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)