MEG 373
CHAPTER – 1
INTRODUCTION
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A mechanism is a mechanical device that has
the purpose of transferring motion and/or force
from a source to an output.
A linkage consists of links (or bars) generally
considered rigid, which are connected by joints.
Kinematic chains, with at least one link fixed,
become mechanisms if at least two other links
retain mobility, or structures if no mobility
remains, in other words, a mechanism permits
relative motion between its “rigid” links; a
structure does.
A large majority of mechanisms exhibit motion of
all it’s links in parallel planes which is called two
dimensional or planer motion.
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THE FOUR-BAR LINKAGE
The simplest closed- loop
linkage is the four-bar,
which has three moving
links (plus one fixed link)
and
four
“revolute,”
“pivoted,” or “pin” joints.
The link that is connected to the power source or prime
mover is called the input link (A0A). The follower link
connects the moving pivot B to ground pivot B0. The
coupler or floating link connects the two moving
pivots, A and B, thereby “coupling” the input link to the
output link.
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The four –bar linkage can be classified into three
categories depending on the task that the
linkage performs:
1- Function generator : is a linkage in which the
relative motion (or forces) between links
connected to ground is of interest.
2-Path generation : we are concerned only with
the path of a tracer point and not with the
rotation of the coupler link.
3-Motion generation : the entire motion of the
coupler link is of concern.
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JOINTS
Joints are the most important aspect of a mechanism to
examine during an analysis. They permit relative motion
in some directions while constraining motion in others.
The types of motion permitted are related to the number
of degrees of freedom (dof) of the joint. The number of
degrees of freedom of the joint is equal to the number of
independent coordinates needed to specify uniquely the
position of one link relative to the other constrained by
the joint.
Theoretically , two element of LOWER PAIR are in
surface contact with one another, while the HIGHER
PAIR are in point or line contact.
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9/22/2019
The degree Of Freedom Of
Mechanisms
Is the number of independent
input required to determine
the position of all links of the
mechanism with respect to
ground.
How many independent variables will completely
specify the position of this link?
Two translations and one rotation, xA, yA and θ , ( three
independent coordinates) associated with the position
of a link in the plane. In other words, an unconstrained
rigid link in the plane has three degrees of freedom.
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An assembly of n links, possess a total of 3n degrees
of freedom before they are joined to form a linkage
system. Connections between links result in the loss
of degrees of freedom of the total system of links.
Each pin connection will remove two degrees of
freedom of relative motion between successive links.
For an n-link chain connected by pin joints, with
ground (the fixed link) considered as one of the links:
Gruebler’s
equation
Number of
Mobile links
f1 is the number
of joints
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For Four – link mechanism
with 4 pin joints:
i.e. a single degree of freedom
Six – Bar Chain
One degree of freedom
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Mobility analysis of a linkage when more than two
members come together at a single point location.
There are 2 pin joints
f1 = m-1 = 3-1 = 2
n=6
f1 = 5 + (3-1) = 7
F = 3(6 – 1) – 2(7) = 1
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Example:
Determine the mobility of the linkage shown The linkage
is planar and not all of the joints have connectivity one.
n = 11
f1 = 6+ (4-1) + (3-1)+(3-1) = 13
f2 = 1
F = 3(11– 1) – 2(13) - 1(1) = 3
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Example:
Determine the degrees of freedom of the mechanism shown
n=7
f1 = 7
f2 = 1
F = 3(7-1) – 2(7) – 1(1) = 3
The spring is not
counted
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Kinematics Inversion
It is the process of fixing different links of a chain to
create different mechanisms. The relative motions of
the links do not change in different inversions.
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Hand pump
Slider -crank
Gnome air craft engine
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Marine engines
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CLASSIFICATION OF CLOSED PLANAR FOUR-BAR
LINKAGES:
In four- bar linkages, if one of the links can perform a full
rotation relative to the other three links, the linkage is
called a GRASHOF MECHANISM.
Grashof’s Law:
l+s<p+q
shortest link s, longest
link l, intermediate
length links p and q.
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Creating momentarily a second
degree of freedom when
centerline of all links become
collinear. Relative motion may
depend on inertia, spring force,
or other forces at that point.
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1986 Ford Mustang rear seat
linkage moves through the dead
center position in the seat down,
to open the seat, push the cover
down through the dead center
into stable latched position.
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Assignment
Write a computer
program to classify
four bar mechanism
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TRANSMISSION ANGLE
Is the angle between the
coupler centerline and the
driven crank centerline.
To maximize output torque and minimize friction torque, we
try to keep transmission angle Φ near 90°. A transmission
angle no less than 45° and no greater than 135° is usually
satisfactory. Values outside this range may result in binding
of the linkage.
As link 1 tends to rotate through the position shown, the
direction of force transmitted along link 2 to link 3, results in
very little torque on link 3 but a high bearing force at 03.
Wear would probably be excessive.
If friction torque exceeded driving torque, the mechanism
would jam and could cause the driven crank to buckle.
Dimensional tolerances, including looseness at pins and
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Dr. Nabil
A.Rahimthe
- MENG
373
9/22/2019
bearings,
often tend to
worsen
situation.
…… (1)
…… (2)
Rearranging Eq. 2
We are most interested in extreme values of transmission
angle Φ. For the crank rocker mechanism, maximum and
minimum transmission angles occur when the driver crank
and fixed link are collinear. Transmission angle Φ max
corresponds to Ld(max) = L1 + L0, and Φ min corresponds to
Ld(min) = L0 — L1.
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