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