# EXERCISE BOOK by mikeholy

VIEWS: 82 PAGES: 70

• pg 1
```									Name                  Class      Student No.               Date
Ex.2-1 Draw the kinematic diagrams of the mechanisms shown below.

4

1             3
2

1
4

2

3

1
Name                  Class      Student No.               Date
Ex.2-2 Draw the kinematic diagrams of the mechanisms shown below.

1
4

2
3
5

4
6

2
Name                  Class      Student No.               Date
Ex.2-3 Draw the kinematic diagram of the mechanism shown below.

3
Name                        Class       Student No.          Date
Ex.2-4 Calculate the degree of freedom of the mechanisms shown below. Indicate
all points for attention before the calculation of the DOF.

A            B

C

I                                 F

H                 D               E

J                         G

Fig.2-4(a)

I             H           D
B
J                              C           A
G
K         F           E

Fig.2-4(b)

4
Name                        Class       Student No.          Date
Ex.2-5 Calculate the degree of freedom of the mechanisms shown below. Indicate
all points for attention before the calculation of the DOF.

M                N
L                                        C

O
B
D       A
F
E
G
Fig.2-5(a)

A
D
B

Fig.2-5(b)

5
Name                        Class       Student No.          Date
Ex.2-6 Calculate the degree of freedom of the mechanisms shown below. Indicate
all points for attention before the calculation of the DOF.

B
C
A

D

E

Fig.2-6(a)

AB=CD
C
B

A                             D
Fig.2-6(b)

6
Name                       Class        Student No.               Date
Ex.2-7 Shown below is the kinematic diagram of an engine mechanism.
(1) Calculate the degree of freedom of the mechanism. Indicate all points for
attention before the calculation of the DOF.
(2) Carry out the structural analysis for the mechanism.
(3) Carry out the structural analysis for the mechanism if link EFG is a driver.
Note: During structural analysis, list the assembly order of Assur groups, the
numbers, the inner pair and the outer pairs of each group in each mechanism.

B               D
2           C
1           4
A             E                                 3
5
8
F
7
G               H
6

7
Name                       Class      Student No.                 Date
Ex.2-8 Carry out the structural analysis for the mechanism
(a) if link 1 is a driver.
(b) if link 5 is a driver.
Note: During structural analysis, list the assembly order of Assur groups, the
numbers, the inner pair and the outer pairs of each group in each mechanism.

D               5
4       E
B
2
1
A
3       C
6

8
Name                      Class        Student No.                Date
Ex.2-9 Someone tries to design a punch machine which will transform a
continuous rotation of gear 1 into a translation of the punch 4. Shown below is the
schematic diagram of the mechanism he designs. Can the mechanism realize the
task? How do you rectify it?

3
2
4
5                        1

Ex.2-10 Someone tries to design a mechanism which would transform a
continuous rotation into an oscillation. Shown below is the schematic diagram of
the mechanism he designs. Can the mechanism realize the task? How do you
rectify it?

E

C
2   3
B
4
1
A                   D

9
Name                          Class        Student No.                Date
Ex.3-1       Locate all instant centres of mechanisms for the position shown.

2
2
3
1                           3                                1
4
4
Fig3-1(a)                                            Fig3-1(b)

3                               n           C
3                 4
2                                   F                                  D
A   1                n                   E
2
5
B
1

Fig3-1(c)                                            Fig3-1(d)

3
2
2                                          4
3                       1
4                                                                     1

Fig3-1(e)                                            Fig3-1(f)

10
Name                      Class       Student No.                  Date
Ex.3-2 For the position shown of a geared linkage, determine graphically the
ratio 3/1 of the angular velocity of gear 3 to that of gear 1, using the method of
instant centres.

2
C
E
4
B                    F 5
1
A                            D
6 3

Ex.3-3 For the position shown of cam mechanism, determine graphically the ratio
2/1 of the angular velocity of follower 2 to that of cam 1, using the method of
instant centres.

