism

13. Inversions of single slider crank mechanism
 single slider crank mechanism:

14.  Pendulum pump or Bull engine:
 In this type of mechanism, the link 4 is fixed and link4
act as a cylinder.
 The link 2 rotates 360° and the link3 oscillates about a
pin located on the fixed link at A.
 The link2 is crank and link 3 is a connecting rod. The
link 1 is piston rod and piston reciprocates which is
attached to the piston rod.
 For duplex pump two pistons are attached to the link 1.

15.  Oscillating cylinder engine:
 It can convert the motion from
reciprocating to rotary.
 The link3 (the connecting rod) is fixed.
The link 2 rotates about a pin at one end of
the connecting rod.
 The link 1 is reciprocates and link 4
oscillates about the pin at other end of the
connecting rod.

16.  Rotary internal combustion engine:
 Currently, gas turbines are used instead
of rotary internal rotary combustion
engines in aviation.
 The Rotary internal combustion engine
has 7 cylinders in one plane.
 Cylinders revolve about a fixed centre.
The crank (link 2) is fixed.
 Link 4 (connecting rod) rotates, link 3
(piston) reciprocates inside the
cylinders (link1).

17.  Crank and slotted lever quick return motion
mechanism:
 The applications are rotary internal combustion
engines, shaping machines and slotting machines.
 The link AC which forms the turning pair was
fixed. Link 2 act as a driving crank.
 The Crank rotates with uniform angular speed
about C. Link 1 (slider) slides in link 4 (slotted
bar AP).
 A short link PR is used to transmit the motion
from AP to the tool which is located in ram.
 The link PR reciprocates through the line of
stroke (R1R2). R1R2 is at 90 degrees to AC.

18.  Whitworth quick return mechanism:
 It can be used in rotary internal combustion engines,
shaping machines and slotting machines.
 The link CD which forms a turning pair was fixed.
 The link 3 act as a driving crank and it rotates with
uniform angular speed about C.
 Link 4 (slider) slides in the link 1 (slotted bar PA).
 Tool is placed in ram and ram is connected to the
connecting rod.
 The movement of the tool is fixed along RD.

19. Inversions of Double slider crank mechanism
 Double slider crank mechanism:

20.  Elliptical trammel:
 Elliptical trammel can be used to draw ellipses.
 To get this inversion the slotted plate (link 4) should be fixed.
 Two straight grooves are made to cut along fixed plate.
 The two grooves are at 90 degrees angle.
 Link 1 and link 3 act as a slider and link 2 is the bar.

21.  While link 1 and link 3 sliding along grooves, then any point on link 2 generates an
ellipse.

22.  Scotch yoke mechanism:
 It can convert motion from rotary to
reciprocating.
 To get this inversion, fix either link1 or link3.
 Here the link1 was fixed. The link2 and link3
becomes crank and slider respectively.
 The fixed link guides the frame. While crank
rotates about B, then link 4 reciprocates.

23.  Oldham’s coupling:
 It can be used to couple the two shafts. The shafts has minor distance between them.
 To get this inversion, link 2 should be fixed.
 Flange C and Flange D connected at the ends of two shafts with the help of forging
method.
 Diametrical slots are present in each flange.
 Link 4 has diametrical projections (T1, T2) and these projections completely insert
through the slots of two flanges.

24.  The rotary motion transmits from flange C (link 1, located on the driving shaft) to flange
D (link 3, located on the driven shaft) through an intermediate piece (link 4).

25. References
 THEORY OF MACHINES BY R.S. KHURMI, J.K. GUPTA
 https://en.wikipedia.org/wiki/Four-bar_linkage