P1.1(a)n = 6; turning pair, 5; sliding pair, 1; rolling pair, 1; 2 dof pair,0; m=1 (b) n = 6 turning pair, 5; sliding pair, 2; rolling pair, 0; 2 dof pair,0; m=1

P1.2(a)m = 1 (b)m = 1

P1.3(a)n = 6; turning pair, 7; sliding pair, 0; rolling pair, 0; 2 dof pair,0; m=1 (b) n = 8 turning pair, 10; sliding pair, 0; rolling pair, 0; 2 dof pair,0; m=1

P1.4(a)n = 4; turning pair, 0; sliding pair, 5; rolling pair, 0; 2 dof pair,0; m = -1 (by inspection, m = 1) (b) n = 4 turning pair, 0; sliding pair, 3; rolling pair, 0; 2 dof pair,2; m=1

P1.5(a)n = 4; turning pair, 3; sliding pair, 0; rolling pair, 2; 2 dof pair,0; m = -1 (by inspection, m = 1) (b) n = 8 turning pair, 9; sliding pair, 0; rolling pair, 2; 2 dof pair,0; 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 (b) r3 > 0 (cm)

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 (b)2 = 0 or 180 vs max =v2 = 52.36 (c)2 = 0 or 180 (cm/s) (cm/s)

a4 max =a2N = 548.1 (cm/s2)

P2.3(a) 2 = 53.1 or 306.9 2 = 0 (b)v6 = 150 (cm/s),

P2.4 (a)( 4,avg )cw = 7.22 (b)( 4,avg )ccw = 7.58(c)TR = 0.953

(rad/s) (rad/s)

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.

P2.120 r2 0.76 (cm)

P2.13r2 4.95 P2.14 (a)m = 1 (cm)

Cleghorn Ch3 answers 3.1 v B = 60 in/sec, vC = 39.5 in/sec, v D = 15 in/sec, 3.2 v3 = 47.1 in/sec 3.3 v 4 = 6.28 cm/sec 3.4 & (a) 4 = 21.1 rad/sec CW (b) v D = 20.52 in/sec 3.5 v D = 84 cm/sec 3.6

&6 = 3.7 rad/sec CW3.7 vC = 2.89 in/sec 3.8 v D = 7.2 in/sec 3.9

& (a) 3 = 6.28 rad/sec CCW (b) v 4 = 40.84 cm/sec to the left3.10 (a) v P 2 = 5.6 cm/sec (b) v P 3 = 13.6 cm/sec (c) v P 3 P 2 = 9.6 cm/sec

(d)

&3 = 1.8 &2

3.11 (a) v P 2 = 18.4 cm/sec (b) v P 3 = 18 cm/sec (c) v P 3 P 2 = 11.2 cm/sec

(d)

&3 = 1.7 &2

3.12 (b)

(i) v B = 25.13 in/sec@ 45 (ii) vC = 24.4 in/sec@ 29 (iii) v D = 27.5 in/sec@ 0 (iv) v BD = 20.0 in/sec@ 118.1 & (v) 3 = 6.7 rad/sec CCW3.13(b)

(i) v B = 22.0 in/sec@ 30 (ii) vC = 8.1 in/sec@ 18& (iii) v D = 13.1 in/sec@ 10 (iv) 3 = 5 rad/sec CCW & (v) 4 = 5.24 rad/sec CCW3.14(b)

(i) v D = 45 cm/sec@ 98 (ii) v E = 24 cm/sec@ 180 & & (iii) 3 = 6.1 rad/sec CW (iv) 5 = 16 rad/sec CCW3.15(c)s & & (i) a B 2 B 3 = 120 cm/sec2 (ii) &3 = 27.1 rad/sec2 CW, &5 = 13.9 rad/sec2 CCW

3.16(c)

& &7 = 154 rad/sec2 CCW3.17(c)

& &5 = 80 rad/sec2 CW3.18(c)

& &6 = 87 rad/sec2 CCW3.19(c)

& &6 = 33 rad/sec2 CCW3.20 (c)

& & (i) a B 6 = 1280 cm/sec2 (ii) &3 = 48 rad/sec2 CW, &6 = 160 rad/sec2 CW & (d) &6 = 60.6 rad/sec2 CW3.21(c) & (i) &4 = 634 rad/sec2 CW (ii) aC = 650 cm/sec2 3.22(c) s (i) a B 2 B 4 = 1880 in/sec2 & (ii) &2 = 488 rad/sec2 CW 3.23(d)

& & &3 = 177 rad/sec2 CCW, &4 = 353 rad/sec2 CCW3.26 (b)

