Machine Design Databook Episode 3 part 7 potx

For external ratchet

For internal ratchet

The ratio of a=d (internal ratchet)

The module

The bending moment on pawl

The bending stress

The diameter of pawl pin

¼ 148 to 178 ð24-266Þ

¼ 178 to 308 ð24-267Þ

a=d ¼ 0:35 to 0:43 ð24-268Þ

m ¼ 2 3

ffiffiffiffiffiffiffiffiffiffiffiffi

Mt

z ba s

ð24-269Þ

Mb1 ¼ Fne2 ð24-270Þ

b ¼ 6Mb1

bs2

1

þ

Fn

bs1

 ba ð24-271Þ

d1 ¼ 2:71 3

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

Fn

2ba b

2 þ th

s

ð24-272Þ

where th ¼ thickness of hub on pawl

Particular Formula

p

s2

s1

r1

r2

h1

d2

2

h2

FIGURE 24-53 Definitions and dimensions of ratchet wheel.

TABLE 24-23

F b

Material kN/m lbf/in MPa kpsi

Cast iron 49–98 280–560 19.5–29.5 2.85–4.27

Steel or

cast steel

98–196 560–1120 39–68.5 5.69–10.0

Hardened

steel

196–392 1120–2240 58.8–98 8.54–14.23

MISCELLANEOUS MACHINE ELEMENTS 24.81

Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com)

Copyright © 2004 The McGraw-Hill Companies. All rights reserved.

Any use is subject to the Terms of Use as given at the website.

MISCELLANEOUS MACHINE ELEMENTS

24.9 GENEVA MECHANISM

SYMBOLS2,3

a ¼ r1

sin  center distance, m (in)

F1 the component of force acting on the crank or the driving shaft

due to the torque, M1t, kN (lbf ) (Fig. 24-57)

F2 the component of force acting on the driven Geneva wheel shaft

due to the torque M2t, kN (lbf ) (Fig. 24-57)

F2ðmaxÞ maximum force (pressure) at the point of contact between the

roller pin and slotted Geneva wheel, kN (lbf )

FðmaxÞ the component of maximum friction force at the point of

contact due to the friction torque M2t, on the driven Geneva

wheel shaft, kN (lbf )

FiðmaxÞ the component of maximum inertia force at the point of contact

due to the inertia torque on the driven Geneva wheel shaft,

kN (lbf )

i ¼ z
2

z gear ratio

J polar moment of inertia of all the masses of parts attached to

Geneva wheel shaft, m4 (in4

)

k the working time coefficient of the Geneva wheel

M1t total torque on the driver or crank, N m (lbf in)

M2t total torque on the driven or Geneva wheel, N m (lbf in)

M2ti inertia torque on the Geneva wheel, N m (lbf in)

M2t friction or resistance torque on Geneva wheel, N m (lbf in)

n0 speed, rps

n speed, rpm

P power, kW (hp)

r1 radius to center of driving pin, m (in)

r2 radius of Geneva wheel, m (in)

r

0

2 distance of center of semicircular end of slot from the center of

Geneva wheel, m (in)

ra2 outside radius of Geneva wheel, which includes correction for

finite pin diameter, m (in)

rp pin radius, m (in)

Rr ¼ r2

r1

radius ratio

t total time required for a full revolution of the driver or crank, s

ti time required for indexing Geneva wheel, s

tr time during which Geneva wheel is at rest, s

v velocity, m/s

z number of slots on the Geneva wheel

crank angle or angle of driver at any instant, deg (Fig. 24-54)

2a angular acceleration, m/s2 (ft/s2

)

angular acceleration of Geneva wheel, m/s2 (ft/s2

)

m angular position of the crank or driver radius at which the

product ! 2a is maximum, deg

angle of the driven wheel or Geneva wheel at any instant, deg

(Fig. 24-54)

 ¼ r1

a the ratio of the driver radius to center distance

 efficiency of Geneva mechanism

24.82 CHAPTER TWENTY-FOUR

Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com)

Copyright © 2004 The McGraw-Hill Companies. All rights reserved.

Any use is subject to the Terms of Use as given at the website.

MISCELLANEOUS MACHINE ELEMENTS

 locking angle of driver or crank, rad or deg

 ratio of time of motion of Geneva wheel to time for one

revolution of driver or crank

 ¼ 360

2z semi-indexing or Geneva wheel angle, or half the angle

subtended by an adjacent slot, deg (Fig. 24-54)

crank or driver angle, deg (Fig. 24-54)

! ¼ 2n

60 angular velocity of driver or crank (assumed constant), rad/s

!1, !2 angular velocities of driver or crank and Geneva wheel,

respectively, rad/s

a1 β

α

φ

ψ

a2

a3

ω2

r2

r1

ω1

a

FIGURE 24-54 Design of Geneva mechanism.

The angular velocity (constant) of driver or crank

Gear ratio

The semi-indexing angle or Geneva wheel angle or

half the angle subtended by two adjacent slots

The angle through which the Geneva wheel rotates

EXTERNAL GENEVA WHEEL

The angle of rotation of driver through which the

Geneva wheel is at rest or angle of locking action

(Fig. 24-55)

The crank or driver angle

!1 ¼ 2n

60 ð24-273Þ

i ¼ angle moved by crank or driver during rotation

angle moved by Geneva wheel during rotation

i ¼ z
2

z ð24-274Þ

 ¼ 360

2z or 

z ð24-275Þ

2 ¼ 360

z or 2

z ð24-276Þ

 ¼ 2ð
Þ ¼  þ 2 ¼ 

z

ðz þ 2Þ ð24-277Þ

¼ 

2
 ¼ ðz
2Þ

2z ð24-278Þ

Particular Formula

MISCELLANEOUS MACHINE ELEMENTS 24.83

Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com)

Copyright © 2004 The McGraw-Hill Companies. All rights reserved.

Any use is subject to the Terms of Use as given at the website.

MISCELLANEOUS MACHINE ELEMENTS

DISPLACEMENT

The center distance (Fig. 24-55)

The radius ratio

The ratio of crank radius to center distance

The relation between crank angle and Geneva wheel

angle

VELOCITY

The angular velocity of the Geneva wheel

The maximum angular velocity of Geneva wheel at

angle ¼ 0

a ¼ r1

sin  ð24-279Þ

Rr ¼ r2

r1

¼ cot  ð24-280Þ

 ¼ r1

a ¼ sin  ¼ sin 

z ð24-281Þ

¼ tan
1

 sin

1
 cos

ð24-282Þ

!2 ¼ d

dt ¼ ðcos
Þ

1
2 cos þ 2 !1 ð24-283aÞ

!2 ¼ sinð=zÞðcos
sin =zÞ

1
2 sinð=zÞ cos þ sin2 =z

!1 ð24-283bÞ

!2ðmaxÞ ¼

d

dt

max

¼ 

1
 !1

¼



sin 

z

1
sin 

z

!1 ð24-283cÞ

Particular Formula

ro2

r1

90”

r’2

a

ω1

ω2

ψ

φ

FIGURE 24-55 External Geneva mechanism.

24.84 CHAPTER TWENTY-FOUR

Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com)

Copyright © 2004 The McGraw-Hill Companies. All rights reserved.

Any use is subject to the Terms of Use as given at the website.

MISCELLANEOUS MACHINE ELEMENTS