3
2

1       O

ω1

11
Name                        Class       Student No.               Date
Ex.3-4 In the pivot four-bar linkage shown below, 1= -10rad/sec. Using the
method of instant centers graphically,
(a) find the velocity of point C for the position shown.
(b) for the position shown, locate point E on the line BC (or its extension) which
has the minimum velocity among all the points on line BC and its extension,
and then calculate its velocity.
(c) draw two positions of crank AB corresponding to VC=0.

C
2
3
B
1      ω1
4                    D
A

12
Name                     Class       Student No.                 Date
Ex.3-5 In the six-bar mechanism shown below, XA=0, YA=0, XD=450mm, YD=0,
LAB=150mm, LBC=400mm, LDC=350mm, CDE=30, LDE=150mm, LEF=400mm.
Crank AB rotates at a constant speed 10rad/sec. A main program is required to
analyze the output motions of the point F. The mechanism will be analyzed for the
whole cycle when the driver AB rotates from 0 to 360 with a step size of 1 =5.

C
2
B                     E
3
ω θ
1
5
1                                      F
A
D           4         6

13
Name                      Class       Student No.                  Date
Ex.3-6 The mechanism shown below has the following dimensions: X A=0, YA=0,
XD=200mm, YD=0, LAB=80mm, LCD=60mm and LBE=380mm. Crank AB rotates at
a constant speed of 10rad/sec. A main program is required to analyze the output
motions of the point E. The mechanism will be analyzed for the whole cycle when
the driver BA rotates from 0 to 360 with a step size of 1 =5.
E
C
θ1                     3
A                            D
ω1 2                 4

14
Name                     Class       Student No.                 Date
Ex3-7 . In the mechanism shown below, XG=YG=0, XB= - 42, YB=39, XD=10,
YD=75, LBA=23mm, LGF=12mm, LFE=95mm, LEC=69mm, LDC=48mm, EFG=90.
Crank BA rotates at a constant speed of 10 rad/sec. A main program is required to
analyze the output motions of the point C. The mechanism will be analyzed for the
whole cycle when the driver BA rotates from 0 to 360 with a step size of 1 =5.

E                           6
D

2           4
A
B                                   5
1
6           3               C

G
F
6

15
Name                       Class     Student No.                Date
Ex.3-8 In the six-bar mechanism shown below, XB=0, YB=0, XF=37.2, YF=17.5,
YC=28.8, LFE=16.8mm, LEC=39.2mm, LCD=20.633mm, LDE=36.4mm, BGA=90,
LBG=9mm, LGA=58mm. Crank FE rotates clockwise at a constant speed of -10
rad/sec. A main program is required to analyze the output motions of point A. The
mechanism will be analyzed for the whole cycle when driver FE rotates from 360
to 0 with a step size of 1 =-5.

A

D   6
5            C
3
F
4
2                   ω1
B                           E

16
Name                   Class     Student No.                Date
Ex.4-1 According to link dimensions, determine the type of the pivot four-bar

90

100

110
70
70
45

40                             120

50

100
100
90
70

60                       70

17
Name                       Class       Student No.                Date
Ex.4-2 In the revolute four-bar mechanism shown below, the crank AB is a driver.
(a) Find the pressure angle  and the transmission angle  of the mechanism at the
position shown.
(b) Find the angular stroke max of the link DC.
(c) Find the crank acute angle  between the two limiting positions.
(d) Find the maximum pressure angle max and the minimum transmission angle
min.
(e) Are there any dead-points in the whole cycle of the motion if link DC is the
driver? If so, when or where? Draw the dead-point positions of the mechanism.

C

3
2

A
D
1                                   4
B

18
Name                     Class       Student No.             Date
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
acute angle  between the two limiting positions.

B

A
e

Ex.4-4 Determine graphically the angular strokes of rockers AB and CD,
respectively.

