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

turning pair, 7; turning pair, 10; sliding pair, 0; sliding pair, 0; rolling pair, 0; rolling pair, 0; 2 dof pair,0; 2 dof pair,0; m = 1 m = 1

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

turning pair, 0; turning pair, 0; sliding pair, 5; sliding pair, 3; rolling pair, 0; rolling pair, 0; 2 dof pair,0; 2 dof pair,2; m = -1 (by inspection, m = 1) m = 1

P1.5 (a)n = 4; (b) n = 8

turning pair, 3; turning pair, 9; sliding pair, 0; sliding pair, 0; rolling pair, 2; rolling pair, 2; 2 dof pair,0; 2 dof pair,0; m = -1 (by inspection, m = 1) m = -1 (by inspection, m = 1)

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) l < s + p + q, link can form a mechanism (ii) s + l = p + q, change point mechanism (c) (i) l < s + p + q, link can form a mechanism (ii) s + l < p + q, class I four-bar kinematic chain, crank-rocker four-bar mechanism (d) (i) l < s + p + q, link can form a mechanism (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) l < s + p + q, link can form a mechanism (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)

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

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

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

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)

(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)

876 =&& rad/sec2 CCW 3.19(c)

336 =&& rad/sec2 CCW 3.20 (c)

(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/sec2 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)

413 =&& rad/sec2 CCW 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/sec2

p4.1 w)rad/sec(cc212.02 =& ov 70@sec)/(53.132 = inv s

p4.2 3&& =42.3 (ccw)sec2rad

p4.3

sin)sin( 21

2+= rr

sinsin 21

3rr = =2r&

sin

)cos( 221 +&r

sin)sin()cos( 2

221221

2++= &&&&& rrr

sinsin 21

3rr =

sin

cos 2213

&& rr =

sinsincos 2

221221

3

&&&&& rrr =

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/sec 2 @-101.8 o

p4.7 (a) ov 0@sec/2690 2cmaB = (b) ov 225@sec/2990 2

42cma s AA =

p4.8 (ccw)sec/69.13 rad=& p4.9 (a) sec/)7.10671.4( cmjivc

vvv = (b) sec/)8.241( cmjvB

vv = 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

cmv PP =

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( cmjivc

vvv = p4.15 (a) sec/1.44

13cmv DD =v @16.3 o

(b) )sec(/13.23 cwrad=&

5.1 5.97d in= 5.2 450 min

rev = 5.3 66.3 rpm = 5.4 (a) velocity ratio=1.333 (b) 3 30N = 5.5 3 2100 20N N= = 5.6 3 225 15 2356 sec

mmN N pitch line velocity= = = 5.7 (a) 64BN = (b) c=13 in (c) 0.785cp in= (d) 16.5in (e) 15.49 in 5.8 (a) 2 323.3 11.7d in d in= = (b) 3 5.48br in= (c)

3cp in=

(d) c=17.5 in (e) 600rpm CCW (f) m=1.75 5.9 5.10 5.11 3 117N = (a) 2 12.56cp mm= (b) 3 219.9br mm=

(c) 4 192d mm= (d) c=282 mm

5.12 (a) 3 2.69br in= (b) c=4.65 in (c ) 0.395cp 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) 2.27

Bbr in=

(d) 0.131 in 5.14 (a) Z=0.546 in (b) 1.48cm = 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

