Chapter 2 Content

1. The Four-bar Mechanisms

2. Slider Crank Mechanisms
3. Scotch Yoke Mechanism
4. Intermittent Motion Mechanisms
• The Geneva Mechanism
• Linear Geneva Mechanism
• Ratchet and Paul Mechanism

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 Example for Mechanism
Bike

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 Example for Mechanism
Cam – Follower

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 Common Mechanisms
The four-bar Mechanism
– The simplest and most common linkage.
– It is a combination of four links, one being
designated as the frame and connected by four
pin joints.

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Automotive rear-window wiper system
• a four-bar mechanism b/s it is comprised of four
links connected by four pin joints and one link is
unable to move (frame).

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 Mobility of a four-bar mechanism
n = 4, jp = 4 pins, jh = 0
M = 3(n - 1) - 2jp - jh = 3(4 - 1) - 2(4) - 0 = 1
• B/s the four-bar mechanism has one DOF, it is
constrained or fully operated with one driver.
• The wiper system is activated by a single DC electric
motor.
• The pivoted link that is connected to the driver or power
source is called the input link.
• The other pivoted link that is attached to the frame is
designated the output link or follower.
• The coupler or connecting arm “couples” the motion of
the input link to the output link. 6
 Grashof ’s Criterion
• The Grashof condition is a very simple relationship which
predicts the rotation behavior or rotatability of a four-bar
linkage's inversions based only on the link lengths.
– s = length of the shortest link
– l = length of the longest link
– p = length of one of the intermediate length links
– q = length of the other intermediate length links
Grashof’s theorem states that “the sum of the shortest (s) and
longest (l) links of a planar four-bar linkage cannot be greater
than the sum of the remaining two links (p, q) if there is to be
continuous relative motion between two links and at least one
rotating link relative to the frame”. s + l <= p + q
Conversely, the three non-fixed links will merely rock if:
s+l>p+q
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 The inversions of four-bar mechanism
Crank-Rocker (two non-distinct inversions)

• It has the shortest link (crank) configured adjacent to the frame.

(ground either link adjacent to the shortest link)
• If this shortest link is continuously rotated, the output link
(rocker ) will oscillate between limits.
• The wiper system in slide 3 is designed to be a crank-rocker.
– As the motor continuously rotates the input link, the output link
oscillates, or “rocks.” The wiper arm and blade are firmly attached to
the output link, oscillating the wiper across a windshield. 8
The inversions of four-bar mechanism
Crank-Rocker Mechanism

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 The inversions of four-bar mechanism
Double Crank

• A double crank, or crank-crank (drag link) has the shortest link

configured as the frame.
• If one of the pivoted links is rotated continuously, the other
pivoted link will also rotate continuously as does the coupler.
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 The inversions of four-bar mechanism
Double Rocker

• The double rocker, or rocker-rocker has the link opposite the

shortest link configured as the frame.
• In this configuration, neither link connected to the frame will
be able to complete a full revolution.
• Both input and output links are constrained to oscillate
between limits, and are called rockers. However, the coupler is
able to complete a full revolution. 11
 Change Point Mechanism
• If l + s = p + q, the same four mechanisms exist, but, change-
point condition occurs where the centerlines of all links become
collinear and the mechanism can toggle.
• All inversions will be either double-cranks or crank-rockers but
will have "change points“ twice per revolution of the input crank
when the links all become collinear. At these change points the
output behavior will become indeterminate (unpredictable) as it
may assume either of two configurations. Its motion must be
limited to avoid reaching the change points or an additional, out-
of-phase link provided to guarantee a "carry through" of the
change points.

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 Triple Rocker Linkage
If l + s > p + q, four non-distinct inversions of a non-Grashof
linkage mechanisms exist, depending on which is the ground
link, but continuous rotation is not possible.

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 Example 1: Aircraft Landing Gear
A nose assembly for a small aircraft is shown below. Classify the
motion of this four-bar mechanism based on the configuration
of the links.

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 Example 1: Solution
1. Distinguish the Links Based on Length
• The motion of the wheel assembly would be determined relative
to the body of the aircraft. Therefore, the aircraft body will be
designated as the frame.
• Kinematic diagram for the wheel assembly, numbering and
labeling the links. The tip of the wheel was designated as point
of interest X.

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 Example 1: Solution
• The lengths of the links are:
s = 12 in.; l = 32 in.; p = 30 in.; q = 26 in.
2. Compare to Criteria
• The shortest link is adjacent to the frame. According to
the criteria, this mechanism can be either a crank-
rocker, change point, or a triple rocker.
• The criteria for the different categories of four-bar
mechanisms should be reviewed.
3. Check the Crank-Rocker (Case 2) Criteria
• Is s + l < p + q? (12 + 32) < (30 + 26); 44 < 56 : {yes}
• Because the criteria for a crank-rocker are valid, the
nose-wheel assembly is a crank-rocker mechanism.16
 Slider Crank Mechanism
Another mechanism that is commonly encountered is a slider-crank;
consists of a combination of four links, with one being
designated as the frame. This mechanism, however, is connected
by three pin joints and one sliding joint.
• A mechanism that drives a manual water pump and the
corresponding kinematic diagram is given.