C

A
D

19
Name                      Class       Student No.               Date
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. Describe briefly the drawing steps.

B1
C1
B2                                     C2

20
Name                       Class         Student No.                   Date
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, as shown below.
The position C1 of the slider is its left limiting position. Find the first position B1 of
the revolute B. Describe briefly the drawing steps.

E1

E2
A
C1              C2

21
Name                       Class       Student No.                 Date
Ex.4-7 In a revolute four-bar linkage ABCD, side link AB is the driver. The
positions of side link CD and line segment CE on the coupler CBE
corresponding to two positions of the linkage are known. The first position of the
linkage is also a dead point. Find the second position B2 of the revolute B. Describe
briefly the drawing steps.

2                      E1

C2
C1
D                              A

22
Name                        Class       Student No.                Date
Ex.4-8 In a crank-rocker linkage ABCD, side link AB is the driver. The positions
of the rocker CD corresponding to two positions of the linkage are shown below. At
the first position of the linkage, the pressure angle of the linkage is zero. Position
DC2 is one of the limit positions of the rocker. Find the first position B1 of the
revolute B. Describe briefly the drawing steps.

C1                       C2

A
D

23
Name                       Class       Student No.                  Date
Ex.4-9 In an offset slider-crank mechanism ABC, two sets of corresponding
positions between crank AB and point F on slider are known. When the crank AB is
located at position AB1, the slider reaches its left limit position. Find the first
position C1 of the revolute C on the slider. Describe briefly the drawing steps.

B2

F1                      F2
A
B1

24
Name                      Class     Student No.              Date
Ex.4-10 Design a crank-rocker mechanism ABCD that will give a k value of 1.25
with an angular stroke =60o for rocker DC, as crank AB rotates in a constant
speed. The length of the rocker DC is 60mm. The length of frame AD is 75mm.
Describe briefly the drawing steps.

ψ

D

25
Name                      Class       Student No.               Date
Ex.4-11 In an offset slider-crank mechanism, the offset e is 20mm. The
coefficient k of travel speed variation is to be 1.3. The working stroke H of the
slider is to be 50mm. Design the offset slider-crank mechanism

Ex.4-12 Design an offset slider-crank mechanism. The ratio of the length of the
coupler BC to the length of the crank AB is to be 4. The coefficient k of travel
speed variation is to be 1.2. The working stroke H of the slider is to be 200mm.

26
Name                        Class      Student No.                Date
Ex.5-1 A plate cam with positive-offset translating roller follower is to have the
following motion: a rise through lift h=40mm with a sine acceleration motion
curve during 0=150, S=30, a return with a 3-4-5 polynomial motion curve
during 0'=120, and S'=60. The cam rotates clockwise. The given dimensions
are: rP=40mm. rR=12mm, e=12mm and rC=25mm. Construct the pitch curve and
the cam contour graphically with a scale of 1:1. Label in red ink the centreline of
the follower, S, the roller and the pressure angle  corresponding to  = 60 and 
= 0.
   0   30   60   90   120   150   180    210   240   270   300   330   360
S

27
Name                      Class       Student No.                Date
Ex.5-2 A plate cam with translating offset roller follower has the same motion
curve and dimensions as those in Ex.5-1. Write a program to calculate the
co-ordinates of the pitch curve, the cam contour and the locus of the centre of the
milling cutter, the pressure angle , and the radius B of curvature of the pitch
curve.

28
Name                       Class       Student No.                  Date
Ex.5-3 For the plate cam with translating offset roller follower as shown below,
arcs GH and IJ are two arcs with centre at O. Indicate the radius rP of prime circle,
offset e, cam angle 0 for rise, cam angle S for outer dwell, cam angle 0' for return,
cam angle S' for inner dwell and lift h. For the position shown, indicate pressure
angle , displacement S and the corresponding cam angle .

