Passion - LOVE to Create

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Passion - LOVE to Create

• "Enthusiasm is one of the most powerful engines
  of success. When you do a thing, do it with all
  your might. Put your whole soul into it. Stamp it
  with your own personality. Be active, be
  energetic, be enthusiastic and faithful and you
  will accomplish your object. Nothing great was
  ever achieved without enthusiasm"
• Ralph Waldo Emerson
• American author, poet and philosopher

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The Theory of Machines and Mechanisms Chapter 2.
Kinematic Analysis

• Sun Zhihong
• Zhsun_at_dhu.edu.cn
• 67792564

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Main Topics of Today

• Kinematic analysis by vector equation and
  graphic method
• ????????????????

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• Two Points A ?B at the same link
• VB VA VBA
• VBA ?B????A????,???AB,????.

vA
5

• Example 1In a four-bar linkage mechanism ABCD,
  the length of link AB, BC, CD and AD are known,
  and the angular velocity of link AB is ?1.
• Find ?2,?3,VC,VE.

p
e
c
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• Velocity polygon
• Velocity polygon is similar to the shape of the
  link, e.g. velocity polygon ?abc ? link ? ABC,
• but the corresponding sides are vertical to each
  other,
• and the order of the point are same.

B
VB
VC
A
C
VA
c
VC
VCB
p
VB
b
VCA
VA
VAB
a
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• Two coincide points B1?B2 at two links
• VB2VB1VB2B1

• Example 2 the length of AB, AC are known, and
  angular velocity of link AB is ?1. Please
  decide ?3

b3
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• Example 3 the angular velocity of link AB and
  the size of all links are known. Please find ?5

E
4
D
B
(D4,D5)
5
2
1
C
?1
A
F
3
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Clue

• ?VB--- ????? VB     ?1LAB
• ?VC--- ???????????????? VC    
  VB    VCB
• ?VD2(VD4)--- ??????
• ?VD5---- ????????????????
• ??5---- ?????

E
?1
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• General laws of vector equation and graphic method

1. ??????????????,????????????????.
2. ?????,???p????????????????????,?pb????VB?
3. ????????????,??????????????????1?bc??VCB,???b??c?
   2?b2b3??VB3B2,???b2??b3
4. ?1?????bce??????BCE???????,??bce??BCE??,??????????
   ??????bce????BCE??????
5. ???????????,??????????????????????

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• Advantages and disadvantages of vector equation
  and graphic method

1. .????????????????,????????????????,??????????????
2. ????????????????????,????????????
3. ????????,?????????????,????????????????????????,??
   ???.

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• Examples 4 ??????????????,????????,???r30mm,??e
  10mm, lAB90mm, lBC30mm,?120rad/s???
• 1 ?????????
• 2 ????????C???? vc
• 3 ??????????C???? vc.

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Step 1 First find the instant centers Step 2
Method 1 Instant center method
vP12?1e?2lBO    ?2?1e/lBO20(1090)/10
00 2rad/s  vc?2lBC20.030.06m/s
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• Method 2 vector equation and graphic method
• Firstly, replace higher pair with lower pair
• Then, enlarge link 2, the velocity relationship
  between coincidental point O2 and O4 is
•   vO2       vO4        
  vO2O4
• ?? ?        ?1lOA      ?
• ?? ?BO    ?AO       ?DC  

So,vO4 vO1 ?1lOA 200.01 0.2m/s
(???) ??????? vO2 vO4   ?2 vO2/lBO vc
 ?2lBC 20.03 0.06m/s
p
o2
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• Example 5 ???????????????????????LAB140mm,LBCL
  CD420mm,???1??????120rad/s??????????VC ?VE5
  ??2? ?3?

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b
e2
c
c
p
e4,e5
e2
b
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Dont forget to do your homework Page 75
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