& & (i) 3 = 2.9 rad/sec CW, 4 = 10.8 rad/sec CW (ii) v D = 59 cm/sec, v E = 102 cm/sec, v F = 42 cm/sec (d) & & (i) &3 = 286 rad/sec2 CCW, &4 = 490 rad/sec2 CCW (ii) a D = 1780 cm/sec2 , a E = 3240 cm/sec2 , a F = 2780 cm/sec23.27(c)

& &3 = 41 rad/sec2 CCW3.28(c)

& & (i) &3 = 25 rad/sec2 CW, &5 = 220 rad/sec2 CCW (ii) a D = 30 cm/sec23.29(b) (i) vG = 43 cm/secc (ii) a E 5 E1 = 627 cm/sec2

p4.1

&2 = 0.212rad/sec(ccw)& &3 =42.3r2 =&& r2 && r3

vs v32 = 1.53(in / sec) @ 70 o

p4.2p4.3

rad (ccw) sec 2

& r1 sin( 2 + ) r sin 2 r cos( 2 + ) & r3 = 1 r2 = 1 2 sin sin sin 2 & & & r & cos( 2 + ) r1 2 sin( 2 + ) r sin 2 r cos 2 & = 1 2 r3 = 1 r3 = 1 2 sin sin sin 2 & & r & cos 2 r1 2 sin 2 = 1 2 sin

p4.4 p4.5

v vc = 102.3(cm / sec) @119.4 o

& (a) 3 = 2.39rad / sec(cw)(b) 37.4 cm/sec @71.9 o vc (c) a A2 A3 = 179 cm/sec 2 @-18.1 o

p4.6

& (a) 3 = 7.29rad/sce (cw)c (b) a B3 B4 = 718 cm/sec 2 @-101.8 o

p4.7

v (a) a B = 2690cm / sec 2 @ 0 ovs (b) a A2 A4 = 2990cm / sec 2 @ 225o

p4.8 p4.9

&3 = 1.69rad / sec(ccw)v v v (a) vc = (4.71i 106.7 j )cm / sec v v (b) v B = (241.8 j )cm / sec & (a) 3 = 7.39rad / sec(cw)

p4.10

v (b) v B3 B1 = 29.7cm / sec @-16.8 oc (c) a B3B1 = 439cm / sec 2 @ 106.8o

p4.11

& (a) 3 = 28.8rad / sec(cw)v (b) v P2 P3 = 140cm / sec@ 215.8o

p4.12 p4.13

v v v vc = (10.98i + 11.41 j )in / sec 1 v & cos 2 ) = 11.78 sin 2 + 0.577 cos 2 in / sec (a) vc = r2 2 (sin 2 + 3v (b) v B4 B2 = 13.6 cos 2 in / sec (c) && = 106.8 sin 2 in / sec 2 r3v (d) v B4 B2 = 13.6in / sec

max

p4.14

& (a) 3 = 8.5rad / sec(ccw) v v v (b) vc = (177.2i 19 j )cm / sec v (a) v D3D1 = 44.1cm / sec @16.3 o & (b) 3 = 2.13rad / sec(cw)

p4.15

5.1 d = 5.97 in 5.2 = 450 rev min

5.3 = 66.3 rpm 5.4 (a) velocity ratio=1.333 (b) N3 = 30 5.5 N 3 = 100 N 2 = 20 5.6 N 3 = 25 5.7 (a) N B = 64 (b) c=13 in (c) pc = 0.785 in (d) 16.5in (e) 15.49 in 5.8 (a) d 2 = 23.3 in (b) rb 3 = 5.48 in (c) pc = N 2 = 15 pitch line velocity = 2356 mm sec

d3 = 11.7 in

3

in

(d) c=17.5 in (e) 600rpm CCW (f) m=1.75 5.9 5.10 5.11 N 3 = 117 (a) pc 2 = 12.56 mm (b) rb 3 = 219.9 mm (c) d 4 = 192 mm (d) c=282 mm 5.12 (a) rb 3 = 2.69 in (b) c=4.65 in (c ) pc = 0.395 in (d) 4 = 5 = 18.4

(e) d 4 = 3.52 in (f) 3.76 in 5.13 (a) 2.17 in (b) N B = 60 (c) rbB = 2.27 in

(d) 0.131 in 5.14 (a) Z=0.546 in (b) mc = 1.48 5.15 (a) rb 4 = 1.496 in (b) c=3.501 in (c) mc = 1.93 (d) 0.55 in (e) 3 = 24.6 (f) d3 = 10.85 in (g) 10.53 in

