B3 B B1 A
θ
30°
B2 C1 C3 C2
e
H
Ex.4-4 Determine graphically the angular strokes of rockers AB and CD, respectively.
C
A
D
VB动画
B
C
A
D
φ AB
φ CD
VB动画
Ex.4-5 Shown are the two positions, B1C1 and B2C2, of coupler BC of a revolute four-bar linkage ABCD. Link AB is the driver. The pressure angle at the first position is 0o. The second position of the mechanism is a toggle position. Design the linkage.
A C1 C2
E2
B is UMRC. AE is reference link. C is circumference point. 1
A C1 C2
E2
因C1为滑块的左极限位置，所以B1点在AC1 连线上。 1
A C1 C2
E2
AC1E1和AC2E2分别代表C点相对于CE的第 一和第二个位置。 1
D
C2
1
B1
4
B
(c) Find the crank angle
VC C1 B2 F C
α 2 γ
3
ψmax
D
C2
θ
A
1
B1
4
B
(d) Find max and min.
C3
α max γ min
4
A B3
B4
D
4
Two dead-points if link DC is the driver.
A C1 C2
E2
有人将AE1C2拿来转。
1
A C1 C2
E2
Ex.4-7 In a revolute four-bar linkage ABCD, side link AB is the driver. The first position of the linkage is also a dead point.
B2 F1 F2
A B1
C is UMRC. Slider is reference link. B is circumference point.
B2
C1
C2
A B1
F1
F2
When the crank AB is located at position AB1, the slider reaches its left limit position. 所以，C1在B1A的延长线上。
100
70 45 120
Crank-rocker mechanism
Ex.4-1 According to link dimensions, determine the type of the pivot four-bar linkages shown below.
50
Double-rocker mechanism
B2
C1
A B1
F1
F2
作B1B1’=F1F2，得B1’点。
B2
C1
A B1 ' B1
F1
F2
作B2B1’的中垂线，交B1A的延长线于待定活 动铰链点C的第一个位置点C1。
B2
C1
A B1 ' B1
F1
F2
机构第一个位置AB1C1
B2
C1
A B1 ' B1
F1
F2
作C1C2=F1F2，得C2点。
70
100
60
Ex.4-1 According to link dimensions, determine the type of the pivot four-bar linkages shown below.
Double-rocker mechanism
90
100
70
Ex.4-2 In the revolute four-bar mechanism shown below, the crank AB is a driver.
C1
C2
A
D
因为AB为原动件, 且机构第一位置的压力角 =0, 所以B1C1C1D. 不是AB1B1C1！！！
C1 B1
C2
A
D
又因为C2D为摇杆CD的一个极限位置, 所以 AB2C2三点共线。 因此BC和CD均为运动已知构件。
C1 B1
C2
A
B2
D
B is UMRC. BC is reference link. A is circumference point.
D B1 C1 A B2 C2
The second position of the mechanism is a toggle position. A, B2, C2三点共线.
D B1 C1 A B2 C2
Ex.4-6 In a crank-slider mechanism, two sets of corresponding positions between the slider and a line segment AE on the crank ABE are known. The position C1 of the slider is its left limiting position. 1
D
机构的第一个位置
C1 B1 A2 '
C2
A
B2
D
截取B2C2=B1C1 ，得B2点。
C1 B1 A2 '
C2
A
B2
D
检验运动未知构件AB的杆长：AB1=AB2。
C1 B1 A2 '
C2
A
B2
D
Ex.4-9 In an offset slider-crank mechanism ABC, when the crank AB is located at position AB1, the slider reaches its left limit position.
Ex.4-1 According to link dimensions, determine the type of the pivot four-bar linkages shown below.
90
Double-crank mechanism
70 40
110
Ex.4-1 According to link dimensions, determine the type of the pivot four-bar linkages shown below.
E2
E1
C2 D
C1 A
A2
作AA2’的中垂线，B1在此中垂线上。
E2
E1
B1
C2 D
C1 A
A2
因AB为原动件且机构第一位置为死点，所以 B1点在DC1的延长线上。AA2’的中垂线与DC1 的延长线交于B1。
E2
E1
B1
C2 D
C1 A
A2
去掉辅助线后。机构的第一个位置。
E2
E1
B1
C2 D
C2
C1
B2 A D
4
B1
Ex.4-3 In an offset slider-crank mechanism ABC, crank AB is the driver. The maximum pressure angle MAX=30. Find the stroke H of the slider and the crank angle between the two limiting positions.
D B1 C1 A B2 C2
The link AB is a driver. The pressure angle at the first position is 0o. B1C1C1D
D B1 C1 A B2 C2
The second position of the mechanism is a toggle position. A, B2, C2三点共线
C1 B1
C2
A
B2
D
A点相对于BC的第一和第二个位置。
C1 B1
C2
A
B2
D
因A点在C2B2延长线上, 故在C1B1延长线上截 取C1A2’=C2A，得A2’点。
C1 B1 A2 '
C2
A
B2
D
作AA2’的中垂线与C1B1交于待定活动铰链点 B的第一个位置点B1。
C1 B1 A2 '
C2
A
B2
C
3 2
A
D
1
4
B
(a) Find and
VC C
3 2
F A D
1
4
B
(a) Find and
VC C
3 α 2 γ
F A D
1
4
B
(b) Find the angular stroke max of the link DC.
VC C1 B2 F A C
α 2 γ
3
ψmax
B1 C1 B2 C2
The fixed pivot A must be located on the bisector of B1B2. D must be located on the bisector of C1C2. D