Kafrelsheikh University
Faculty of Engineering
Theory of machines
Lecture No. 3
Four-bar mechanism
Dr. Taher Atia
Grashof ’s Criterion
• Grashof’s theorem states that a four-bar mechanism has at least one
revolving link if
s+l≤p+q
Conversely, the three nonfixed links will merely rock if
s+l>p+q
Where:
s = length of the shortest link
q = length of the other intermediate length links
p = length of one of the intermediate length links
l = length of the longest link
Categories of four-bar mechanisms.
A- Double Crank
The shortest link configured as
the frame
B- Crank rocker
The shortest link configured
adjacent to the frame
Crank rocker application
Rear window Wiper mechanism
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C- Change Point
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s+l=p+q
a parallelogram linkage
D- Double rocker
The link opposite the shortest link
configured as the frame
E- Triple Rocker
• s+l>p+q
• The triple rocker has no links that are
able to complete a full revolution.
• All three moving links rock.
Double rocker V.s Triple Rocker Mechanism
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All four-bar mechanisms fall into one of the five
categories listed in Table 1.2
Example: Classify the motion of this four-bar mechanism (Nosewheel
assembly) based on the configuration of the links.
Kinematic diagram
s = 12 in.; l = 32 in.; p = 30 in.; q = 26 in.
s+l < p+q
(12+32) < (30+26)
44 < 56
(yes)
The shortest link is a side, or adjacent to the frame.
Nosewheel assembly is a Crank-Rocker (Case 2)
Example:
• Determine the number of fully rotating cranks in the planar
mechanisms shown below. Show your calculations
Solution of (a)
l = 3.0 in
s = 2.25 in
p = 3.0 in
q = 2.5 in
s+l <p+q
3+ 2.25 < 3 + 2.5
Grashof type 1
5.25 < 5.5
❑ Choosing l as the frame results in a double rocker with two fully rotating cranks.
❑ Choosing l, p or q as the frame results in a crank rocker of double rocker with one or
zero rotating cranks, respectively
SLIDER-CRANK MECHANISM
• Also consists of a combination of four links
manual water pump
Find mobility??
kinematic diagram
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SPECIAL PURPOSE MECHANISMS
Straight-Line Mechanisms
• Permits a point to travel in a straight line or nearly
straight-line motion without being guided by a flat
surface
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A- Watt linkage
•
Quality prismatic joints that permit straight, smooth motion
without backlash have been difficult to manufacture
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B- Peaucellier-Lipkin linkage
Parallelogram Mechanisms
• Consist of links that form parallelograms to move an
object without altering its pitch
• Create parallel motion for applications such as
balance scales, glider swings, and jalousie windows
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a scissor linkage
Drafting machine linkage
Walking Mechanisms
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Quick-Return Mechanisms
They are commonly used on machine tools that require a
slow cutting stroke and a fast return stroke.
a crank-shaper linkage
Shaper machine
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Scotch Yoke Mechanism
• Converts rotational motion to linear sliding motion, or vice versa.
• In comparison to the slider-crank, the scotch yoke has the advantage of smaller
size and fewer moving parts
• Experience rapid wear in the slot
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TECHNIQUES OF MECHANISM ANALYSIS
1. Traditional Drafting or Graphical Techniques
• Old method, imprecise.
• Drafting equipment was used to draw the needed scaled lines at
specific angles such as (triangles, parallel straight edges,
compasses, protractors, engineering scales).
• However, with proper attention to detail, accurate solutions can
be obtained.
• This method illustrates the concepts behind graphical mechanism
analysis
• By using traditional drawing techniques, you can concentrate on
the kinematic theories and learn CAD commands easily
2. CAD Systems
• such as AutoCAD, have the capability to draw highly accurate lines at
designated lengths and angles.
• the lines do not need to be scaled to fit on a piece of drawing paper
Inventor, SolidWorks, and ProEngineer
- useful for planar kinematic analysis.
- Geometric constraints, such as length, perpendicularity, and parallelism, need to be
enforced when performing kinematic analysis.
- These constraints are automatically executed in the solid modeler’s sketching mode
3. Analytical Techniques
• Achieves precise results.
• Advanced analytical techniques often involve intense mathematical
functions.
• Disadvantages:
• The calculations is often difficult to visualize.
• This approach does have the drawback of laborious calculations
for more complex mechanisms.
4. Computer Methods
1.
Spreadsheets
• Very popular for routine mechanism Problems).
• A cell containing input data is changed, all other results are updated.
• This allows design iterations to be completed with ease.
• For complex problems, they can be difficult to manage on a spreadsheet
2.
Commercially available dynamic analysis programs:
• Working Model, ADAMS (Automatic Dynamic Analysis of Mechanical Systems), Dynamic
Designer
3.
User-written computer programs in a high-level language, such as Matlab, Mathematica,
VisualBasic, or C++
• Due to the time and effort required to write special programs, They are most effective
when a complex problem needs to be solved
• Not commonly encountered
References
• David H. Myszka, Mechanics & Mechanisms, Applied Kinematic Analysis
Thank you