PROBLEM

SThe gear has the angular motion shown. Determine the angular velocity and

angular acceleration of the slotted link BC at this instant. The pin at A is

fixed to the gear.

=2 rad/s

=4 rad/s20.5 m

0.7 m

2 m

O

B

A C

PROBLEM

S

37o

37o

10 cm

20 cm

A

O

2

1

1=5 rad/s

C

16 cm

B

OABO

Link 1, of the plane mechanism shown, rotates about the fixed

point O with a constant angular speed of 5 rad/s in the cw

direction while slider A, at the end of link 2, moves in the circular

slot of link 1. Determine the angular velocity and the angular

acceleration of link 2 at the instant represented where BO is

perpendicular to OA. The radius of the slot is 10 cm.

Take sin 37=06, cos 37=0.8

PROBLEM

SFor the instant shown, particle A has a velocity of 12.5 m/s towards point C

relative to the disk and this velocity is decreasing at the rate of 7.5 m/s

each second. The disk rotates about B with angular velocity =9 rad/s and

angular acceleration =60 rad/s2 in the directions shown in the figure. The

angle remains constant during the motion. Telescopic link has a velocity of

5 m/s and an acceleration of 2.5 m/s. Determine the absolute velocity and

acceleration of point A for the position shown.

Problem 7

Velocity Analysis

j4.1i8.4v

j25

7i

25

245v

B

B

relBA vrvv

7

24

25

vB

Velocity Analysis

j6i6r

j3

2i

3

2k9r

m3

2x

9

2x

3

2

9

2xy 22

j10i5.7v

j5

4i

5

35.12v

rel

rel

3

4x2

dx

dytan

m3

2x

9

2x

3

2

9

2xy

3/2x

22

4

3

5

vrel

j4.17i3.6vA

Velocity Analysis

j7.0i4.2a

j25

7i

25

245.2a

B

B

relrelBA av2rraa

7

24

25

aB

Acceleration Analysis

j40i40j3

2i

3

2k60r

j54i54j6i6k9j3

2i

3

2k9k9r

m3

2x

9

2x

3

2

9

2xy 22

Acceleration Analysis

j135i180v2

j10i5.7k92v2

rel

rel

Acceleration Analysis

j6i5.4j5

4i

5

35.7a

j494.40i992.53j5

3i

5

449.67a

s/m49.67315.2

5.12va

trel

nrel

222

relnrel

m315.2

dxyd

dxdy

1

2dx

yd

3

4x2

dx

dy

2

2

2/32

2

2

3/2x

j794.74i892.254aA

4

3

5

(arel)t

vrel

+t+n

(arel)n

Acceleration Analysis

PROBLEM

SThe pin A in the bell crank AOD is guided by the flanges of the

collar B, which slides with a constant velocity vB of 0.9 m/s along

the fixed shaft for an interval of motion. For the position =30o

determine the acceleration of the plunger CE, whose upper end is

positioned by the radial slot in the bell crank. .

Problem 8

Velocity Analysis

)1(jvv CC

)2(jv5.0iv866.0j56.1i9.0v

j30sini30cosvj13.0i225.0k928.6vrvv

relrelC

relrelO/C

0

OC

vA

vA

vB=(vA)x

30o

s/rad928.615.0

039.1

s/m039.130cos

9.0

30cos

vv

AOD

BA

60o 30o

129.9 mm

vrel

(1)=(2) vrel=1.039 m/svc=2.079 m/s

vrel

2

AOD

AODtA2

AtA

2nAA

222nA

s/rad695.27

AOas/m154.430sinaa

s/m308.830cos

aa

s/m195.715.0928.6OAa

129.9 mm

aA

60o 30o

vrel(aA)n

30o

(aA)t

aA

VB=constant

So aA must be vertical.

