The Theory of Machines and Mechanisms Chapter 3. Planar

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The Theory of Machines and Mechanisms Chapter 3.
Planar  Linkage and Its Design

• Sun Zhihong
• Zhsun_at_dhu.edu.cn
• 67792564-108

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Todays topics

• Basic knowledge of four-bar mechanism
• The condition for having a crank(???????)
• Pressure angle and transmission angle(???????)
• Toggle positions and Dead-points(?????)
• Quick return characteristics (??????)

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1. Condition for having a crank(???????)
If there is a revolute pair ? there could be a
crank
Suppose altd, if side link AB could revolute,it
must be collinear with the frame twice
From ?BCD
ad b c
From ?BCD
b(d a) c
? ab c d
c(d a) b
? a c b d
a b, ac, ad
B
d- a
AB is the shortest link
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1. Condition for having a crank(???????)

• The sum of the shortest and the longest links
  must be less than the sum of the remaining two
  links (Grashof condition),

• The shortest link is the side link or the frame.

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• If the four-bar mechanism fits the Grashof
  condition,there could be a crank.
• If assign different link as the frame, different
  mechanisms could be got

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2. Pressure angle and transmission angle
Pressure angle a (???)The acute angle between
the directions of the force F and the velocity of
the point receiving the force on the follower
Transmission angle ?(???) The complement of the
pressure angle a is called transmission angle ?
Tangential force F Fcosa
Fsin?
Normal force F Fcos?
??, it is good for the mechanism
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2. Pressure angle and transmission angle
The position of ?min
When ?BCD90, ??BCD
When ?BCDgt90,
?180- ?BCD
When the driving crank and the frame link are
collinear, ?BCD reaches its extreme,?min will
occur.
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According the law of cosines
?B1C1Darccosb2c2-(d-a)2/2bc
?1?B1C1D
If ?B1C1D90,
?B2C2Darccosb2c2-(da)2/2bc
If ?B2C2Dgt90,
?2180-?B2C2D
?min?B1C1D, 180-?B2C2Dmin
The a and ? must be drawn on the driven link
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3. The toggle positions and the Dead points
In a crank-rocker mechanism,when the crank AB and
the coupler BC overlapping collinear or extended
collinear, the rocker CD reaches its two limiting
positions DC1 and DC2, they are called toggle
positions(??)?
The angle between DC1 and DC2 at the two limiting
positions is denoted as ?(????) ?
Crank-rocker mechanism
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3. The toggle positions and the Dead points
?0
If the rocker is a driver,then at its limiting
positions,
?0
Transmission angle of the mechanism is?0
These positions are called Dead-points (??)
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3. The toggle positions and the Dead points
Methods to overcome dead-points Stagger two
sets of the same mechanism wheel driving
mechanism of trains
The inertial force of flywheel Sewing machine
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Applications of Dead-points Landing
mechanism in an airplane,
Clamping device on machine tools?
Landing mechanism
Clamping device
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4.Quick return characteristics(??????)
180?
Crank rocker mechanism
If the crank AB rotates 180? counter-clockwise
at a constant angular speed of ?,the rocker DC
swing from C1D to C2D?
The time t1 it needs is
The average speed V1 are
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When the crank goes on rotating the rest
180-?,the rocker will swing from DC2 back to
DC1, then t2 and v2 are
B2
180-?
Obviously, t1 gtt2 v2 gt v1
Quick return property
K is called time ratio(??????)?
When design a new mechanism,usually time ratio K
is assigned first,then
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Quick return property of slider-crank mechanism
180?
180?
180-?
180-?
Questions If the following mechanisms have quick
return property? in-line crank mechanism(????????)
?oscillating guide-bar mechanism (??????)
Applicationsave the time of return
stroke. Example, shaper (???)?
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