P6.1 (a). 0.75 (b). ( )56.25 rpm CCW P6.2

(a). 2 3 4 515 120 150 75N N N N= = = =

(b). 2 3 4 539 120 150 115N N N N= = = = P6.3

Choose 1 8150 250N N= =

5 6 1

3 4 2

2 7 3

229 171 0.8035182 218 0.5009267 133 0.2989

N N eN N eN N e

= = == = == = =

P6.4

Select 6 732 64N N= =

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

Select 6 60N =

11 24N =

10 16N =

P6.5 1 2 3 4 5

All locked at x rpm

x x x x x

Fix 2, move 1 at

y rpm y 0 1

3

N yN

14

N yN

15

N yN

Absolute rpm

x y+ x 13

Nx yN

14

Nx yN

+ 15

Nx yN

+

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 0 1

3

N yN

13

N yN

1 43 5

N N yN N

1 43 5

N N yN N

1 4 63 5 7

N N N yN N N

Absolute rpm

x y+ x 13

Nx yN

13

Nx yN

1 43 5

N Nx yN N

+ 1 43 5

N Nx yN N

+ 1 4 63 5 7

N N Nx 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 0 13

N yN

13

N yN

1 43 5

N N yN N

1 43 6

N N yN N

Absolute rpm

x y+ x 13

Nx yN

13

Nx yN

1 43 5

N Nx yN N

+ 1 43 6

N Nx yN N

+

P6.8

10 4

19825

=

10 264 rpm = P6.9

(a). 1 4 63 5 7

1 N N NeN N N

= +

(b). 1

3 5 7

1 4 6

1 N N NeN N N

=

(c). 1

3 5 7

1 4 6

1 N N NeN N N

=

(d). 1 54 6

1 N NeN N

=

P6.10 56 rpm P6.11

(a). (i) 1412.5 rpm

(ii) 2087.5 rpm

(b). 3n = P6.12

(a). 405 turns (opposite to indicated direction) 1108turns (in the indicated direction)

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

P6.13

(a). ( )9442 rpm CW (b). ( )6328 rpm CW P6.14

3 105N = 0.429e =

P6.15

19.61 rad s

P6.16

(a) 21

17

e = (b) 21

17

e =

P6.17 P6-18 P6-19

(a). 1 4 481

1 3 7 7

1N N NeN N N N

= +

(b). 4

78

1 4

71

NNe N

N=

P6-18 1 17542 rpm(opposite to output)c x = =

P6-19 2 5198.7 rpm(CW) =

P6-20

1 1

1 2 2

11 1 2

4

2 62 2

5 7

0

x yx x y

Nx y xNN Nx yN N

+ = = + = + =

,

condition: 1 4

2 6 5 7

1 1 0 01 0 1 1

det 01 / 1 00 0 1 /

N NN N N N

P6-21

16

17

2

2

1 1 1 00

31 0 1 022

01 51/ 20 0 0

00.48 0 1 1

xN

yN

xy

=

required relation: 6

7

1 1 1 031 0 122det 0

1 51/ 20 0 00.48 0 1 1

NN

=

P6-22 (a) 2 1 28.571 rpm(CCW)x = = (b) 2 1 28.571 rpm(CCW)x = =

P6-23 output 3 5750 rpm, 700 rpm = = P6-24 (a) Carrier makes 12 rotation clockwise.

Angular displacement is 30rortations.

(b) 4 37c

f g +=

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)fT =

P6-27 7 19.9 rad/s =

P6-28 316.67 NmfT =

P6-29 (a) 3 /5 inp =

(b) 190 rpm(same direction as the input)c = (c) 324.3 NmfT =

P6-30 2 7312.5 rpm(same direction as output) = 546.84 Nm(same direction as output)fT =

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)

(d)

'C

270'D

270'A

'E

1

2

34

5

P6-33 (a) 2

1.496 inbr = (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

P7.2

= cos1

2Ls = 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 Interval

End of Interval

(deg)

1 0.5 +2.0 0 1203601.50.5 = 120

2 0.3 0 120 1923601.50.3120 =+ 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

(a) one rotation occurs in 1.5sec

sec188.440

sec666.0

sec5.11 radrpmrevrev ==== 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 ;

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 Mpa796.0P8.10 )(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

11.1cm786.02 r ; cm364.13 r ; cm384.14 r

11.2cm700.11 r ; cm326.22 r ; cm047.43 r

11.3

Employing: os 100)( 2 ; cm2ss

cm881.51 r ; cm3216.52 r ; cm082.33 r11.4

Employing: os 120)( 2 ; os 70)( 4

cm000.11 r ; cm759.12 r ; cm724.03 r ; cm066.24 r11.6

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

Chapter 1Chapter 2Chapter 3Chapter 4Chapter 5Chapter 6Chapter 7Chapter 8Chapter 11

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