978-0073380308 Chapter 6 Solution Manual Part 22

Problem 6.149

Bar

AB

rotates about point

A

with angular speed

!1

and angular

acceleration

˛1

, both in the directions shown. The curved bar

BC

is pinned to bar

AB

at

B

and rotates with angular speed

!2

and

angular acceleration

˛2

about the pin at

B

in the directions shown,

relative to bar

AB

. At this instant, collar

D

is at the top of the

curved bar

BC

. The speed and acceleration of

D

relative to bar

BC

are given by

v0

and

a0

, respectively. Express your answers in

the

xy´

frame that is attached to bar

BC

with its origin at

B

.Hint:

As we will see in Eq. (10.14),

E!BC D E!AB C E!BC=AB D E!1C E!2

.

Determine the acceleration of the collar

D

in terms of

d

,

R

,

!1,!2,˛1,˛2,v0, and a0.

Solution

Using the given rotating reference frame, we can determine the acceleration of Dusing

or,

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Dynamics 2e 1361

Problem 6.150

The reciprocating rectilinear motion mechanism consists of a disk pinned

at its center at

A

that rotates with a constant angular velocity

!AB

, a slotted

arm

CD

that is pinned at

C

, and a bar that can oscillate within the guides

at

E

and

F

. As the disk rotates, the peg at

B

moves within the slotted

arm, causing it to rock back and forth. As the arm rocks, it provides a slow

advance and a quick return to the reciprocating bar due to the change in

distance between Cand B.

For the position shown, determine

(a)

The angular velocity of the slotted arm

CD

and the velocity of the

bar

(b)

The angular acceleration of the slotted arm

CD

and the acceleration

of the bar

Evaluate your results for !AB D120 rpm, R=h D0:5, and dD0:12 m.

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permission of McGraw-Hill, is prohibited.

Solving these two equations for !CD and PrB=C results in

Writing sin and cos in terms of given quantities

the solutions in Eq. (6) become

h2CR2D.R= h/2!AB

1C.R= h/2D2:513 rad=s and PrB=C DhR!AB

where we have used

!AB D120 rpm D120 

30 rad=s

and

R= h D0:5

to obtain the numerical result.

Therefore, the angular velocity of the slotted arm CD is

If

Q

is the contact point in common between the gear and the bar at this instant, the velocity of the bar is

where we have used the fact that O

KDO

kand dD0:12 m.

Part (b).

We first determine the acceleration of point

B

by relating it

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permission of McGraw-Hill, is prohibited.

Dynamics 2e 1363

Equation (13) is equivalent to the following two scalar equations

AB

Solving these two equations for ˛CD and RrB=C and substituting for sin and cos from Eq. (7), we obtain

AB

30 rad=s

Therefore, the angular acceleration of the slotted arm CD is

If

Q

is the contact point in common between the gear and the bar at this instant, the acceleration of the bar is

equal to the tangential acceleration of the point Qon the arm CD, that is,

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permission of McGraw-Hill, is prohibited.

Problem 6.151

The reciprocating rectilinear motion mechanism consists of a disk pinned

at its center at

A

that rotates with a constant angular velocity

!AB

, a slotted

arm

CD

that is pinned at

C

, and a bar that can oscillate within the guides

at

E

and

F

. As the disk rotates, the peg at

B

moves within the slotted

arm, causing it to rock back and forth. As the arm rocks, it provides a slow

advance and a quick return to the reciprocating bar due to the change in

distance between Cand B.

For the position shown, determine

(a)

The angular velocity of the slotted arm

CD

and the velocity of the

bar

(b)

The angular acceleration of the slotted arm

CD

and the acceleration

of the bar

Evaluate your results for !AB D90 rpm, R=h D0:5, and dD0:12 m.

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permission of McGraw-Hill, is prohibited.

Dynamics 2e 1365

of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the

permission of McGraw-Hill, is prohibited.

Problem 6.152

The reciprocating rectilinear motion mechanism consists of a disk pinned

at its center at

A

that rotates with a constant angular velocity

!AB

, a slotted

arm

CD

that is pinned at

C

, and a bar that can oscillate within the guides

at

E

and

F

. As the disk rotates, the peg at

B

moves within the slotted

arm, causing it to rock back and forth. As the arm rocks, it provides a slow

advance and a quick return to the reciprocating bar due to the change in

distance between Cand B.

For the position shown, determine

(a)

The angular velocity of the slotted arm

CD

and the velocity of the

bar

(b)

The angular acceleration of the slotted arm

CD

and the acceleration

of the bar

Evaluate your results for !AB D60 rpm, R=h D0:5, and dD0:12 m.

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permission of McGraw-Hill, is prohibited.

Dynamics 2e 1367

of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the

permission of McGraw-Hill, is prohibited.

If

Q

is the contact point in common between the gear and the bar at this instant, the acceleration of the bar is

equal to the tangential acceleration of the point Qon the arm CD, that is,

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permission of McGraw-Hill, is prohibited.

Dynamics 2e 1369

Problem 6.153

The reciprocating rectilinear motion mechanism consists of a disk pinned

at its center at

A

that rotates with a constant angular velocity

!AB

, a

slotted arm

CD

that is pinned at

C

, and a bar that can oscillate within

the guides at

E

and

F

. As the disk rotates, the peg at

B

moves within

the slotted arm, causing it to rock back and forth. As the arm rocks, it

provides a slow advance and a quick return to the reciprocating bar due to

the change in distance between Cand B.

For the arbitrary position shown, determine

(a)

The angular velocity of the slotted arm

CD

and the velocity of the

bar

(b)

The angular acceleration of the slotted arm

CD

and the acceleration

of the bar

as functions of ,ıDR= h,d, and !AB

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permission of McGraw-Hill, is prohibited.