Gears, Gears and More Gears

1. Gears, Gears and More Gears

2. Basic Physics Terms • In this lesson, we will review some basic physics terms and • demonstrate them using our LEGO® gearbox. • Force and Torque • Mechanical Advantage • Newton’s Laws • Work and Power • Friction

3. Gear Box Please make the following modifications to the gear box from the Gear Box building Instructions. Place bushings here and here. Remove the motor and double beam. Remove the rotational sensor.

4. Gear Box Please make the following modifications to the gear box from the Gear Box Building Instructions. Add another 1x16 beam here. Add pulley wheels and gray pegs (for handles).

5. Basic Terms - Force What is a “force?” A force causes something with mass to move (accelerate). This can be summed up with Newton’s 2nd Law. F = m x a (In fact, units of force are called “Newtons.”) Question: What force do we experience every single day? Answer: The force of gravity.

6. Basic Terms - Torque What is “torque?” Torque can be thought of as rotational force. Torque causes something with mass to rotate. This motor produces a torque. We are interested in “torque” because we deal with rotational motors and axles.

7. Force and Torque How are force and torque related? moment arm A force can create a torque by acting through a moment arm. …produces a torque here. A force here... The relationship is t = F x r. r is the length of the moment arm (in this case, the length of the wrench).

8. Gears and Torque Up to now, we have been talking about how gears change speed. But they can also change torque. Question: What is the gear ratio of this gear box? Answer: 75 to 1 That means the last axle rotates 75 times slower than the first axle. It also means the last axle has 75 times the torque as the first axle.

9. Gears and Torque Try this experiment. Have one person turn this wheel. And have another person try to hold on to this wheel.

10. Gears and Torque Where does all this “torque” come from? Consider a pair of gears that are meshed together. F A torque on this axle... …produces a force at the tooth. t r The moment arm is the radius of the gear. Remember: t = F x r

11. Gears and Torque The force from the small gear’s tooth pushes against the large gear’s tooth. This creates an equal (and opposite) force in the large gear. This is Newton’s 3rd Law. F …and produces a larger torque on this axle. r t The force acts through this larger moment arm...

12. F1 = -F2 t1 r2 r1 t2 Gears and Torque Analyzing the forces... t1 = F1 x r1 t2 = F2 x r2 • F1 = t1 / r1 • F2 = t2 / r2 • F1 = - F2 • t1 / r1 = -t2 / r2 • -t2 / t1= r2 / r1 The ratio of torques is the ratio of the gear radii. This is the gear ratio!

13. Gears and Torque Gears can increase the torque (and force) that they exert on something. This is known as mechanical advantage. torque increases BUT, it comes at a price. Do you know what it is?

14. Work in terms of rotation is a torque acting over an angle. W = t x q Basic Terms - Work Work (in physics) is defined as a force acting over a distance. W = F x d

15. Mechanical Advantage Understanding the 2 components of work is the key to understanding mechanical advantage. Question: Where would you hold the wrench for it to be most effective?

16. Mechanical Advantage …but your hand moves a long way. …but you don’t move very far. If you hold the wrench here, you don’t need as much force... If you hold the wrench here, you need a lot of force...

17. Mechanical Advantage It takes the same amount of work to turn the bolt. You can opt for a lot of force and little distance. W = F x d Or you can choose a little force but a lot of distance. W = f x D In many of our machines, we want to increase our force, so we don’t mind going the extra distance.

18. Mechanical Advantage Question: Which ramp would you prefer to use to move a heavy weight to the top of the box? Answer: This ramp requires less force, but you have to move the weight a longer distance.

19. Mechanical Advantage With our gear box, you were able to create a large torque here... …but you had to turn this handle many times. Remember: W = t x q

20. Power Power is the rate at which work is done. It can be thought of as work per second. Power = Work / sec. Like work, power has 2 components, force and speed. P = F x v (v stands for velocity). Question: Can you name 2 units for power? Answer: Horsepower and watts.

21. Power Power has the same trade-offs as work. A motor produces the same amount of power. So, you can make a robot that’s fast, but weak. Or you can make a robot that’s slow, but strong. The total power in must equal the total power out. (with an exception)...

22. Friction = Bad Friction is caused by two surfaces rubbing together. Friction in our gear box causes a loss in the input power. It is lost in the form of heat and sound energy.

23. Friction = Good But friction is also what makes our robot move. The turning wheel produces a frictional force against the ground, which causes the robot to move.

24. Summary - Key Points • A force causes something with mass to move. • Torque is rotational force. • Work has 2 components, force and distance. • Mechanical advantage lets you increase one component of work at the expense of the other. • Gears are one way to get mechanical advantage. They can increase the robot’s torque. • Power is the product of force and speed. • A robot can either be slow and strong, or fast and weak. • Friction causes both losses in power, but also makes robots move on the ground.