C
γ
A B
C
m i n
γ
m i n
D
B A
D
(3) If the side link DC is a driver, (a) find the pressure angle α’ and the transmission angle γ’ of the mechanism at that position. C
A D
4-7 In the double-crank linkage ABCD shown in Fig.4-1(b), LAB=80mm, LBC=180mm, LDC=230mm, LAD=200mm. The driver BC rotates at a constant speed. Find the minimum transmission angle γmin of the linkage.
B
a e
A
b
C
(1)the length of stroke H of the slider, (2) the crank acute angle θ (3) the time ratio k , 180° + θ k= 180° − θ
B 1
a
e
ω
A
θ
B 2
b
C 1 H C 2
(4) α and γ at that position, (5) αmax and γmin.
B
D
Can BC LAB L BC L DC LAD Type of Type of Type of rotate 360° linkage DC AB 45 50 60 20 20 35 70 90 20 45 70 90 80 20 45 60 40 30 20 35
B
D
LAB LBC L DC LAD Type of linkage 45 50 60 20 Dou. C 20 35 70 90 Dou. R C-R 20 45 70 90 80 20 45 60 Dou. R 40 30 20 35 C-R
C B A D
α
F
γ
(b) find the angular stroke ψmax of the link DC. (c) find the crank acute angle θ between the two limiting positions. 180° + θ (d) calculate the time ratio k . k = 180° − θ
C B
2 4
3
1
A
D
4-8 According to the data in Problem 4-3, find the range of values for the driving crank AB if the linkage is to be a crank-rocker mechanism and the minimum transmission angle γmin is larger than 50o. Compare the result with that in Problem 4-3(1a).
B ' B
a e
A
b
m a x
α
γ
m i n
γ
C C '
4-3 In a revolute four-bar linkage ABCD, LBC=100mm, LDC =80mm, LAD=110mm. (1)Find the range of the values for the length LAB of link AB if the linkage is either (a) a crank-rocker mechanism with crank AB, or (b) a double-rocker mechanism. (2) Can the linkage C be a double-crank mechanism by B choosing LAB suitably? Why?
C 1
b a
B 2
C 2 m a x D
Ψ
c
A B 1 F
d
ω
α
V
若DC为原动件，图示两位置的γ不是γmin！！
γ
γ
4-5 In the offset slider-crank mechanism shown in Fig.4-5, the driver crank AB rotates at a constant speed. Let LAB=120mm, LBC=250mm, offset e=60mm, and ϕAB=60o. Find
Type of AB Crank Rocker Crank Rocker Rocker
Can BC Type of rotate 360° DC Yes Crank Rocker No No Rocker Rocker Yes Crank No
B
D
4-4 In the revolute four-bar mechanism similar to the one in Fig.4-23(b), let LAB=60mm, LBC =130mm, LDC=140mm, LAD=200mm, and ∠BAD=135o. (1) Determine the type of the revolute four-bar V C mechanism. α F C Crank-Rocker γ
B A D
4-4(2) If the side link AB is a driver and rotates at a constant speed, (a) find the pressure angle α and the transmission angle γ of the mechanism at that V C position.
C 1
b a
B 2
C 2
θ
Ψ
m a x D
c
ω
1
A
d
B 1

(e) will any dead-point occur during the whole cycle of the motion? No. (d) find the maximum pressure angle αmax and the minimum transmission angle γmin. γmin =min{γmin′, γmin′′} 不能只求γmin′ !!!
4-9 The crank-rocker mechanism shown in Fig.4-31 has no quick-return characteristics. Prove that the lengths of links of the linkage satisfy the following equation: (LAB)2 + (LAD)2 =(LBC)2 + (LDC)2
C2 C1 B2 A B1 max
=0°
D
V
B
F
α
Aγ
B
D
(b) will any dead-point occur during the whole cycle of the motion? If so, when? Yes. (c) find the maximum pressure angle αmax and the minimum transmission angle γmin.
4-2 Determine the type of the linkage and the type of the two side links AB and DC (crank or rocker) according to the Grashof criterion. Can the coupler BC rotate 360o with respect to the frame (Yes or No)?