Mechanics of Machines Cleghorn Answers

7/27/2019 Mechanics of Machines Cleghorn Answers

1/23

P1.1

(a)n = 6; (b) n = 6

turning pair, 5; turning pair, 5;

sliding pair, 1; sliding pair, 2;

rolling pair, 1; rolling pair, 0;

2 dof pair,0; 2 dof pair,0;

m = 1 m = 1

P1.2

(a)m = 1

(b)m = 1

P1.3(a)n = 6; (b) n = 8





m = 1 m = 1

P1.4(a)n = 4; (b) n = 4





m = -1 (by inspection, m = 1) m = 1

P1.5

(a)n = 4; (b) n = 8





m = -1 (by inspection, m = 1) m = -1 (by inspection, m = 1)


2/23

P1.6

(a)

(i)

l < s + p + q, link can form a mechanism

(ii)

s + l < p + q, class I four-bar kinematic chain, drag link mechanism.

(b)

(i)


(ii)

s + l = p + q, change point mechanism

(c)

(i)


(ii)

s + l < p + q, class I four-bar kinematic chain, crank-rocker four-bar mechanism

(d)

(i)


(ii)

s + l < p + q, class I four-bar kinematic chain, rocker-rocker four-bar mechanism(e)

(i)

l > s + p + q, link cannot form a mechanism

(f)

(i)


(ii)

s + l > p + q, rocker-rocker four-bar mechanism

P1.7

(a)0 < r2 < 0.5 (cm)

(b)1.5 < r2 < 3.5 (cm)

(c) r2 = 0.5 or r2 = 1.5 or r2 = 3.5 (cm)

(d)0.5 < r2 < 1.5 or 3.5 < r2 < 5.5 (cm)


3/23

P1.8

(a)0 < r4 < 0.5 (cm)

(b)1.5 < r4 < 4.5 (cm)

(c) r4 = 0.5 or r4 = 1.5 or r4 = 4.5 (cm)

(d)0.5 < r4 < 1.5 or 4.5 < r4 < 6.5 (cm)

P1.9

(a)0 < r2 < 1.5 (cm)

(b) r2 > 0 (cm)

P1.10

(a) r3 3.5 (cm)

(b) r3 > 0

P1.11


4/23

P2.1

(a)2 = 200 or 20

3 max = 50 rpm

(b)2 = 110 or 290

P2.2

(a)2= 90 or 270

v4 max =v2 = 52.36 (cm/s)

(b)2 = 0 or 180

vs max =v2 = 52.36 (cm/s)

(c)2 = 0 or 180

a4 max =a2N

= 548.1 (cm/s2)

P2.3

(a) 2 = 53.1 or 306.9

(b)v6 = 150 (cm/s), 2 = 0

P2.4

(a)(

4,avg )cw = 7.22 (rad/s)

(b)(

4,avg )ccw = 7.58 (rad/s)

(c)TR= 0.953

P2.5

(a) (v4,avg )right = 124.18 (cm/s)

(b) (v4,avg )left = 85.56 (cm/s)

(c) TR= 1.45

P2.6

(a)2 = 306.9

(b)2 = 0 or 360

(c) 2 = 306.9 or 0 or 360

P2.7

w3 ,max = 72.4 rad/s CW ; 2 =180


5/23

P2.10

(a) 2.79 r2 3.1 (cm)

(b)The four-bar mechanism is a drag link.

P2.11

(a) 1.82 r4 2.71 (cm)

(b)The four-bar mechanism is a drag link.

P2.12

0 r2 0.76 (cm)

P2.13

r2 4.95 (cm)

P2.14

(a)m = 1


6/23

Cleghorn Ch3 answers

3.1

60=Bv in/sec, 5.39=

Cv in/sec, 15=

Dv in/sec,

3.2

1.473 =v in/sec

3.3

28.64 =v cm/sec

3.4

(a) 1.214 =& rad/sec CW

(b) 52.20=Dv in/sec

3.5

84=Dv cm/sec

3.6

7.36 =& rad/sec CW

3.7

89.2=Cv in/sec

3.8

2.7=Dv in/sec

3.9

(a) 28.63 =& rad/sec CCW

(b) 84.404 =v cm/sec to the left

3.10

(a) 6.52 =Pv cm/sec

(b) 6.133 =Pv cm/sec

(c) 6.923 =PPv cm/sec

(d) 8.12

3=

&

&

3.11

(a) 4.182 =Pv cm/sec

(b) 183 =Pv cm/sec

(c) 2.1123 =PPv cm/sec

(d) 7.12

3=

&

&

3.12 (b)


7/23

(i) 13.25=Bv in/sec@ 45

(ii) 4.24=Cv in/sec@ 29

(iii) 5.27=Dv in/sec@ 0

(iv) 0.20=BDv in/sec@ 1.118

(v) 7.63 =& rad/sec CCW

3.13(b)

