KINEMATICS OF RIGID BODIES - Dokuz Eylül University€¦ · · 2014-11-261. The center O of the...
Transcript of KINEMATICS OF RIGID BODIES - Dokuz Eylül University€¦ · · 2014-11-261. The center O of the...
KINEMATICS OF
RIGID BODIES
1. The center O of the disk has the velocity and acceleration shown. If the disk rolls
without slipping on the horizontal surface, determine the velocity of A and the
acceleration of B for the instant represented.
PROBLEMS
2. For an interval of its motion the hydraulic cylinder gives the piston rod A a
velocity vA = 1.2 m/s which is increasing by 0.9 m/s each second for the
instant when q = b = 60°. For this instant, determine the angular acceleration
of link BC.
PROBLEMS
3. The elements of a power hacksaw are shown in the figure. The saw blade is
mounted in a frame which slides along the horizontal guide. If the motor turns the
flywheel at a constant counterclockwise speed of 60 rev/min, determine the
acceleration of the blade for the position where q = 90°, and find the corresponding
angular acceleration of the link AB.
PROBLEMS
s/rad.f 286180
260 ==
f
A
B
100 mm
438 mm O
Velocity Analysis
Link AB Blade
Acceleration Analysis
1
2 1 = 2
o90=q
j.i.k.rVVV O/BfO/BOB
628010286 ====
j.i.j.i.j.j.VVV ABABABB/ABA
43801062804380106280 ===
s/rad.,s/m.ViVV ABAAA 4311430 ===
22 46708854
4380204500
1089509433
4380108950204509433
43801043801043143110286286
s/rad.s/m.a
..j
...ai
j.i.i.j.i.ia
i.j.ki.j.k.k.i.k.k.a
rrraaa
ABA
AB
ABA
ABABA
ABA
a
B/AABB/AABAB
a
O/BABfB/ABA
B/AB
==
=
=
=
=
==
4. The center O of the disk rolling without slipping on the horizontal surface has the
velocity and acceleration shown. Radius of the disk is 4.5 cm. Calculate the velocity
and acceleration of point B.
PROBLEMS
37o A
O 4 cm
4.5 cm
vo=45 cm/s ao=90 cm/s2
10 cm
6 cm
B
x
y
x=2 cm 2
4
1xy =
5. At a given instant, the gear has the angular motion shown. Determine the
acceleration of points A and B on the link and the link’s angular accelartion at this
instant.
PROBLEMS
O q 45°
B
A
1.5 cm
2.5 cm
1 cm
vo
D y
x x=1.25 cm
1.5 cm
7 cm
6. The stepped disk that acts as a single unit rolls on the horizontal surface without
slipping. The center O of the stepped disk has a velocity of vO= 6 cm/s directed to the
right. For the instant represented, the acceleration of point B on the outer rim of the
disk has an acceleration given as (cm/s2). Point A on the disk is
connected to member AD by a pin. The roller at the end D of member AD can slide freely
along the parabolic slot. For the instant depicted, determine the angular velocity and
angular acceleration of member AD and the magnitude of the absolute acceleration of
point D.
jiaB
39.1275.57 =
4
2xy =
PROBLEMS