Gearing Very Simple Chain Theory 16 Let us

Gearing

Very Simple Chain Theory 16 Let us start with a very simple example 32

Building a Robot Chain Theory 16 32

Building a Robot Chain Theory 16 32

Building a Robot Chain Theory 16 32

Building a Robot Chain Theory 16 32

Building a Robot Chain Theory 16 32

Building a Robot Chain Theory 16 32

Building a Robot Chain Theory 16 32

Building a Robot Chain Theory 16 32

Building a Robot Chain Theory 16 32

Building a Robot Chain Theory 16 32

Building a Robot Chain Theory 16 32

Building a Robot Chain Theory 16 32

Building a Robot Chain Theory 16 32

Building a Robot Chain Theory 16 32

Building a Robot Chain Theory 16 32

Building a Robot Chain Theory 16 32

Building a Robot Chain Theory 16 32

The Effect on Speed 1. When gears are combined, there is also an effect on the output speed. 2. To measure speed we are interested in the circumference of the gear, C= 2 r. 3. If the circumference of Gear 1 is twice that of Gear 2, then Gear 2 must turn twice for each full rotation of Gear 1. 4. => Gear 2 must turn twice as fast to keep up with Gear 1.

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

Gearing Laws

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

Gearing in robots 1. 2. 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. force F=T/ r r T=Fr 3. This is the underlying law behind gearing mechanisms.

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

Gear Radii and Force/Torque 1. By combining gears with different radii, we can manipulate the amount of force/torque the mechanism generates. 2. The relationship between the radii and the resulting torque is well defined 3. 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.

Example of Gearing 1. Suppose Gear 1 with radius r 1 turns with torque t 1, generating a force of t 1/r 1 perpendicular to its circumference. torque t 1 r 1 force of t 1/r 1 2. If we mesh it with Gear 2, with r 2, which generates t 2/r 2, then t 1/r 1 = t 2/r 2 1. To get the torque generated by Gear 2, we get: t 2 = t 1 r 2/r 1 2. 3. If r 2 > r 1, we get a bigger torque, if r 1 > r 2, we get a smaller torque. r 2 Forces are equal

Gearing Law for Torque 1. If the output gear is larger than the input gear, the torque increases. 2. If the output gear is smaller than the input gear, the torque decreases. 3. => Gearing up increases torque 4. => Gearing down decreases torque

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?

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.

Mobile Robot on wheels, Speed considerations

Robot Speed Mobile base design, general assumptions.

Robot Speed

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% 2 136 14. 03 0. 5 1. 4 36% 2 125 18. 71 0. 6 1. 7 36% 3 113 23. 38 0. 7 2. 0 34% 4 102 28. 06 0. 8 2. 1 32% 4 91 32. 73 0. 9 2. 2 29% 5 79 37. 41 1. 0 2. 2 26% 6 68 42. 09 1. 1 23% 7 57 46. 76 1. 2 2. 0 19% 8

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

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

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

Building a 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)?

Building a 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)?

Building a 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)?

Building a 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.

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.

Gears in Series 1. Gears can be organized in series, in order to multiply their effect. 2. E. g. , four 3: 1 gears in series result in 12: 1 reduction. This requires a clever arrangement of gears (see book). 3. Gears in series can save space 4. Multiplying gear reduction is the underlying mechanism that makes DC motors useful and ubiquitous.

Principles of using Gears in robots 1. 2. 3. 4. 5. 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 1. 2. 3. 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

Gears (continued) • Worm gears – 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 – http: //www. owlnet. rice. edu/%7 Eelec 201/Boo k/legos. html

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 Motor Wheel

Calculating Gear Ratios

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

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

Practical Lego Designs

Chain Wrap Motor Wheel

Building a Robot Chain Wrap Wheel Motor

Building a Robot Chain Wrap Wheel Motor

Chain Tension

Materials used 1. Zan Hecht 2. Nathan Gray 3. Gaurav S. Sukhatme