(i) 0.22=Bv in/sec@ 30 (ii) 1.8=

Cv in/sec@ 18

(iii) 1.13=Dv in/sec@ 10 (iv) 53 =

& rad/sec CCW

(v) 24.54 =& rad/sec CCW

3.14(b)

(i) 45=Dv cm/sec@ 98 (ii) 24=

Ev cm/sec@ 180

(iii) 1.63 =& rad/sec CW (iv) 165 =

& rad/sec CCW

3.15(c)

(i) 12032 =s

BBa cm/sec2 (ii) 1.273 =

&& rad/sec2 CW, 9.135 =&& rad/sec2 CCW

3.16(c)

1547 =&& rad/sec2 CCW

3.17(c)

805 =&&

rad/sec2

CW

3.18(c)


3.19(c)


3.20

(c)


8/23

(i) 12806 =Ba cm/sec2 (ii) 483 =

&& rad/sec2 CW, 1606 =&& rad/sec2 CW

(d) 6.606 =&& rad/sec2 CW

3.21(c)

(i) 6344 =&& rad/sec2 CW

(ii) 650=Ca cm/sec

2

3.22(c)

(i) 188042 =s

BBa in/sec2

(ii) 4882 =&& rad/sec2 CW

3.23(d)

1773 =&& rad/sec2 CCW, 3534 =

&& rad/sec2 CCW

3.26

(b)

(i) 9.23 =& rad/sec CW, 8.104 =

& rad/sec CW

(ii) 59=Dv cm/sec, 102=

Ev cm/sec, 42=

Fv cm/sec

(d)

(i) 2863 =&& rad/sec2 CCW, 4904 =

&& rad/sec2 CCW

(ii) 1780=Da cm/sec2 , 3240=

Ea cm/sec2 , 2780=

Fa cm/sec2

3.27(c)


3.28(c)

(i) 253 =&& rad/sec2 CW, 2205 =

&& rad/sec2 CCW

(ii) 30=Da cm/sec2

3.29(b)

(i) 43=Gv cm/sec

(ii) 62715 =c

EEa cm/sec

2


9/23

p4.1 w)rad/sec(cc212.02 =& o

v70@sec)/(53.132 = inv

s

p4.2 3&& =42.3 (ccw)