)3(jaa CC

)4(ja5.0ia866.0j464.12i58.21a

j30sini30cosarelj30sin039.1i30cos039.1k928.62

j13.0i225.0k695.27j13.0i225.0k928.6k928.6a

av2rraa

relrelC

C

relrel

0

OC

Acceleration Analysis

(3)=(4)

arel=24.92 m/s2

aC=27.92 m/s2

PROBLEMS

1. The uniform 30-kg bar OB is secured to the accelerating frame in

the 30o position from the horizontal by the hinge at O and roller at A.

If the horizontal acceleration of the frame is a=20 m/s2, compute the

force FA on the roller and the x- and y-components of the force

supported by the pin at O.

PROBLEMS

2. The block A and attached rod have a combined mass of 60 kg and are

confined to move along the 60o guide under the action of the 800 N

applied force. The uniform horizontal rod has a mass of 20 kg and is

welded to the block at B. Friction in the guide is negligible. Compute the

bending moment M exerted by the weld on the rod at B.

SOLUTION

x

W=60(9.81) N

60o

N

FBDKinetic Diagram

x

2

.

/84.4

6060sin)81.9(60800

sma

amaF

x

xxforcesextx

FBD of rod

Bx

By

M

W1=20(9.81) N

KD of rod

mTax=60ax

m1ax=20ax

2/196

)60sin7.0)(94.4)(20(7.0)81.9(20

smM

MdmaM xB

PROBLEMS

3. The parallelogram linkage shown moves in the vertical plane with the

uniform 8 kg bar EF attached to the plate at E by a pin which is welded

both to the plate and to the bar. A torque (not shown) is applied to link

AB through its lower pin to drive the links in a clockwise direction. When

reaches 60o, the links have an angular acceleration an angular velocity

of 6 rad/s2 and 3 rad/s, respectively. For this instant calculate the

magnitudes of the force F and torque M supported by the pin at E.

PROBLEMS

4. The uniform 100 kg log is supported by the two cables and used as a

battering ram. If the log is released from rest in the position shown,

calculate the initial tension induced in each cable immediately after

release and the corresponding angular acceleration of the cables.

SOLUTION

W=100(9.81) N

FBD KD

TA TB

nam

tam

+n

+t

+n

+t

When it starts to move, v=0, =0 but ≠0 02 ran

2.

.

/905.430sin

57.849030cos0

smaammgamF

TTmgTTF

tttforcesextt

BABAforcesextn

2/45.22

905.4sradrat

Length of the cables

NTNT

TTTTM

BA

BABAkdG

17.63739.212

30)5.0(60sin)5.1(60sin0..

The motion of the log is curvilinear translation.

*

*

PROBLEMS

5. An 18 kg triangular plate is supported by cables AB and CD. When the

plate is in the position shown, the angular velocity of the cables is 4

rad/s ccw. At this instant, calculate the acceleration of the mass center

of the plate and the tension in each of the cables.

G10 cm

A

B

C

D60°60°

24

cm

20 cm 20 cm

Answer:

NTNT

sma

CDAB 93.7811.143

/23.6 2

PROBLEMS

6. The uniform 8 kg slender bar is hinged about a horizontal axis through

O and released from rest in the horizontal position. Determine the

distance b from the mass center to O which will result in an initial angular

acceleration of 16 rad/s2, and find the force R on the bar at O just after

release.

PROBLEMS

7. The spring is uncompressed when the uniform slender bar is in the

vertical position shown. Determine the initial angular acceleration a of

the bar when it is released from rest in a position where the bar has

been rotated 30o clockwise from the position shown. Neglect any sag of

the spring, whose mass is negligible.

SOLUTIONUnstrecthed length of the spring:

llllo 2

5)4/2( 22

When=30o , length of the spring:

llspring 2

3

When=30o , spring force:

2

3

2

5

2

3

2

5klllkFspring

(in compression)

l

g

m

k

lamml

lF

lmg

amIM

ltspring

tO

857.0864.0

412

1

2460cos

4

2

W

O

G+n

+t

On

Ot

30o

30o

l

Fspring

60o

.

lspringG

+n

+t

04

2 l

mam n

tamI

60o