Mechanics tutorial_4.doc
1
1.
In the mechanism shown in diagram, FED is an offset slidercrank chain, which is given an
oscillatory motion by the rotation of crank AB. When B is vertically above A, the angular
velocity of AB is 3.0rad/s anticlockwise. Determine the corresponding velocity of slider D.
All the lengths are given in mm.
30
A
B
C
D
E
F
150
300
300
220
AB = 70 BC = 250 CD = 570 CE=ED=EF= 300
ans:
0.2m/s
2.
Referring to the diagram, the linkage mechanism is called quickreturn mechanism. Crank AB
rotates about A and the slotted link CD rotates about C. Pin B on the end of AB engages in the
slot of CD; AB=r and AC=l. The angular velocity of AB is
k
and its angular acceleration is
k
. If l/r=R, show that the angular velocity of CD is
k
R
R
R
CD
cos
2
1
)
cos
1
(
2
and its angular acceleration is
k
R
R
R
R
R
R
R
CD
cos
2
1
cos
1
cos
2
1
1
sin
2
2
2
2
if r=50mm, l=40mm,
=1rad/s and
= 2rad/s
2
, determine
CD
and
CD
if
30
.
A
B
C
D
x
y
ans:
0.3571k rad/s, 0.1127k rad/s
2
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3.
The diagram shows a simple two speed epicyclic gearbox. The sun S
1
is keyed to input shaft I
which is rotating at 1000rev/min. The sun wheel S
2
is keyed to the annulus A
1
. The planet
carriers C
1
and C
2
are keyed to the output shaft O. The number of teeth on the annulus and the
sun wheels are T
A1
= T
A2
= 80, T
S1
=30 and T
S2
=28. Determine the speeds of the output shaft O
and the nonstationary annulus when (a) A
1
is fixed and (b) when A
2
is fixed.
S
S
A
A
C
C
1
1
2
2
2
1
1000
rpm
Input
Output
ans:
(a)
368.2 rev/min (b) 151.1 rev/min
4.
A device for testing the resistance to wear between the material of a road (Y) and a shoe (X) is
shown. The crank OA is rotating clockwise at 10rad/s and the shoe is loaded such that contact
is always maintained between the test surfaces and B lies on the line OD. When the angle
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 Spring '09
 GXXY
 Angular velocity, Velocity

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