B
I
H

O
ω                   G
J

29
Name                       Class       Student No.                 Date
Ex.5-4 For the plate cam with translating offset roller follower as shown below,
arcs EA, AB and BCD are three arcs with centre at O, N and P, respectively.
Indicate the radius rP of prime circle, offset e, cam angle 0 for rise, cam angle S
for outer dwell, cam angle 0' for return, cam angle S' for inner dwell and lift h.
For the position shown, indicate pressure angle , displacement S and the
corresponding cam angle .

A                                                         B

O                  P
C
ω                      N

E

30
Name                      Class      Student No.                 Date
Ex.5-5 A plate cam with an oscillating roller follower similar to that in Fig.5-36
of textbook is to have the following motion: an angular lift MAX =20 with a sine
acceleration motion curve during 0=150, S=30, a return with a 3-4-5
polynomial motion curve during 0'=120 and S'=60. The given dimensions are:
rP=40mm, LOA=80mm, LAB=76mm, rR=12mm and rC=16mm. Construct the pitch
curve and the cam contour graphically with a scale of 1:1. Label in red ink the
frame OA, , centreline AB of the follower, the roller and  corresponding to
=60 and =0.
   0   30   60   90   120   150   180   210   240   270   300   330   360


31
Name                       Class      Student No.                   Date
Ex.5-6 A plate cam with an oscillating roller follower has the same motion curve
and dimensions as those in Ex.5-5. Write a program to calculate the co-ordinates
of the pitch curve, the cam contour and the locus of the centre of the milling cutter,
the pressure angle  and the radius B of curvature of the pitch curve.

32
Name                      Class       Student No.                Date
Ex.5-7 For the plate cam with oscillating roller follower as shown below, arcs GH
and IJ are two arcs with centre at O. Indicate radius of prime circle rP, cam angle
for rise 0, cam angle for outer dwell S, cam angle for return 0', cam angle for
inner dwell S' and angular lift MAX. For the position shown, indicate pressure
angle , angular displacement of follower  and the corresponding cam angle .

A

H
B
ω
G               O

I
J

33
Name                       Class       Student No.                    Date
Ex.5-8 A plate cam with a translating flat-faced follower is to have the following
motion: a rise through lift h=50mm with a sine acceleration motion curve during
0=150, S=30, a return with a 3-4-5 polynomial motion curve during 0'=120
and S'=60. The cam rotates clockwise. The given dimensions are: rP=50mm.
rC=20mm. Construct the pitch curve and the cam contour graphically with a scale
of 1:1. Label in red ink the follower centreline, S, the flat face, the tangent point T
between the cam contour and the flat face and  corresponding to =60 and =0.
   0   30   60   90   120   150   180    210   240   270   300   330   360
S

34
Name                       Class       Student No.                Date
Ex.5-9 A plate cam with a translating flat-faced follower has the same motion
curve and dimensions as those in Ex.5-8. Write a program to calculate the
co-ordinates of the pitch curve, the cam contour and the locus of the centre of the
milling cutter and the radius T of curvature of the cam contour.

35
Name                       Class       Student No.                   Date
Ex.6-1 A pair of standard spur involute gears has a module of 5mm, pressure
angle =20 , centre distance a=350mm, transmission ratio i12 =9/5. Calculate the
numbers of teeth(Z1 and Z2), reference diameters(d1 and d2), addendum
diameters(da1 and da2), base diameters(db1 and db2), tooth thickness s, spacewidth e,
pressure angles on the addendum circles(a1 and a2), the radii of curvatures of
tooth profile on the reference circles(1 and 2), and the radii of curvatures of tooth
profile on the addendum circles(a1 and a2).

Ex.6-2 How many teeth would an external standard spur involute gear have when
its dedendum circle and its base circle coincide? Which one is bigger as the number
of teeth increases ?

36
Name                        Class       Student No.                  Date
Ex.6-3 Shown are a pair of involute profiles C1 and C2 with the common normal
n-n passing through the contact point K.
(1) Draw the two base circles and two pitch circles.