sec2rad

p4.3

sin

)sin(212

+

=

rr

sin

sin213

rr = =2r&

sin

)cos(221

+&r

sin

)sin()cos( 22

212212

++=

&&&

&&rr

r

sin

sin 213

rr =

sin

cos 2213

&

&r

r =

sin

sincos 22

212213

&&&

&&rr

r

=

p4.4 ov

4.119@sec)/(3.102 cmvc =

p4.5 (a) (cw)sec/39.23 rad=

&

(b) 37.4 cm/sec @71.9 o

(c) 17932=

c

AAav

cm/sec 2 @-18.1 o

p4.6 (a) (cw)rad/sce29.73 =&

(b) 71843=

c

BBa cm/sec2 @-101.8 o

p4.7 (a)ov

0@sec/2690 2cmaB =

(b) ov

225@sec/2990 242

cma s AA =

p4.8 (ccw)sec/69.13 rad=&

p4.9 (a) sec/)7.10671.4( cmjivc

vvv=

(b) sec/)8.241( cmjvBvv

=

p4.10 (a) (cw)sec/39.73 rad=&

(b) sec/7.2913

cmv BB =v

@-16.8 o

(c) o8.106@sec/439 213

= cmac BB

p4.11 (a) )sec(/8.283 cwrad=&

(b) ov

8.215sec@/14032

cmvPP=


10/23

p4.12 sec/)41.1198.10( injivcvvv

+=

p4.13 (a) sec/cos577.0sin78.11)cos3

1(sin 222222 inrvc +=+=

&v

(b) sec/cos6.13 224 inv BB =v

(c) 223 sec/sin8.106 inr =&&

(d) sec/6.13max24

inv BB =v

p4.14 (a) )sec(/5.83 ccwrad=&

(b) sec/)192.177( cmjivcvvv

=

p4.15 (a) sec/1.4413 cmv DD=

v

@16.3

o

(b) )sec(/13.23 cwrad=&


11/23

5.1 5.97d in=

5.2 450min

rev =

5.3 66.3 rpm =

5.4 (a) velocity ratio=1.333

(b)3

30N =

5.53 2

100 20N N= =

5.63 2

25 15 2356sec

mmN N pitch line velocity= = =

5.7 (a) 64B

N =

(b) c=13 in

(c) 0.785c

p in=

(d) 16.5in

(e) 15.49 in

5.8 (a)2 3

23.3 11.7d in d in= =

(b)3

5.48b

r in=

(c)3

cp in

=

(d) c=17.5 in

(e) 600rpm CCW

(f) m=1.755.9

5.10

5.113

117N =

(a)2

12.56c

p mm=

(b)3

219.9br mm=

(c)4

192d mm=

(d) c=282 mm

5.12 (a)3

2.69b

r in=

(b) c=4.65 in

(c ) 0.395c

p in=

(d) 4 5 18.4 = =D

(e)4

3.52d in=

(f) 3.76 in

5.13 (a) 2.17 in

(b) 60BN =

(c) 2.27Bb

r in=


12/23

(d) 0.131 in

5.14 (a) Z=0.546 in

(b) 1.48c

m =

5.15 (a) 4 1.496br in=

(b) c=3.501 in

(c) 1.93cm =

(d) 0.55 in

(e) 3 24.6 =D

(f)3

10.85d in=

(g) 10.53 in


13/23

P6.1

(a). 0.75 (b). ( )56.25 rpm CCW P6.2

(a).2 3 4 5

15 120 150 75N N N N= = = =

(b).2 3 4 5

39 120 150 115N N N N= = = =

P6.3

Choose1 8

150 250N N= =

5 6 1

3 4 2

2 7 3

229 171 0.8035

182 218 0.5009

267 133 0.2989

N N e

N N e

N N e

= = =

= = =

= = =

P6.4

Select 6 732 64N N= =

4 5 8 969 48 27 48N N N N = = = =

Select6

60N =

1124N =

10 16N =


14/23

P6.5

1 2 3 4 5

All locked

at x rpmx x x x x

Fix 2,

move 1 at

y rpm

y 01

3

Ny

N 1

4

Ny

N 1

5

Ny

N

Absolute

rpmx y+ x 1

3

Nx y

N 1

4

Nx y

N+ 1

5

Nx y

N+

P6.6

1 2 3 4 5 6 7

All locked

& move at

x rpm

x x x x x x x

Fix 2,

move 1 at

y rpm

y 01

3

Ny

N 1

3

Ny

N 1 4

3 5

N Ny

N N 1 4

3 5

N Ny

N N 1 4 6

3 5 7

N N Ny

N N N

Absolute

rpm x y+ x 1

3

N

x yN1

3

N

x yN1 4

3 5

N N

x yN N+1 4

3 5

N N

x yN N+ 1 4 6

3 5 7

N N N

x yN N N+

P6.7

1 2 3 4 5 6

All

locked,

move at

x rpm

x x x x x x

Fix 2,

move 1

at y rpm

y 01

3

Ny

N 1

3

Ny

N 1 4

3 5

N Ny

N N 1 4

3 6

N Ny

N N

Absolute

rpmx y+ x 1

3

Nx y

N 1

3

Nx y

N 1 4

3 5

N Nx y

N N+ 1 4

3 6

N Nx y

N N+


15/23

P6.8

10 4

198

25 =

10 264 rpm =

P6.9

(a). 1 4 63 5 7

1N N N

eN N N

= +

(b).1

3 5 7

1 4 6

1N N N

eN N N

=

(c).1

3 5 7

1 4 6

1N N N

eN N N

=

(d). 1 54 6

1N N

eN N

=

P6.1056 rpm

P6.11

(a).(i) 1412.5 rpm (ii) 2087.5 rpm

(b). 3n = P6.12

(a). 405 turns (opposite to indicated direction)1

108

turns (in the indicated direction)

(b). 2214 turns (opposite to indicated direction)


16/23

P6.13

(a). ( )9442 rpm CW

(b).

( )6328 rpm CW

P6.14

3105N =

0.429e =

P6.15

19.61 rads

P6.16

(a)2

1

1

7e = (b)

21

1

7e =

P6.17 P6-18 P6-19

(a). 1 4 48

11 3 7 7

1N N N

eN N N N

=

+

(b).4

7

81

4

7

1

NN

eN

N

=

P6-181

17542 rpm(opposite to output)c

x = =

P6-192

5198.7 rpm(CW) =


17/23

P6-20

1 1

1 2 2

1

1 1 2

4

2 6

2 2

5 7

0

x y

x x y

Nx y x

NN N

x yN N

+ = = +

=

+ =

,

condition:1 4

2 6 5 7

1 1 0 0

1 0 1 1det 0

1 / 1 0

0 0 1 /

N N

N N N N

P6-21

1

6

1

7

2

2

1 1 1 00

31 0 1 0

220

1 51/ 20 0 00

0.48 0 1 1

xN

yN

x

y

=

required relation:

6

7

1 1 1 0

31 0 122det 0

1 51/ 20 0 0

0.48 0 1 1

NN

=

P6-22 (a)2 1

28.571 rpm(CCW)x = =

(b) 2 1 28.571 rpm(CCW)x = =

P6-23 output3 5

750 rpm, 700 rpm = =

P6-24 (a) Carrier makes 12 rotation clockwise.

