Four Bar Linkages - Penn Engineeringmeam211/slides/SynthesisSlides.pdf · Four Bar Linkages 1....
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Transcript of Four Bar Linkages - Penn Engineeringmeam211/slides/SynthesisSlides.pdf · Four Bar Linkages 1....
MEAM 211
Four Bar Linkages
1. Types of linkages2. Synthesis (Design)
MEAM 211
Four Bar Linkage
Simplest 1 dof linkageUsed very commonly
Types of four bar linkagesGrashof Type I
Crank rockerDouble-rockerDrag-link
Non-Grashof or Grashof Type IITriple-rocker
s + l < p + q
s = smallest link lengthl = longest link lengthp, q = other two lengths
s + l > p + q
r1
r2
r3r4
θ1
θ4θ3
θ2
y
Q
P
OR
x
MEAM 211
Facts
Grashof linkagesThere exists one link that completes a full 360 degree rotation relative to another linkThis is the shortest linkThe pair of joints connecting this link to other links are such that they rotate through 360 degreesThree types of linkages
Crank rotates through 360 deg. (relative to frame)Coupler rotates through 360 deg. (relative to frame)Frame rotates through 360 deg. (relative to, let us say, crank)
Non Grashof linkagesNo link completes a full 360 degree rotation relative to another link
MEAM 211
Geometric significance of Grashof Inequality
s
l
q
p
12
3
4s
MEAM 211
s
lq
p
s
l
q
p
s
lq
p s
l
q
p
1
12
4
3
2
3
4
12
3
4
1
2
3
4
MEAM 211
Position 2
Position 1
Path of the moving pivot on the crank
s + l < p + q
Crank is the shortest link
Q
P
O R
Crank Rocker
MEAM 211
OPEN
CLOSED
OPEN
CLOSED
PROBLEM
DOOR IN OLD DESIGN SWINGS OUT
NEED
DOOR IN NEW DESIGN SWINGS OUT 40% LESS
Synthesis
MEAM 211
0.50"
0.75"
1.00"
2.25"
0.25"
0.50"
0.25"Door swing area
6.25"
Open position
Closed
3.75"
MEAM 211
Position 1 Position 2
Two-Position Synthesis of Linkages
Find a four bar linkage whose coupler, when attached to a specified rigid body, guides the rigid body between two given positions (and orientations).
MEAM 211
Couplerlink
Q
P
Circle pointson coupler
MEAM 211
Position 1 Position 2
Q1
P1 Q2
P2
MEAM 211
Position 1 Position 2
Q1
P1 Q2
P2
O R
LO, 12LR, 12
MEAM 211
Q1
P1 Q2
P2
RO
MEAM 211
Position 1
Position 2
Position 3
Three-Position Synthesis of Linkages
MEAM 211
Position 1
Q1
P1 Q2
P2
O R
Position 2
Position 3
P3
Q3LO, 12
LR, 12
LO, 23 LR, 23
MEAM 211
Q1
P1 Q2
P2
O
R
P3
Q3