(3) Label the theoretical line of action N1N2 and actual line of action B1B2.
(3) Label the working pressure angle ’ and pressure angle K at the point K.
(4) Label the actual working section DG of the profile C2.
(5) Find out point M2 on the profile C2 which will engage with point M1 on the
profile C1.

O1
n

M1
C2
K           C1

n
O2
37
Name                        Class     Student No.                  Date
Ex.6-4 Shown are a pair of involute pinion and rack with their pitch circle and
pitch line. Determine graphically the actual line of action B1B2, the actual working
section EF on the tooth profile of the pinion 1 and the actual working section GH
on the tooth profile of the rack.

O1

P

38
Name                         Class         Student No.             Date
Ex.6-5 A pair of external spur gears have the parameters as: Z1=10, Z2=27,
m=10mm, =20, ha*=1, c*=0.25, working center distance a’=185mm. Neither
gear has cutter interference.
(1) What type of corrected gear pair does it belong to? Why?
(2) What are the ranges of modification coefficients x1 and x2, respectively?
(3) If x1=0.5, calculate ra2, rb2, S2, a2, and a2 for gear 2.

39
Name                         Class        Student No.        Date
Ex.6-6 A pair of external spur gears have the parameters as: Z1=20, Z2=40,
m=2mm, =20, ha*=1, c*=0.25, df1=37.0mm, S2=2.413652185mm.
(1) What are the modification coefficients x1 and x2?
(2) What type of corrected gear pair does it belong to? Why?
(3) Calculate rb1, ra1, a1, a1, S1, and 1 for gear 1.

40
Name                           Class   Student No.                   Date
Ex.6-7 There is a pair of external standard spur gears in a shaping machine with
Z1=17, Z2=118, m=5mm, =20, ha*=1, c*=0.25. The pinion is worn out and the
gear is worn to such an extent that the tooth thickness is decreased by 0.75mm. The
gear is to be repaired by addendum modification and a new pinion is to be
manufactured to mesh with the repaired gear. What is the minimum modification
coefficient of the new pinion if the original frame is still used? If x 1=0.3, calculate
ra1, rf1, S1, a1, a1, and .

41
Name                         Class        Student No.            Date
Ex.6-8 In the gear train shown below, both gear pairs must have the same
working center distance. Z1=27, Z2=60, Z2’=63, Z3=25, ha*=1, c*=0.25, m=5mm.
The gear pair 2’ and 3 is a corrected gear pair with reference center distance. The
modification coefficient x2 of the gear 2 is zero. What type of corrected gear pair
should the gear pair 1 and 2 adopt? Give the brief reason.
(2) Is the gear 2 a standard gear? Why?
(3) Calculate x1, S1, rb1, rf1, a1, and a1.

1             3

2            2'

42
Name                     Class     Student No.                  Date
Ex.6-9 The following dimensions of a pair of external spur gears are known: m,
Z1, i12, , ha*, c*, S1, and rf2. Write all formulae to calculate  according to
calculation steps.

43
Name                        Class       Student No.                   Date
Ex.6-10 A pair of standard external helical gears have the following parameters:
Z1 =20, Z2 =40, mn =8mm, n =20, han*=1, B=30mm, a=250mm. Find the helix
angle , total contact ratio  and the virtual numbers of teeth Zv1, Zv2.

44
Name                       Class        Student No.                Date
Ex.6-11 A pair of standard external helical gears with transmission ratio i3.5 is
to be designed. According the strength calculation, mn=2.5mm, amin=111.5mm.
Find a integral center distance a, Z1, Z2, and the helix angle  .

45
Name                       Class      Student No.              Date
Ex.6-12 A standard worm wheel has the number of teeth Z2 = 40, reference
diameter d2=320mm. It meshes with a single-threaded worm.
(1) Determine module of the worm gear set on the mid-plane mt2 and mx1;
(2) Determine axial pitch px1 and lead l of the worm;
(3) Choose reference diameter of worm;
(4) Calculate lead angle 1 of the worm;
(5) Calculate centre distance a without modification.

