Mechanism Design Graphical Method

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Mechanism Design Graphical Method
2
Mechanism Synthesis
Design a mechanism to obtain a specified motion
or force.

• Dimensional Synthesis

• 
  deals with determining the length of all links,
  gear diameter, cam profile.

3
Mechanism Synthesis
Type Synthesis The Associated Linkage Concept
It is desired to derive various types of
mechanisms for driving a slider with a linear
translation along a fixed path in a machine.
Also, assume that the slider must move with a
reciprocating motion.
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Mechanism Synthesis
Type Synthesis - The Associated Linkage Concept
(6-Bar)
6-Bar
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Limiting Conditions 4 Bar Mechanism
Toggle positions of a crank-rocker mechanism.
Links 2 and 3 become collinear.
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Transmission Angle 4 Bar Mechanism
The angle between link 3 and link 4 is defined as
the transmission angle
T4 F34sin(µ) x (O4D)
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Minimum Transmission Angle 4 Bar Mechanism
Minimum transmission angle occurs when link 2
(crank) becomes collinear with link 1 (ground
link)
µ
The minimum transmission angle should be greater
than 40o to avoid locking or jamming the mechanism
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Mechanical Advantage 4 Bar Mechanism
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Mechanical Advantage 4 Bar Mechanism
B
µ
A
O4B 2(O2A) rin rout µ 60O, v 5O M.A. 20
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Mechanism Synthesis
Dimensional Synthesis
Analytical Methods
this
approach is suitable for automatic computation.
Once a mechanism is modeled and coded for
computer, parameters are easily manipulated to
create new designs.
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Graphical Synthesis Motion Generation Mechanism
Two positions, coupler as the output
B1

• Draw the link AB in its two desired positions,
  A1B1 and A2B2

A2
A1
B2
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Graphical Synthesis Motion Generation Mechanism
Three positions, coupler as the output

• Same procedure as for two positions.
• Draw the link AB in three desired positions.

A2
B1
A1

• Draw the midnormals to A1A2 and A2A3, the
  intersection locates the fixed pivot point O2.
  Same for point B to obtain second pivot point O4.

A3
B2

• Check the accuracy of the mechanism, Grashof
  condition and the transmission angle.

B3

• Change the second position of link AB to vary the
  locations of the fixed points

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Graphical Synthesis Motion Generation Mechanism
Adding a Dyad to a non-Grashof mechanism.

• Draw the four bar in both positions

B1
3
A2
A1
B2
2
4
O2
O4
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Graphical Synthesis Motion Generation Mechanism
6-Bar Grashof mechanism
B1
A
A1
5
2
B
3
4
C
D
O2
O4
6
O6
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Three Position, 6-Bar Grashof ,Motion Generation
Mechanism
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Three Position, 6-Bar Grashof ,Motion Generation
Mechanism
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Graphical Synthesis Motion Generation Mechanism
Two positions Grashof 4-Bar mechanism with rocker
as the output
D1
C2
C1
D2
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Graphical Synthesis Motion Generation Mechanism
Two positions Grashof 4-Bar mechanism with
rocker as the output
D1
C2
C1
D2
B2
A2
O2
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Two Position, 4-Bar Grashof Motion Generation
Mechanism
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Graphical Synthesis Motion Generation Mechanism
Three positions with specified fixed pivot
points, coupler as the output

• Draw the link CD in its three desired positions,
  C1D1, C2D2 and C3D3 and locate the fixed pivot
  points O2 and O4.
• Draw an arc from C1 with radius O2C2 and another
  arc from D1 with radius O2D2. Locate the
  intersection, O2.
• Draw an arc from C1 with radius O4C2 and another
  arc from D1 with radius O4D2. Locate the
  intersection, O4.

C2
D2
D1
D3
C1
C3
O2
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Graphical Synthesis Motion Generation Mechanism
Three positions with specified fixed pivot
points, coupler as the output

• Draw an arc from C1 with radius O2C3 and another
  arc from D1 with radius O2D3. Locate the
  intersection, O2.
• Draw an arc from C1 with radius O4C3 and another
  arc from D1 with radius O4D3. Locate the
  intersection, O4.

C2
D2
D1
D3
C1
C3
O2
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Graphical Synthesis Motion Generation Mechanism
Three positions with specified fixed pivot
points, coupler as the output
O4
O2

• Connect O2 to O2 and O2 to O2 . Draw two
  midnormals and locate the intersection, G.
• Connect O4 to O4 and O4 to O4 . Draw two
  midnormals and locate the intersection, H.
• O2G is link 2 and O4H is link 4.
• Construct a link (3) containing GH and CD.
• Verify the solution by constructing the mechanism
  in three position

O4
C2
D2
D1
D3
O2
C1
C3
O2
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Graphical Synthesis Motion Generation Mechanism
C2
D2
D1
H
D3
G
C1
C3
O2
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Graphical Synthesis Motion Generation Mechanism
Three positions with specified fixed pivot
points, coupler as the output.
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Graphical Synthesis Path Generation Mechanism
Three prescribed points.
Design a 4-Bar in such a way that a point on the
coupler passes thru three specified points
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Graphical Synthesis Path Generation Mechanism
Three prescribed points. Locate moving pivot B by
means of kinematic inversion. Fix coupler AP in
position 1 and rotate O2O4.
P1
P2

• Draw an arc from O2 with radius O2O4 , draw
  another arc from P1 with radius P2O4 , locate
  the intersection, O4 .

P3
A1
O2

• Verify the mechanism.

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Graphical Synthesis Path Generation
Mechanismwith Prescribed Timing
Three prescribed points Timing requirements
input crank rotation a, mechanism moves from P1
to P2 input crank rotation ß, mechanism moves
from P1 to P3
P1
P2
P3
Note timing takes away the free choices of the
crank length and coupler length AP.

• Follow the same procedure as before , for without
  timing, to locate the moving pivot point B.

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Graphical Synthesis Quick Return Mechanism
4-Bar crank-Rocker mechanism
Advance stroke mechanism operates under the
load.
Return stroke mechanism operates under no load.
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Quick Return Mechanism
Consider the two toggle positions of a
crank-rocker mechanism.

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Quick Return Mechanism
B1
4
3
A1
2
O4
O2
Q advance / Return (180 a) / (180 a),
Time Ratio
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Synthesis of a Quick Return Mechanism
Known or selected Rocker angle, f Rocker
length, r4 Time ratio, Q
Determine r1, r2, r3
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Synthesis of a Quick Return Mechanism

• Calculate the length of link 3, AB r3 O2 B1
  r2