GENERAL SIR JOHN KOTELAWALA DEFENCE UNIVERSITY
DEPARTMENT OF MECHANICAL ENGINEERING
MECHANICS AND CONTROL LABORATORY
STUDY THE MOTION IN FOUR
BAR LINKAGES
INSTRUCTOR Miss E.A.D.N. WIJESINGHE
NAME
A.M.E.R.B. ADASOORIYA
INDEX NO
D/ENG/23/0194/AE
INTAKE
40
STREAM
AERONAUTICAL
ENGINEERING
GROUP NO
AE 06
GROUP
MEMBERS
K.K.H. FERNANDO
P.A.S.D. PALIHAWADANA
K.V.L.P. KODAGODA
K.M.D.K.R. KULATHUNGA
T.D.L. WIJESINGHE
DATE OF
25/03/2024
PERFORMANCE
DATE OF
08/04/2024
SUBMISSION
PRE LAB QUESTIONS
1. Define terms such as linkage, crank and rocker.
 Linkage: A linkage is a mechanical system or assembly of links (also known
as bars or rods) connected by joints (also known as hinges or pivot points) to
manage forces and movement. Linkages are used to transmit motion and force,
often transforming input motion into a different type of output motion.

Crank: A crank is an arm that rotates around a shaft, usually used for changing
circular motion into straight-line reciprocating motion. The crank consists
primarily of a lever attached at one end to the rotating shaft, while the other
end is either supported on a pivot or sliding connection point.

Rocker: Rocker is such a level which rocks back and forth around one fixed
point(fulcrum). It’s utilized in various mechanical systems for converting or
controlling movements. They may be simple like see-saws as well as
complicated having many attachment points for linkages.
2. How do you have a circle, line, straight line or figure 8 motion?
 For circular motion, a crank is one of the ways of achieving it. A rotating shaft
and a crank form a pair; while the shaft turns, the crank makes the rotary
motion to linear motion change. If you connect any rod to one end of your
crank and pivot its other end, that linear motion will be changed into circular.

Straight-line Motion: Linear movement along a straight trajectory is the easiest
kind of movement. In such a case, it is possible to use the piston in a cylinder
in order for there to be movement which follows an exact path.

To achieve straight-line motion that isn’t pure back-and-forth, devices such as
Watt’s linkage or Peaucellier-Lipkin linkage can be used. Consequently, these
mechanisms transform rotational movements into precise linear motions.

A figure-eight motion on the other hand is more complex and often require
specialized mechanisms. For example, using additional linkages with a Crank
and Slider mechanism would guide this type of motion in a figure-eight
pattern.
AIM
To investigate how the four bar linkages covert motion
APPARATUS
THEORY
Mechanical production of machines is set upon kinematic mechanisms. Therefore,
understanding the kinematics of machines in modern engineering is very important. Besides,
classical concepts-based view on kinematics conceals numerous actual mechanisms features
such as links’ distortions, pin clearance and manufacturing inaccuracies. If these are not taken
into account during designing, linkages will not be able to make accurate
function/path/motion for generation by it. In some cases designers choose composites
materials to make a four-bar mechanism lighter for common driving mechanism. So if we
consider what a four bar linkage is, A four-bar linkage is a mechanical linkage that consists of
four rigid bars connected by joints or pivots; it forms a closed loop, so as to demonstrate
motion and offers mechanical advantage. Four-bar linkages are used in different applications,
such as machinery, robotics, and automotive systems for controlled, predictable movements
including rotation, translation and oscillation.
Now lets consider the below figure.
The above figure shows some of the simplest linkages which are made from four links. The
fixed surface forms one link. Mathematical relationships between the lengths of the links give
different conversions of motion.
Crank Rocker
Double Rocker
Drag Link
Parallelogram
- Converts a fully circular (Continuous) motion of link D into a
reciprocating arc or rocking motion of link B
- Converts one radius rocking motion into another radius rocking
motion.
- Converts one fully circular (Continuos) motion of link D into another
fully circular motion of link B with a different radius.
- Dupicates a fully circular (Continuous) motion of link D with link B,
straight line.
Grashof’s Law for Four Bar Linkages
For a planar linkage, the sum of the shortest and longest links cannot be greater than the sum
of the remaining links if there is to be continuous relative rotation between the two members.
From this,