46
Name                           Class       Student No.              Date
Ex.6-13 A pair of straight bevel gears have parameters Z1 =15, Z2 =30, m=5mm,
ha*=1, c* =0.2,  =90 . Determine other dimensions d1, d2, da1, da2, df1, df2, 1, 2,
a1, a2, f1, f2 , R, Zv1 and Zv2 with constant bottom clearance.

47
Name                       Class        Student No.                 Date
Ex.7-1 Shown below is a hoist. The teeth numbers of all the gears are: Z1=20,
Z2=50, Z2’=15, Z3=30, Z3’=1, Z4=40, Z4’=18, Z5=52. Find the train ratio i15 and
point out the rotating direction of the handle to raise the weight.

4                  5

4'
3'
2

3
1

2'

48
Name                      Class      Student No.                Date
Ex.7-2 Shown below is the gear train in a clock. S, M and H denote the pointers
of second, minute and hour, respectively. The given numbers of teeth are Z1=Z2’=8,
Z2=64, Z3’=12, Z4’=15. If the modules of gear 4 and gear 5 are equal, find the
numbers of teeth Z3, Z4, and Z5.

4
4'

3               M
3'
H
5
2'
2
S
1

49
Name                    Class        Student No.                Date
Ex.7-3 Shown below is a gear train in which gear 3 engages with gears 2 and 4
simultaneously. What kind of gear train is it? If Z1=34, Z2=Z3=20, and Z4=74, find
the train ratio i1H.

2

H

1

4

50
Name                      Class       Student No.               Date
Ex.7-4 Shown below is a differential gear train with Z1=15, Z2=25, Z2’=20, Z3=60,
n1=200 r/min, n3=50 r/min. Find both the magnitude and the direction of nH when
(1) n1 and n3 are in the same direction;
(2) n1 and n3 are in the opposite directions.
2

2'

H
1

3

51
Name                     Class     Student No.            Date
Ex.7-5 In the combined gear train shown below, Z1=36, Z2=60, Z2’=23, Z3=49,
Z3’=69, Z4=31, Z5=131, Z6=94, Z7=36, Z8=167, n1=3549 r/min. Find both the
magnitude and the direction of nH.

H       7        4       3

6       3'
2'
8       5
n1
1
2

52
Name                    Class       Student No.                 Date
Ex.7-6 In the combined gear train shown below, Z1=20, Z2=25, Z3=15, Z1’=30,
Z4=70, Z4’=60, nH=110 r/min. Find both the magnitude and the direction of n1.

2
3
1    1'
H
nH

4       4'

53
Name                    Class       Student No.                Date
Ex.7-7 In the combined gear train shown below, Z1= Z5= Z6=17, Z2=18, Z2’=27,
Z3=34, Z4=51. n1=110 r/min. Find both the magnitude and the direction of n6.

2'
n1
2
6

5
1      3
4

54
Name                  Class       Student No.                Date
Ex.7-8 Shown below is a gear train with Z1=16, Z2= Z2’ =25, Z3=57, Z4=56. Find
the train ratio i14.

2
2'
H

1

3           4

55
Name                     Class     Student No.              Date
Ex.7-9 In the gear train shown below, Z2=15, rotation speed of the shaft M of
electric motor relative to the rotating frame H is n M =12rpm, nH= － 2rpm.
H

Calculate Z1.

M
H
2                             1

56
Name                     Class       Student No.                Date
Ex.7-10 In the gear train shown below, Z1=20 and i1H=4.5. All the gears are
*
standard spur gears with h a =1. Determine the numbers of teeth Z2 and Z3 and the
number of planet gears k. If the mechanical efficiency of every pair of gears is
=0.9, find the mechanical efficiency of the gear train 1H.