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

P6.2 (a). N 2 = 15 N 3 = 120

N 4 = 150 N 4 = 150

N 5 = 75 N 5 = 115

(b). N 2 = 39 P6.3

N 3 = 120

Choose N1 = 150 N 5 = 229 N 2 = 267 P6.4 Select N 6 = 32

N8 = 250

N 6 = 171 e1 = 0.8035 N 7 = 133 e3 = 0.2989

N 3 = 182 N 4 = 218 e2 = 0.5009

N 7 = 64

N 4 = 69 N 5 = 48 N8 = 27Select N 6 = 60

N 9 = 48

N11 = 24 N10 = 16

P6.5 1 All locked at x rpm Fix 2, move 1 at y rpm Absolute rpm P6.6 1 All locked & move at x rpm Fix 2, move 1 at y rpm Absolute rpm 2 3 4 5 6 7 x y 2 x 0 3 x N1 y N3 4 x N1 y N4 5 x N1 y N5

x+ y

x

x

N1 y N3

x+

N1 y N4

x+

N1 y N5

x

x

x N1 y N3N1 y N3

x N1 y N3N1 y N3

xN1 N 4 y N3 N5 x+ N1 N 4 y N3 N5

xN1 N 4 y N3 N5 x+ N1 N 4 y N3 N5

x N1 N 4 N 6 y N3 N5 N7x+ N1 N 4 N 6 y N3 N5 N7

y

0

x+ y

x

x

x

P6.7 1 All locked, move at x rpm Fix 2, move 1 at y rpm Absolute rpm 2 3 4 5 6

x

x

x

x

x

x

y

0

N1 y N3 N1 y N3

N1 y N3 N1 y N3

N1 N 4 y N3 N5 x+ N1 N 4 y N3 N5

N1 N 4 y N3 N6 x+ N1 N 4 y N3 N6

x+ y

x

x

x

P6.8

10 =

198 4 25

10 = 264 rpmP6.9 (a). e = 1 +

N1 N 4 N 6 N3 N5 N71

NNN (b). e = 1 3 5 7 N1 N 4 N 6 NNN (c). e = 1 3 5 7 N1 N 4 N 6 (d). e = 1

1

N1 N 5 N4 N6

P6.10 56 rpm P6.11 (a). (i) 1412.5 rpm (ii) 2087.5 rpm (b). n = 3 P6.12 (a). 405 turns (opposite to indicated direction) 10 1 turns (in the indicated direction) 8

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

P6.13 (a). 9442 rpm ( CW ) (b). 6328 rpm ( CW ) P6.14

N 3 = 105e = 0.429P6.15 19.61 rad P6.16 (a) e2 = 1

s

1 1 (b) e2 = 1 7 7

P6.17 P6-18 P6-19 N1 N N (a). e8 = 4 1 4 1 N1 + N 3 N 7 N 7 N4

(b). e8 =1

N7 1

N4

N7

P6-18 c = x1 = 17542 rpm(opposite to output) P6-19 2 = 5198.7 rpm(CW)

x1 + y1 = x = x + y 2 2 1 N P6-20 x1 1 y1 = x2 , N4 N2 N6 y2 = 0 x2 + N5 N7

1 1 1 0 condition: det 1 N1 / N 4 0 0

1 1 0 1 0 1 N 2 N6 / N5 N7 0 0

1 1 0 1 x1 0 3 N6 1 y 1 0 0 22 N 7 1 = P6-21 x 0 1 51/ 20 0 0 2 y 0 0.48 0 1 1 2 1 0 1 1 3 N6 1 0 1 22 N 7 = 0 required relation: det 1 51/ 20 0 0 0.48 0 1 1 P6-22 (a) 2 = x1 = 28.571 rpm(CCW) (b) 2 = x1 = 28.571 rpm(CCW) P6-23 output 3 = 750 rpm, 5 = 700 rpm P6-24 (a) Carrier makes 12 rotation clockwise. Angular displacement is 30rortations. 4 f + 3g (b) c = 7

P6-25 f = 1.4 rpm(CCW) P6-26 (a) e = 0.4985, c = 249.25 rpm(same direction as the input) (b) T f = 564.71 Nm(opposite to input ratation) P6-27 7 = 19.9 rad/s P6-28 T f = 316.67 Nm P6-29 (a) p3 = / 5 in (b) c = 190 rpm(same direction as the input) (c) T f = 324.3 Nm P6-30 2 = 7312.5 rpm(same direction as output) T f = 546.84 Nm(same direction as output)