Crank Rocker, for continuous motion D + A not greater than B + C
Double Rocker – Non continuous motion
Drug Link, for continuous motion, B + C not greater than D + A
Parallelogram, for continuous motion, A + D not greater than C + B
PROCEDURE
1. The linkages were assembled as shown in the above figure 02, along with the
wipeable magnetic sheets behind the linkages.
2. A pen was fitted into the pen holder and the two movements for each linkage were
traced.
3. Lengths of each sides A,B,C, and D of each linkage were measures and compared for
their relative sizes.
DISCUSSION
A𝑐𝑡𝑢𝑎𝑙 𝑙𝑒𝑛𝑔𝑡ℎ𝑠
A = 220 mm
B = 240 mm
C = 200 mm
D = 80 mm
Aℎ𝑜𝑟𝑡𝑒𝑠𝑡 𝐿𝑒𝑛𝑔𝑡ℎ+𝐿𝑜𝑛𝑔𝑒𝑠𝑡 𝐿𝑒𝑛𝑔𝑡ℎ=240 𝑚𝑚+80 𝑚𝑚=320 𝑚𝑚
S𝑢𝑚 𝑜𝑓 𝑜𝑡ℎ𝑒𝑟 𝑡𝑤𝑜 𝑙𝑒𝑛𝑔𝑡ℎ𝑠=220 𝑚𝑚+200𝑚𝑚=420 𝑚𝑚
320 𝑚𝑚<420𝑚𝑚
Sℎ𝑜𝑟𝑡𝑒𝑠𝑡 𝐿𝑒𝑛𝑔𝑡ℎ+𝐿𝑜𝑛𝑔𝑒𝑠𝑡 𝐿𝑒𝑛𝑔𝑡ℎ < 𝑆𝑢𝑚 𝑜𝑓 𝑜𝑡ℎ𝑒𝑟 𝑡𝑤𝑜 𝑙𝑒𝑛𝑔𝑡ℎ𝑠
Linkage Satisfies Grashof’s Law, so there is a continuous relative rotation.
80 mm bar in circular motion and 240 mm bar in a back-and-forth oscillating motion
Therefore, this is a crank rocker.
A𝑐𝑡𝑢𝑎𝑙 𝑙𝑒𝑛𝑔𝑡ℎ𝑠
A = 80 mm
B = 240 mm
C = 160 mm
D = 160 mm
Sℎ𝑜𝑟𝑡𝑒𝑠𝑡 𝐿𝑒𝑛𝑔𝑡ℎ+𝐿𝑜𝑛𝑔𝑒𝑠𝑡 𝐿𝑒𝑛𝑔𝑡ℎ=240 𝑚𝑚+80 𝑚𝑚=320 𝑚𝑚
S𝑢𝑚 𝑜𝑓 𝑜𝑡ℎ𝑒𝑟 𝑡𝑤𝑜 𝑙𝑒𝑛𝑔𝑡ℎ𝑠=160 𝑚𝑚+160 𝑚𝑚=320 𝑚𝑚
320 𝑚𝑚=320𝑚𝑚
Sℎ𝑜𝑟𝑡e𝑠𝑡 𝐿𝑒𝑛𝑔𝑡ℎ+𝐿𝑜𝑛𝑔𝑒𝑠𝑡 𝐿𝑒𝑛𝑔𝑡ℎ= 𝑆𝑢𝑚 𝑜𝑓 𝑜𝑡ℎ𝑒𝑟 𝑡𝑤𝑜 𝑙𝑒𝑛𝑔𝑡ℎ𝑠
Linkage Satisfies Grashof’s Law, so there isn’t a continuous relative rotation.
160 mm bar and 240 mm bar in a back-and-forth oscillating motion
Therefore, this is a double rocker.
A𝑐𝑡𝑢𝑎𝑙 𝑙𝑒𝑛𝑔𝑡ℎ𝑠
A = 140 mm
B = 160 mm
C = 100 mm
D = 140 mm
Sℎ𝑜𝑟𝑡𝑒𝑠𝑡 𝐿𝑒𝑛𝑔𝑡ℎ+𝐿𝑜𝑛𝑔𝑒𝑠𝑡 𝐿𝑒𝑛𝑔𝑡ℎ=100 𝑚𝑚+160 𝑚𝑚=260 𝑚𝑚
S𝑢𝑚 𝑜𝑓 𝑜𝑡ℎ𝑒𝑟 𝑡𝑤𝑜 𝑙𝑒𝑛𝑔𝑡ℎ𝑠=140 𝑚𝑚+140 𝑚𝑚=280 𝑚𝑚
260 𝑚𝑚<280 𝑚𝑚
Sℎ𝑜𝑟𝑡𝑒𝑠𝑡 𝐿𝑒𝑛𝑔𝑡ℎ+𝐿𝑜𝑛𝑔𝑒𝑠𝑡 𝐿𝑒𝑛𝑔𝑡ℎ < 𝑆𝑢𝑚 𝑜𝑓 𝑜𝑡ℎ𝑒𝑟 𝑡𝑤𝑜 𝑙𝑒𝑛𝑔𝑡ℎ𝑠
Linkage Satisfies Grashof’s Law, so there is a continuous relative rotation.
140 mm bar and 160 mm bar in a circular motion
Therefore, this is double crank mechanism.
A𝑐𝑡𝑢𝑎𝑙 𝑙𝑒𝑛𝑔𝑡ℎ𝑠
A = 200 mm
B = 200 mm
C = 200 mm
D = 200 mm
Sℎ𝑜𝑟𝑡𝑒𝑠𝑡 𝐿𝑒𝑛𝑔𝑡ℎ+𝐿𝑜𝑛𝑔𝑒𝑠𝑡 𝐿𝑒𝑛𝑔𝑡ℎ=200 𝑚𝑚+200 𝑚𝑚=400 𝑚𝑚
S𝑢𝑚 𝑜𝑓 𝑜𝑡ℎ𝑒𝑟 𝑡𝑤𝑜 𝑙𝑒𝑛𝑔𝑡ℎ𝑠=200 𝑚𝑚+200𝑚𝑚=400 𝑚𝑚
400 𝑚𝑚=400𝑚𝑚
Sℎ𝑜𝑟𝑡𝑒𝑠𝑡 𝐿𝑒𝑛𝑔𝑡ℎ+𝐿𝑜𝑛𝑔𝑒𝑠𝑡 𝐿𝑒𝑛𝑔𝑡ℎ= 𝑆𝑢𝑚 𝑜𝑓 𝑜𝑡ℎ𝑒𝑟 𝑡𝑤𝑜 𝑙𝑒𝑛𝑔𝑡ℎ𝑠
Linkage Satisfies Grashof’s Law, so there is a continuous relative rotation.
Both 200mm bars in a circular motion and opposite bars have same lengths.
Therefore, this is a parallelogram mechanism.
Figure 8
One can create a motion of eight with a figure in four-bar linkage only if he or she designs the
bars’ lengths and joint locations well. This sort of movement finds application in different
areas where there is need to follow given path or trajectory. Below is an easy way of
achieving figure eight motion using four bar linkage:



Select the sizes for all four linkages (bars) very carefully so that they could produce
desired movements. These dimensions are responsible for defining the amplitude as
well as shape of ellipses formed by this system.
Consider where connections are made between bars because it greatly affects their
behavior during operation; hence, making appropriate choices regarding joint
positions becomes crucial here too.
Identify which of these two – input or output – will act as driver while other acts
driven; then connect motor/actuator accordingly.
When creating the figure 8 motion,
Start with the four bars in a specific initial position, such as all bars aligned horizontally or
vertically. Apply rotational motion to the input bar. Other bars follow when the input bar
moves, which is guided by the lengths and joint positions such that through careful design, it
makes an output bar traces out a figure 8 pattern at its end. Adjustments should be made on
lengths and joint positions until desired figure eight motion is achieved.
These types of figure eights can be used in different applications such as conveyor belt
systems, robotic arms or mechanical toys where specific path needs to be followed.
REFERENCES
dynref.engr.illinois.edu. (n.d.). Four-Bar Linkages. [online] Available at:
https://dynref.engr.illinois.edu/aml.html.
luisce89 (2023). Four-Bar Mechanism Examples: Understanding its Applications and
Principles. [online] ME Virtuoso. Available at: https://mevirtuoso.com/others/four-barmechanism-examples/.
Testbook. (n.d.). Four Bar Linkage: Explained with Inversions & Solved Examples. [online]
Available at: https://testbook.com/mechanical-engineering/four-bar-linkage-mechanism-andanalysis.
www.cs.cmu.edu. (n.d.). Chapter 5. Planar Linkages. [online] Available at:
https://www.cs.cmu.edu/~rapidproto/mechanisms/chpt5.html.