1. Gearing

2. Very Simple Chain Theory16 32
Let us start with a very simple example

3. Building a Robot
Chain Theory 16 32

4. Building a Robot
Chain Theory 16 32

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Chain Theory 16 32

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Chain Theory 16 32

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Chain Theory 16 32

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Chain Theory 16 32

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Chain Theory 16 32

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Chain Theory 16 32

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Chain Theory 16 32

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Chain Theory 16 32

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Chain Theory 16 32

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Chain Theory 16 32

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Chain Theory 16 32

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Chain Theory 16 32

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Chain Theory 16 32

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Chain Theory 16 32

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Chain Theory 16 32

20. The Effect on Speed
When gears are combined, there is also an effect on the output speed.
To measure speed we are interested in the circumference of the gear, C= 2  r.
If the circumference of Gear1 is twice that of Gear2, then Gear2 must turn twice for each full rotation of Gear1.
=> Gear2 must turn twice as fast to keep up with Gear1.

21. Gearing Law for Speed
If the output gear is larger than the input gear, the speed decreases.
If the output gear is smaller than the input gear, the speed increases.
=> Gearing up decreases speed
=> Gearing down increases speed

22. Gearing Laws

23. Gearing Law for Speed
These are all important when you are building a robot

24. Gearing in robots
Gears are used to alter the output torque of a motor.
The force generated at the edge of a gear is equal to the ratio the torque and the radius of the gear (T = F r), in the line tangential to its circumference.
This is the underlying law behind gearing mechanisms.
force
F = T / r r
T = F r

25. Building a Robot Chain Theory
Torque output = Torque input radius output / radius input

26. Gear Radii and Force/Torque
By combining gears with different radii, we can manipulate the amount of force/torque the mechanism generates.
The relationship between the radii and the resulting torque is well defined
The torque generated at the output gear is proportional to the torque on the input gear and the ratio of the two gear's radii.

27. Example of Gearing
Suppose Gear1 with radius r1 turns with torque t1, generating a force of t1/r1 perpendicular to its circumference.
If we mesh it with Gear2, with r2, which generates t2/r2,
then t1/r1 = t2/r2
To get the torque generated by Gear2, we get: t2 = t1 r2/r1
If r2 > r1, we get a bigger torque,
if r1 > r2, we get a smaller torque.
torque t1 r1
force of t1/r1 r2
Forces are equal

28. Gearing Law for Torque
If the output gear is larger than the input gear, the torque increases.
If the output gear is smaller than the input gear, the torque decreases.
=> Gearing up increases torque
=> Gearing down decreases torque

29. Exchanging Speed for Torque
When a small gear drives a large one, torque is increased and speed is decreased. Analogously, when a large gear drives a small one, torque is decreased and speed is increased.
Gears are used in DC motors (which are fast and have low torque) to trade off extra speed for additional torque.
How?

30. Gear Teeth
The speed/torque tradeoff is achieved through the numbers of gear teeth
Gear teeth must mesh well.
Any looseness produces backlash, the ability for a mechanism to move back & forth within the teeth, without turning the whole gear.
Reducing backlash requires tight meshing between the gear teeth, which, in turn, increases friction.

31. Mobile Robot on wheels,
Speed considerations

32. Robot Speed
Mobile base design, general assumptions.

33. Robot Speed

34. Building a Robot
Motor Performance Data
Speed (RPMs)
Torque (oz. in.)
Current (Amps)
Power Out (Watts)
Efficiency
Heat (Watts)
170
0.00
0.1
0.0 0% 1
159
4.68
0.3
0.5
26% 2
147
9.35
0.4
1.0
34%
136
14.03
1.4
36%
125
18.71
0.6
1.7 3
113
23.38
0.7
2.0 4
102
28.06
0.8
2.1
32% 91
32.73
0.9
2.2
29% 5 79
37.41 6 68
42.09
1.1
23% 7 57
46.76
1.2
19% 8

35. Robot Speed
What size wheel should I use if I want my robot’s maximum speed to be 3 feet per second?

36. Robot Speed
What size wheel should I use if I want my robot’s maximum speed to be 3 feet per second?

37. Building a Robot (6 inches) Robot Speed
What size wheel should I use if I want my robot’s maximum speed to be 3 feet per second?
(6 inches)

38. Building a Robot Robot Speed
If the 6” wheels are the largest in the kit, how would I make my robot’s maximum speed 1.5 feet per second (without damaging the motor or making custom wheels)?

39. Building a Robot Robot Speed
If the 6” wheels are the largest in the kit, how would I make my robot’s maximum speed 1.5 feet per second (without damaging the motor or making custom wheels)?

40. Building a Robot Robot Speed
If the 6” wheels are the largest in the kit, how would I make my robot’s maximum speed 1.5 feet per second (without damaging the motor or making custom wheels)?

41. Building a Robot Robot Speed
If the 6” wheels are the largest in the kit, how would I make my robot’s maximum speed 1.5 feet per second (without damaging the motor or making custom wheels)?
Put a sprocket on the motor that is half the size of the sprocket on the wheel.

42. Gear Reduction Example
To achieve “three-to-one” gear reduction (3:1), we combine a small gear on the input with one that has 3 times as many teeth on the output
E.g., a small gear can have 8 teeth, and the large one 24 teeth
=> We have slowed down the large gear by 3 and have tripled its torque.

43. Gears in Series
Gears can be organized in series, in order to multiply their effect.
E.g., four 3:1 gears in series result in 12:1 reduction. This requires a clever arrangement of gears (see book).
Gears in series can save space
Multiplying gear reduction is the underlying mechanism that makes DC motors useful and ubiquitous.

44. Principles of using Gears in robots
Transfer rotation from one axle to another
Even number of gears reverses the direction of rotation
The radii determine gear spacing, transferred speed, and power
Inverse relationship between power and speed
There are lots of gear spacing issues beyond the scope of this talk
Special half-stud beams or diagonal spacing sometimes help
An eight tooth gear has a diameter equal to one stud
8, 24, and 40 tooth gears work well together because their radii are all multiples of 0.5

45. Gears (continued) Worm gears Some good gear info at
Are effectively one tooth gears
Significant efficiency lost to friction
Since they can’t be back driven, they are great for arms that should hold their position
Some good gear info at

46. Gears: Basics
DC motors usually run at too high a speed or too low a torque for controlling a small robot. Thus, a DC must be geared down.
Drive Gear
Pinion
Wheel
Motor

47. Calculating Gear Ratios

48. Calculating Gears Ratios for a Gear Train
Wheel
Motor
Increase torque
Gear Train: ratio 1:6
Decrease speed

49. Gears: Types and Descriptions
Straight Gears
Worm Gears
Bevel Gears
Helical Gears
Spur Gears

50. Practical Lego Designs

51. Chain Wrap
Motor
Wheel
Wheel

52. Building a Robot
Chain Wrap
Wheel
Wheel
Motor

53. Building a Robot
Chain Wrap
Wheel
Wheel
Motor

54. Chain Tension

55. Materials used
Zan Hecht
Nathan Gray
Gaurav S. Sukhatme