2

H

1

3

57
Name                      Class     Student No.                  Date
Ex.9-1 In the cam-linkage shown below, the driving rotary block 1 rotates
continuously. By designing the contour of the fixed cam correctly, the sliding block
4 can get a predetermined motion. Analyze the motion transmission route and draw
its structural block diagram. What is the combination pattern of this combined
mechanism?

B
2              3
A                          C
1                              4
5

5

Ex.9-2 In the combined gear train shown below, gear 1 is the driver, link 6 is the
output. Analyze the motion transmission route and draw its structural block
diagram. What is the combination pattern of this combined mechanism?

2'
n1
2
6

5
1      3
4

58
Name                      Class      Student No.                Date
Ex.9-3 In the gear-linkage shown below, crank AB is the driver. The output
pinion 4 is located on shaft A. Analyze the motion transmission route and draw its
structural block diagram. What is the combination pattern of the combined
mechanism?
5
D

A
3
4       1

B                2       C

Ex.9-4 The kinematic chain shown below is similar to that in Fig.9-16a of
textbook. However, in the kinematic chain shown below, the driver is link 3 instead
of gear 1, while gear 5 is still an output gear. Analyze the motion transmission route
and draw its structural block diagram. What is the combination pattern of this
combined mechanism?

6
C
2
B                     3
1                                 5
A                            D
4

59
Name                       Class     Student No.                 Date
Ex.10-1 There are four imbalances in a disk-like rotor. The masses, rotating radii
and angular orientations are: m1=8kg, m2=10kg, m3=8kg and m4=7kg, r1=10mm,
r2=10mm, r3=15mm and r4=20mm. The rotor is to be balanced by removing a mass
mC at a rotating radius of 25mm. Find the magnitude mC and its location angle C.

m1
m2 r2 r r
1   4
r3       m4
m3

Ex.10-2 Among the following rotors, rotors                              are statically
balanced only, rotors          are dynamically balanced.
m
r                 r                 r                   r
r             r                 r          r
m                         m        m               m
L          L     L                 L         L     L

(a)                              (b)
2m                     m            3m
r                     r             r
r                                              r
3m                           2r                 m
L       L L                               m
1.5L           1.5L

60
Name                      Class       Student No.                  Date
Ex.10-3 On a circular rotating disk, there are two circular holes. d 1=40mm,
d2=50mm. The rotating radii of the hole centers is r1=100mm and r2=140mm,
respectively. The location of the two holes are shown below. The disk is to be
balanced by drilling third hole. The rotating radius of the third hole center is to be
r3=150mm. Find the diameter d3 and its location angle 3.

d2
r2

30°              r1
d1

61
Name                       Class      Student No.              Date
Ex.10-4 Four unbalanced masses m1, m2, m3 and m4 exist on four transverse
planes spaced equally. Their mass-radius products are: m1r1=3kgmm, m2r2=2kgmm,
m3r3=5kgmm, and m4r4=4kgmm, respectively. Their locations are as shown.
Suppose the system is to be balanced fully by two balancing mass-radius products,
Pb1 and Pb3, on the planes I and III, respectively. Determine the amounts and
angular locations of the two balancing mass-radius products.

III
I
y

m2
m3
r2        r3

r1                                        r4
m1                                             m4
x
L             L             L

62
Name                     Class        Student No.                Date
Ex.10-5 On the non-disk rigid rotor shown below, there exist four unbalanced
masses. Their masses, rotating radii and angular locations are: m1=10kg, m2=15kg,
m3=20kg and m4=10kg, r1=40mm, r2=30mm, r3=20mm and r4=30mm and 1=120,
2=240, 3=300 and 4=30. L12 =L23 =L34. The system is to be balanced
dynamically by adding a mass mA on the balancing plane A at a rotating radius rA
of 50mm and removing a mass mB on the balancing plane B at a rotating radius rB
of 60mm. Determine the magnitudes (mA and mB) and angular locations (A and B)
of the required masses.

