The objective of the assignment was to make a race car out of LEGO bricks and gears. The car would have to carry a 1kg load and race in a 4m race track, and we were only allowed to use one motor to power the car.
We started out by thinking about the physics behind gears.
Starting out with the basics, we considered torque and angular velocity.
Given a force, the torque is the tendency of the force to rotate an object about an axis.The equation for torque is T(torque)=r x F = rFsin(theta). For gears, we are dealing with theta=90 degrees, so torque is equal to rF. r is the distance from the axis to the applied force. As r increases, torque also increases with the same amount of force. This is why it is easier to open a door when force is applied far away from the hinge.
Angular velocity (omega) is equal to v/r, meaning that it is inversely proportional to r.
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| http://hyperphysics.phy-astr.gsu.edu/hbase/imgmec/vtord.gif |
So how is torque and angular velocity applied to gears?
Consider a small 8 tooth gear connected to a motor. Due to the very small radius of the gear, it rotates with a big angular velocity but with a small torque. If a 24 tooth gear is meshed to the 8 tooth gear, the 24 tooth gear would rotate with less speed, but with a greater torque. The gear ratio for this example is 3:1. This process of lowering speed and increasing torque is called 'gearing down'. The opposite process (increasing speed and decreasing torque) is called 'gearing up'. The ratio of torque and angular velocity change is proportional to the gear ratio. For the example, the gear ratio of 3:1 in the above example would increase the torque by 3 times and decrease the speed by 1/3.
After going through the basics of gears, Sunnia and I decided to try out several different gear ratios.
Trial 1
We felt very ambitious and decided to go for a big gear ratio for our first car. We had 3 24-tooth gears and 2 40-tooth gears, and 5 8-tooth gears to use as output gears for the gear train. The total gear ratio was 675:1 (3x3x3x5x5:1). Our gear produced a lot of torque but very little speed. With the weight on its back, the car could not move forward. Since the results were so abysmal, we did not bother to take a picture of the car.
Trial 2
For the second iteration, we decided to lower the gear ratio. We tried using 1 24-tooth gear and 2 40-tooth gears with 8-tooth gears connecting the big gears.The total gear ratio was 75:1 (5x5x3:1). The wheels were about 1.5inches in diameter and about 0.7inches in thickness. The design of the car was kept very simple and light, minimizing any unnecessary structures. The car was very slim, with the width being just wide enough to fit the 1kg weight.
We tested the car out on the 'race track' and it finished the race in 40 seconds.
Trial 3
After the second iteration, we decided to make a small structural change. Instead of using the smaller/thicker wheels, we decided to use the larger/thinner wheels so it would reduce the friction and increase the torque.
When we tested out the car on the track, the time was down to 25 seconds.
Trial 4
In order to make our car go faster, we tried out a smaller gear ratio. 2 24-tooth gears and 1 40-tooth gear was used and the gear ratio was 45:1 (3x3x5:1). We also made the car slightly shorter.
The car was dramatically faster than the previous iteration, and it took about 15 seconds for the car to go through the race track.
Trial 5
For the final iteration of our race car, we decided to focus on the aesthetics. We found a way to make the car even shorter by changing the orientation of the pico block. The car was just big enough to fit all of the necessary structures, including the weight. We also decorated the car a little bit in order to make it more pleasing to the eye. We also made the structure more stable by having more supporting LEGO bricks, so the car is not prone to damage.
The car was slightly faster than the previous iteration, it took just about 14 seconds to go through the 4m track.
(To be continued.....)
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