Angular displacement is 30rortations.

(b)

4 3

7cf g

+

=


18/23

P6-25 1.4 rpm(CCW)f

=

P6-26 (a) 0.4985, 249.25 rpm(same direction as the input)ce = =

(b) 564.71 Nm(opposite to input ratation)f

T =

P6-277

19.9 rad/s =

P6-28 316.67 Nmf

T =

P6-29 (a)3

/ 5 inp =

(b) 190 rpm(same direction as the input)c

=

(c) 324.3 Nmf

T =

P6-302

7312.5 rpm(same direction as output) =

546.84 Nm(same direction as output)f

T =

P6-31 (a) 34.9 rpm(CCW)c

=

(b) 2/ 258 rpm(CCW)c =

(c) max. number: 4

P6-32 (a) 7 / 4 rev(CCW)x =

(b) 7.15 rev(CCW)

(c) 2.75 rev(CW)


19/23

(d)

'C

270

'D

270

'A

'E

1

2

34

5

P6-33 (a)2

1.496 inb

r =

(b) 4.77 inc =

(c) 1.64(d)

4 5 6 739, 19, 33, 27N N N N= = = =

(e) 0.517 in

(f)4

14.8 =

(g)4

0 =

(h) 5 3.127 ind =

(i) 3.455 in

P6-34 (a) 159.3 rpm(CW)

(b) 1614 rpm(CC W)

(c) max. number: 8


20/23

P7.2

=

cos12

L

s = 120L = 35

P7.4

Required length of follower face:

= max.length min.length + 2 clearance

= 13.1 - 9.6 + 2 0.5 = 4.5cm

P7.5

(b) @= 30 = 23

@= 60 = 13

@= 90 = 3

P7.6

Cam Rotation (deg)Duration

(sec)

Motion

(cm)Start of

IntervalEnd of Interval

(deg)

1 0.5 +2.0 0 1203601.5

0.5= 120

2 0.3 0 120 1923601.5

0.3120 =+ 72

3 0.7 -2.0 192 360 168

(deg)

cos s = (deg)

0 1 0

20 2/3 2.4

40 1/2 8.8

60 0 17.5

80 -1/2 26.3

100 - 2/3 32.7

120 -1 35.0


21/23

(a)one rotation occurs in 1.5secsec

188.440sec

666.0sec5.1

1 radrpm

revrev==== ccw* ( *direcrtion selected )

(b)maximum velocity and acceleration of follower occur during interval I( L = 2.0cm ; = 120 = 2.094rad ; = 60)

Form Figure 7.13 :

2

2

=

Ls ;


22/23

Chapter 8 Graphical Force Analysis of Planar Mechanics

Ans:

P8.1 NQNF 1800,150012

P8.2 NQblbPa 129)(,14)(

P8.3 NFNFbccwmNmNMa 24,28)(),(.090.0032.028)( 131212

P8.4 lbFlbP 5.17,5.157 41

P8.5 lbF 20P8.6 )(1.68.14.33212 cwlbininlbdFM

P8.7 Mpa2.8

P8.8 )(90012 cwcmNM

P8.9 Mpa796.0

P8.10 )(49.2 cwcmNM

P8.11 )(5.012 cwmNM

P8.12 lbF 5.10

P8.13

)(9155)(),(7.89)(),(5.55)(),(9300)( cwlbindccwlbincccwlbinbcwlbina

P8.14 )(32.0 cwmN

P8.15 )(16.4 cwcmN

P8.16 )(875)(),(710)(),(165)( ccwlbincccwlbinbccwlbina

P8.17 )(04.1)(),(71.0)(),(33.0)( ccwmNcccwmNbccwmNa

P8.18 )(7.2 ccwmN

P8.19 )(011.0 ccwmN

P8.20 )(1.8 ccwcmN

P8.21 )(85.1)(),(21.1)(),(64.0)( ccwcmNcccwcmNbccwcmNa


23/23

11.1

cm786.02 r ; cm364.13 r ; cm384.14 r

11.2

cm700.11 r ; cm326.22 r ; cm047.43 r

11.3

Employing: os

100)( 2 ; cm2ss

cm881.51 r ; cm3216.52 r ; cm082.33 r

11.4

Employing: os

120)( 2 ;o

s70)( 4

cm000.11 r ; cm759.12 r ; cm724.03 r ; cm066.24 r

11.6

cm099.51 r ; cm177.12 r ; cm898.23 r ; cm225.64 r

Documents

Mechanics of Machines Cleghorn Answers