A                B             m1
m1                                   Y
r     1             m4
m4         1             r4
4
r3        X
m3                2        3        m3
m2                              r2
m2
L 12 L 23 L 34

63
Name                     Class       Student No.                 Date
Ex.11-1 Shown below is a slider-crank mechanism driven by a pair of gears. Z1
=20, Z2=60. The moment of inertia of pinion 1 about its centre of mass A is
J1=0.15kgm2. The moment of inertia of gear 2 about its centre of mass B is
J2=1.8kgm2. The length of crank BC is 100mm. The mass of coupler CD is
m3=10kg. Its centre of mass is located at the middle of CD. Its moment of inertia is
J4=1kgm2. The mass of slider 4 is m4=5kg. The resistant force F4 acts on slider 4.
F4=25kN. Take the pinion 1 as the equivalent link. Find the equivalent resistant
moment of force Mr of F4 and the equivalent moment of inertia J of the whole
mechanism for the position shown.

2
4
B                            F4
A    1                                         D
5
3
C

64
Name                      Class       Student No.                Date
Ex.11-2 A planetary gear train with two planets is shown below. The module of
all the gears is m. The numbers of teeth are Z1, Z2, and Z3, respectively. The
moments of inertia of the links are J1, J2, and JH. The mass of a planet is m2. The
resistant moment of force MH acts on the planet carrier H. Take gear 1 as the
equivalent link. Find the equivalent resistant moment of force Mr of MH and the
equivalent moment of inertia J of the whole gear train.

2
MH      H
OH                          O1
1

65
Name                     Class      Student No.               Date
Ex.11-3 Shown below is a hoister driven by a pair of gears. Z1 =20, Z2=60. The
moment of inertia of the pinion 1 about its centre of mass is J1=0.25kgm2. The
moment of inertia of the gear 2 about its centre of mass is J 2=1.8kgm2. The
diameter of the tub wheel is D=300mm. The mass lifted is Q=100kg. Take the the
pinion 1 as the equivalent link. Find the equivalent moment of inertia Je of the
whole mechanism and the equivalent resistant moment Mr of weight Q.

2
D
1

Q

66
Name                      Class     Student No.              Date
Ex.11-4 The driven moment Mr of a machine on the equivalent link is a given
function of the rotating angle  as shown in the figure. The angular period of
moment is T=2. The input moment Md is constant.
(1) Calculate the input moment Md.
(2) Calculate the maximum increment of work Wmax.
(3) The average speed is nm =620 r/min. The allowable coefficient of speed
fluctuation is []=0.01. Masses and moments of inertia of all the links are
neglected. Find the minimum moment of inertia JF of the flywheel on the

Mr
100Nm

T
0                 3                   6      7      2
4                   4      4

67
Name                       Class       Student No.              Date
Ex.11-5 In a mechanical system running at a periodic and stable speed, a rotating
link is selected as the equivalent link. The equivalent input moment Md and the
equivalent driven moment Mr on the equivalent link are given functions of the
rotating angle  as shown in the figure. The works of the some phases are:
f2=1000Nm, f3=800Nm, f4=700Nm, f5=1000Nm, f6=900Nm, f7=400Nm,
respectively. Therefore, f1=             Nm. The maximum increment of work
Wmax=          Nm. If the equivalent moment of inertia Je is constant, then the
maximum speed of the equivalent link will take place at           , the minimum
speed of the equivalent link will take place at       .

Mr
f2                      f4          Md           f6
f1                      f3                    f5                      f7

a     b             c          d         e             g            h i
0                                                                            T

68
Name                     Class     Student No.                 Date
Ex.12-1 List and draw the schematic diagrams of four mechanisms which have at
most 4 links and can transform a continuous rotation into an oscillation. Give the
name of each mechanism.

69
Name                      Class     Student No.                Date
Ex.12-2 List and draw the schematic diagrams of four mechanisms which have at
most 4 links and can transform a continuous rotation into a translation back and
forth. Give the name of each mechanism.

70

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