9장. 기어 열(Chap 9. Gear Trains)

The earliest known reference to gear trains is

in a treatise by Hero Alexandria. Gear trains

are widely used in all kinds of mechanisms

and machines from automobile engines to

industrial robots. Whenever a change in the

speed or torque of a rotating device is needed,

a gear train or one of its cousins, the belt or

chain drive mechanism, will usually be used.

This chapter will explore the theory of gear

teeth action and its ubiquitous devices for

motion control.

(Excerpted from the textbook)

기어 열

9.9 유성 기어열(Epicyclic or Planetary gear trains)

Sun

Planet

Ring

Arm

Fixed

(Excerpted from the textbook)

기어 열

9.9 유성 기어열(Epicyclic or Planetary gear trains)

(Excerpted

from the textbook)

기어 열

9.9 유성 기어열(Planetary gear trains)

12

3

4

200 rpm

100 rpm

• 표를 이용한 속도 해석(Velocity analysis using the tabular method)

Ring

Sun

Planet

Arm

wgear = warm + wgear/arm

2

3

4

Gear # wgear warm wgear/arm

Gear ratio

(?)

-200

-200

-200

-100 +100

NS = 40NP = 20NR = 80

(-) 40/20

(+) 20/80-200

-50

-400

-250

기어 열

9.9 유성 기어열(Planetary gear trains)

12

3

4

200 rpm

• 표를 이용한 속도 해석(Velocity analysis using the tabular method)

Ring

Sun

Planet

Arm

wgear = warm + wgear/arm

2

3

4

Gear # wgear warm wgear/arm

Gear ratio

(?)

-200

-200

-200

-600 -400

NS = 40NP = 20NR = 80

(-) 20/40

(+) 80/20+800

+200

+600

0

Fixed

기어 열

유성 기어열 : 속도 해석

기어 열

유성 기어열 : 속도 해석

기어 열

Ferguson’s Paradox

Sun Gear #2

Sun Gear #3

Sun Gear #4

Arm

PlanetGear

NS2 = 100NS3 = 99NS4 = 101NP = 20

(Fixed)

100 rpm

Ferguson’s Paradox

• Velocity Analysis (Tabular Method)

2

5

3

5

4

Gear # wgear warm wgear/arm

+100

+100

+100

+100

+100

0 -100(-) 100/20

(-) 20/99+500

-101

Gear ratio

#5

(-) 20/101+500

-99

+600

-1

+600

+1

Tandem Gear Train

• Velocity Analysis (Tabular Method)

Ring #2 Ring #3

ArmPlanet#2

Sun

Planet#3

(Fixed)

(Input)

(Output)

NS = 47NP2 = 20, NP3 = 23NR2 = 87, NR3 =100

R2

P2

S

P3

R3

Gear # wgear warm wgear/arm

+100

+100

+100

+100

+100

0 -100(+) 87/20

(-) 20/47-435

+185

Gear ratio

(+) 23/100-435

-100.05

-335

+285

-335

-0.05

in

outVm

w

w=

285

05.0-= 410754.1 --=

기어 열

Tandem Gear Train

• Velocity Analysis (Tabular Method)

Ring #2 Ring #3

ArmPlanet#2

Sun

Planet#3

(Fixed)

(Input)

(Output)

NS = 47NP2 = 20, NP3 = 23NR2 = 87, NR3 =100

Ring #4 Ring #5

ArmPlanet#4

Sun #2

Planet#5

(Fixed) (Output)

R2

P2

S

P3

R3

Gear # wgear warm wgear/arm

+100

+100

+100

+100

+100

0 -100(+) 87/20

(-) 20/47-435

+185

Gear ratio

(+) 23/100-435

-100.05

-335

+285

-335

-0.05

in

outVm

w

w=

285

05.0-= 410754.1 --=

( ) 824

V 10078.310754.1m -- =-=

Differentials (차동기어)

InstantaneousCenter

23

4

NB2=NB3=NB4 Driving Axis

Left wheel Right wheel

Arm

FrFl

Fr > Fl

F

T (engine)

기어 열

• Straight : wL = wR = v

• Right Turn

wL = v + wwR = v – wwArm = v

Differentials (차동기어)

• Velocity Analysis (Tabular Method)

w(CCW)

2

3

4

w(CCW)

2

3

4

Gear # wgear warm wgear/arm

v

v

v

w-1

+1-w

-w

v+w

v-w

v-w

Gear ratio

Harmonic Drive

NR = 81NF = 80

Rigid (to robot joint)

Wave generator(No gear)to motor

Flexible (Fixed)

81

1

Motor

intJo =w

w

Harmonic Drive

Flexible

Rigid

Gear wgear warm wgear/arm

1

1

-1(+) 80/81

-80/81

Gear ratio0

1/81

기어 열

9.10 유성 기어열 효율 (Efficiency of Planetary gear trains)

(Excerpted from the textbook)