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Bài giảng Kinematics and dynamics of machines - Chapter 10: Gears and spur gear (Part 2) - Phạm Huy Hoàng

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GEAR TRAINS  
PHAM HUY HOANG  
I. Introduction  
1. Definition  
transmit and reduce  
Gear mechanisms arrange in  
various series and parallel  
combinations so that the driven  
gear of one mechanism is the  
driver for another mechanism.  
transmit and reduce  
distribute  
2. Classify  
Type Parallel-axis gear Spatial gear train  
train  
(axes cut or cross  
each other)  
(axes are parallel  
to each other)  
Moved axis  
All axes are fixed  
PLANAR NORMAL SPATIAL NORMAL  
GEAR TRAIN  
GEAR TRAIN  
There exists at least  
one moved axis  
PLANAR  
SPATIAL  
EPICYCLIC GEAR EPICYCLIC GEAR  
TRAIN TRAIN  
II. Planar Normal Gear Train  
1. Simplest planar normal gear train  
a. External gearing  
Two gears rotate in opposite  
directions  
z1  
z
2
1
i     
z
1
2
z2  
b. Internal gearing  
Two gears rotate in the  
same directions  
z  
1
2
i     
z  
2
1
z1  
z2  
2. Planar normal gear train  
z
z
bd j  
cd j  
j
k
1
i   (1)  
12  
2
j
ωi : rotation speed of gear i;  
k : number of gear pairs involving to external gearings;  
zbd i : tooth number of driven gear i;  
zcd j : tooth number of driver gear j;  
1
i   
16  
6
z z z z z  
4
2 3 4 5 6  
(1)  
' ' '  
z z z z z  
1 2 3 4 5  
z z z z  
2 3 4 6  
   
' ' '  
z z z z  
1 2 3 4  
Gear 5 is a driver gear as well as a driven gear. It changes the  
rotation direction, but not involves to the change of ratio.  
III. Spatial Normal Gear Train  
z
bd j  
j
1
i    
12  
z  
2 cd j  
j
ωi : rotation speed of gear i;  
zbd i : tooth number of driven gear i;  
zcd j : tooth number of driver gear j;  
: inward  
: outward  
z z z  
2 3 4  
1
i    
14  
' '  
z z z  
4
1 2 3  
z
2
III. Planar Epicyclic Gear Train  
1. Simplest planar epicyclic gear  
trains  
z
1
External gearing  
Crank arm/carrier  
Sun gear  
Planet gear  
z
2
How many degree of  
freedoms (dof)?  
z
1
External gearing  
Number of moving links: n = 3  
Number of higher pairs : p4 = 1  
Number of lower pairs : p5 = 3  
W = 3n – (p4 + 2p5) = 2  
Crank arm/carrier  
Ring gear  
z
2
Planet gear  
z
1
Internal gearing  
z
2
How many degree of  
freedoms (dof)?  
z
1
Internal gearing  
Number of moving links: n = 3  
Number of higher pairs : p4 = 1  
Number of lower pairs : p5 = 3  
W = 3n – (p4 + 2p5) = 2  
z
2
  
1 c  
z
z
2
1
c
1
i   
12  
1  
  
2 c  
z
1
z
2
  
1 c  
z
z
2
1
c
0
i   
12  
1  
  
2 c  
z
1
2. Double epicyclic gear train  
z
z
z
2
2
z
3
1
z
z
2
2
External – External  
z
z
1
3
z
2
z
z
2
z
1
z
2
3
Crank arm/carrier  
Sun gear  
z
z
2
External – Internal  
Planet gear  
Ring gear  
z
1
3
z
2
z
z
2
z
3
1
z
2
z
z
2
Internal – Internal  
z
3
1
z
2
z
z
2
z
1
3
How many degree of freedoms (dof)?  
Number of moving links: n = 4  
Number of higher pairs : p4 = 2  
Number of lower pairs : p5 = 4  
W = 3n – (p4 + 2p5) = 2  
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