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 Slider Crank Mechanism
• A mechanism found in IC (Internal Combustion) Engines.
• Cylinder and Piston – rod arrangement.

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 Slider Crank Mechanism
The mobility of a slider-crank mechanism is given as:
n = 4, jp = (3 pins + 1 sliding) = 4, jh = 0
M = 3(n - 1) - 2jp - jh = 3(4 - 1) - 2(4) - 0 = 1.
B/s the slider-crank mechanism has one DOF, it is constrained or
fully operated with one driver.
The pump is activated manually by pushing on the handle (link 3).

The pivoted link connected to the frame is called the crank. This
link is not always capable of completing a full revolution.
The link that translates is called the slider. This link is the
piston/rod of the pump.
The coupler or connecting rod “couples” the motion of the crank
to the slider.
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 Inversions of Slider-crank Linkage
Inversion #1, with link 1 as ground and its slider block in pure
translation, is the most commonly seen and is used for piston
engines and piston pumps. Slider block translates.

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 Inversions of Slider-crank Linkage
Inversion #2 is obtained by grounding link 2 and gives the
Whitworth or Crank-shaper quick-return mechanism, in which
the slider block has complex motion.

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 Inversions of Slider-crank Linkage
Inversion #3 is obtained by grounding link 3 and gives the slider
block pure rotation. Slider block rotates.

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 Inversions of Slider-crank Linkage
Inversion #4 is obtained by grounding the slider link 4 and is used
in hand operated well pump mechanisms, in which the handle is
link 2 (extended) and link 1 passes down the well pipe to mount
a piston on its bottom. The slider block is stationary.

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 Straight – Line Mechanism
Straight-line mechanisms cause a point to travel in a
straight line without being guided by a flat surface.
Watt linkage and Peaucellier-Lipkin linkage

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 Parallelogram Mechanisms
Mechanisms are often comprised of links that form parallelograms
to move an object without altering its pitch. These mechanisms
create parallel motion for applications such as balance scales,
glider swings, and jalousie windows.
Scissor linkage and Drafting machine linkage

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 Quick – Return Mechanisms
Quick-return mechanisms exhibit a faster stroke in one direction
than the other when driven at constant speed.
They are commonly used on machine tools that require a slow
cutting stroke and a fast return stroke.
The KDs of two different quick-return mechanisms: Offset slider-
crank linkage and Crank-shaper linkage.

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 Quick – Return Mechanisms
Quick-return Motion Mechanisms

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 Quick – Return Mechanisms
Quick-return Motion Mechanisms

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 Quick – Return Mechanisms
Application of Quick-return Mechanisms

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 Scotch Yoke Mechanism
A common mechanism that converts rotational motion to linear
sliding motion, or vice versa. A a pin on a rotating link is
engaged in the slot of a sliding yoke. With regards to the input
and output motion, the scotch yoke is similar to a slider-crank,
but the linear sliding motion is pure sinusoidal.
In comparison to the slider-crank, the scotch yoke has the advantage
of smaller size and fewer moving parts, but can experience rapid
wear in the slot.

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 Intermittent Motion Mechanisms
Intermittent motion is a sequence of motions and dwells.
A dwell is a period in which the output link remains
stationary while the input link continues to move.
There are many applications in machinery which require
intermittent motion. Two applications are:

1. Geneva Mechanism
2. Ratchet and Pawl Mechanism

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 Geneva Mechanism
This is a transformed four-bar linkage in which the coupler has been
replaced by a half joint.
The input crank (link 2) is typically motor driven at a constant
speed. The Geneva wheel is fitted with at least three equispaced,
radial slots.
The crank has a pin that enters a radial slot and causes the Geneva
wheel to turn through a portion of a revolution. When the pin
leaves that slot, the Geneva wheel remains stationary until the pin
enters the next slot. The result is intermittent rotation of the
Geneva wheel.
The crank is also fitted with an arc segment, which engages a
matching cutout on the periphery of the Geneva wheel when the
pin is out of the slot. This keeps the Geneva wheel stationary and
in the proper location for the next entry of the pin.
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 Geneva Mechanism
The number of slots determines the number of "stops" of the mechanism,
where stop is synonymous with dwell. A Geneva wheel needs a
minimum of three stops to work. The maximum number of stops is
limited only by the size of the wheel.

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 Linear Geneva Mechanism
This is also a variation of the Geneva mechanism which has linear
translational output.
The mechanism is analogous to an open Scotch yoke device with
multiple yokes. It can be used as an intermittent conveyor drive
with the slots arranged along the conveyor chain or belt.
It can be used with a reversing motor to get linear, reversing
oscillation of a single slotted, put slider.

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 Ratchet and Pawl Mechanism
An arm pivots about the center of the toothed ratchet wheel and is moved back
and forth to index the wheel.
The driving pawl rotates the ratchet wheel (or ratchet) in the counterclockwise
direction and does no work on the return (clockwise) trip.
The locking pawl prevents the ratchet from reversing direction while the driving
pawl returns. Both pawls are usually spring-loaded against the ratchet. This
mechanism is widely used in devices such as "ratchet" wrenches, winches, etc.

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 Ratchet and Pawl Mechanism
Ratchet – and – Paul Mechanism

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 Ratchet and Pawl Mechanism
Application of Ratchet – and – Paul Mechanism

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