P6-31 (a) c = 34.9 rpm(CCW) (b) 2 / c = 258 rpm(CCW) (c) max. number: 4 P6-32 (a) x = 7 / 4 rev(CCW) (b) 7.15 rev(CCW) (c) 2.75 rev(CW)

(d)

270 1A'

2C'D'

270

3 4

5

E'

P6-33 (a) rb = 1.496 in2

(b) c = 4.77 in (c) 1.64 (d) N 4 = 39, N 5 = 19, N 6 = 33, N 7 = 27 (e) 0.517 in (f) 4 = 14.8 (g) 4 = 0 (h) d5 = 3.127 in (i) 3.455 in P6-34 (a) 159.3 rpm(CW) (b) 1614 rpm(CC W) (c) max. number: 8

P7.2s= L 1 cos = 120L = 35 2 (deg)

cos

s = (deg) 0 2.4 8.8 17.5 26.3 32.7 35.0

0 20 40 60 80 100 120

1 3/2 1/2 0 -1/2 - 3/2 -1

P7.4Required 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

P7.6Duration (sec) 1 0.5 Motion (cm) +2.0 Cam Rotation (deg) Start of Interval 0 End of Interval (deg)

0.5 360 = 120 1.5120 + 0.3 360 = 192 1.5 360

12072 168

23

0.30.7

0-2.0

120192

(a) one rotation occurs in 1.5sec =

rev rad 1rev = 0.666 = 40rpm = 4.188 ccw* ( *direcrtion selected ) 1.5 sec sec sec

(b) maximum velocity and acceleration of follower occur during interval I ( L = 2.0cm ; = 120 = 2.094rad ; = 60) Form Figure 7.13 : s = 2 L 2

;

0 < < 2

s = 4 L s max

4.188 cm 2.094 = 8.0 sec 2

= s @ = 60 = 4 2.0 2 2

4.188 s = 4 L = 4 2.0 = 32.0 cm 2 sec 2.094

P7.10Nominal values : d b = 2.0cm ; d r = 1.0cm ; s = 0 (a) d b = 2.19cm ; d r = 1.0cm ; s = 0 (b) d b = 2.00cm ; d r = 1.19cm ; s = 0 (c) d b = 2.0cm ; d r = 1.00cm ; s = 0.06cm

P7.12Nominal values : d b = 3.0cm ; s = 0 (a) d b = 3.39cm ; s = 0 (b) d b = 3.00cm ; s = 0.09

Chapter 8 Ans:P8.1 P8.2 P8.3 P8.4 P8.5 P8.6 P8.7

Graphical Force Analysis of Planar Mechanics

F12 1500 N , Q 1800 N ( a ) P lb (b)Q N 14 , 129

( a ) M 12 28 N .032m .090 N .m( ccw ), (b) F12 28 N , F13 24 N 0 0P .5lb , F41 .5lb 157 17

F 20lb M 12 F32 d .4lb .8in .1in ( cw) 3 1 6 lb8.2 Mpa

P8.8 M 12 N ( cw) 900 cm P8.9 0.796 Mpa P8.10 M 2.49 N (cw) cm P8.11 P8.12

M 12 .5N ( cw) 0 mF .5lb 10

P8.13 ( a )9300in ( cw), (b)55.5in ( ccw ), (c )89.7in ( ccw ), ( d )9155in (cw) lb lb lb lb P8.14 P8.15 P8.16 P8.17 P8.18 P8.19 P8.20 P8.210.32 N (cw) m 4.16 N ( cw) cm ( a )165in ( ccw ), (b)710in ( ccw ), ( c)875in (ccw ) lb lb lb ( a )0.33N (ccw ), (b)0.71N ( ccw ), (c )1.04 N ( ccw ) m m m 2.7 N ( ccw ) m 0.011N (ccw ) m 8.1N ( ccw ) cm ( a )0.64 N (ccw ), (b)1.21N (ccw ), ( c )1.85 N ( ccw ) cm cm cm

11.1 r2 .786cm ; r3 .364cm ; r4 .384cm 0 1 1 11.2 r1 .700cm ; r2 2.326cm ; r3 4.047cm 1 11.3 Employing: ( ) s o ; s s 2cm 100 2

r1 .881cm ; r2 .3216cm ; r3 .082cm 5 5 311.4 Employing: ( ) s o ; ( ) s 70 o 120 2 4

r1 .000cm ; r2 .759cm ; r3 0.724cm ; r4 2.066cm 1 111.6 r1 .099cm ; r2 .177cm ; r3 2.898cm ; r4 .225cm 5 1 6