SCHOOL OF MECHANICAL ENGINEERING
DR. YANGA’S COLLEGES INC.
Four-Bar Linkage
Machine Elements 1 & Machine Elements 1 Dftg.
(DYSMEMe1312 & DYSMEMe1311)
Past Board Exam Question
A planar mechanism has 8 links and 10 rotary joints. Using
Grubler’s criterion, calculate the number of degrees of freedom of
the mechanism.
Past Board Exam Question
The number of degrees of freedom of a planar linkage with 8
links and 9 simple revolute joint is:
Four-Bar Linkage
A four bar linkage comprises four bar-shaped links and four
turning pairs forming a simple mechanism.
Four-Bar Mechanism
The simplest and most common linkage is the four-bar
linkage. It is combination of four links, one being designated as
the frame and connected by four pin joints.
Four-Bar Linkage
Crank – it is a side link which revolves(rotate) relative to the
frame. A pivoted link connected to the frame.
Coupler or Connecting rod – it is the link opposite to the fixed
link, a link joining cranks, levers or a combination of a crank and
a lever.
Lever or Rocker – it is the link which oscillates (does not rotate).
Frame – the fixed link of a mechanism
Four-Bar Linkage
Grashof’s Rule
-It states that “for a 4-bar chain, the sum of the lengths of
longest and shortest links should not be more than the sum of
length of the other two links, to have continuous relative motion”.
s+l≤p+q
Case
Critera
Shortest
link
Category
1
s+l<p+q
Frame
Double crank
2
s+l<p+q
Side
Crank-rocker
3
s+l<p+q
Coupler
Double rocker
4
s+l=p+q
Any
Change point
5
s+l>p+q
Any
Triple rocker
Four-Bar Linkage
PROBLEM 1
In a crank-rocker (four-bar linkage), S denotes the shortest
link length, L the longest link length, P and Q are the lengths of
other two links. If there is to be continuous relative motion
between the links, then_______.
A. (S+L)<(P+Q)
C. (S+P)<(L+Q)
B. (S+L)>(P+Q)
D. (S+P)>(L+Q)
PROBLEM 2
In a crank-rocker (four-bar linkage), S denotes the shortest
link length, L the longest link length, P and Q are the lengths of
other two links. If there is to be continuous relative motion
between the links, then_______.
A. (S+L)<(P+Q)
C. (S+P)<(L+Q)
B. (S+L)>(P+Q)
D. (S+P)>(L+Q)
PROBLEM 3
The lengths of links of a 4-bar linkage with revolute pairs only
p, q, r and s units. Given that p<q<r<s. Which of these links
should be the fixed one, for obtaining a “double crank”
mechanism?
A. Link of length p
C. Link of length r
B. Link of length q
D. Link of length s
PROBLEM 4
The lengths of links of a 4-bar linkage with revolute pairs only
p, q, r and s units. Given that p<q<r<s. Which of these links
should be the fixed one, for obtaining a “double crank”
mechanism?
A. Link of length p
C. Link of length r
B. Link of length q
D. Link of length s
PROBLEM 5
Identify the nature of mechanism.
(ANS. Double Crank)
PROBLEM 6
Identify the nature of mechanism.
(ANS. Crank-Rocker)
PROBLEM 7
In the slider crank mechanism shown, determine the length
of the connecting rod BC if the maximum value of the angle θ is
35degrees and if the stroke of C is 8 inches.
(ANS. 6.98in)
PLATE 1
In a crank-rocker four-bar mechanism, AB= 3 in, BC =6 in,
CD = 4 in, and AD = 6 in. Find the two extreme positions (θmin
and θmax) of link 4.
END