Wheels & Axles
The wheel and axle is a simple machine made of a large wheel secured to a smaller wheel which is called an axle.
One of the most common wheel and axles is something that most people use everyday. It is the tire of a car or truck. On most of these, the wheel and axle acts as a lever rotating around the fulcrum or the center point. On doing this the wheel rolls.
One of the most common wheel and axles is something that most people use everyday. It is the tire of a car or truck. On most of these, the wheel and axle acts as a lever rotating around the fulcrum or the center point. On doing this the wheel rolls.
The Chassis
What are Bearings? Can we use some?
Build a Mouse-Trap Car
mouse-trap-car.pdf | |
File Size: | 817 kb |
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mousetrap-vehicle.pdf | |
File Size: | 439 kb |
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Wheels
www.scioly.org
Physical Considerations of the Wheels taken from the SO Scrambler event
The wheel is one of the most critical components of a scrambler. There are several properties of the wheel that are important to consider for the purposes that it is used in this event. The wheels mass, or more appropriately, its rotational inertia is one of the important of those properties. As we know from physics, the resistance to acceleration in a linear motion is different from the resistance to acceleration in a rotational motion. It is notable that the wheel in a scrambler is a rolling object, and thus it is a great mistake to ignore both components of its motion. It is a well known derivation from physics that the total energy of the rolling wheel is:
Note that radial velocity is easily related to the normal velocity of the wheel(and thus the car it is attached to by a simple equation:
It can be noted that the increase in mass, radius and rotational inertia all will lead to the wheel storing more energy in it that can be better used to accelerate the car. Note that the radius term is squared, so any increase in the wheels radius will severely impact its energy properties. Lastly, the inertial component is very often dependent on the squared radius of the wheel as well, further increasing the importance of the radius of the wheel.
Note, that nothing has been said whether having a large mass of the wheel is bad or good. This question cannot be answered decisively in either direction. Smaller mass wheels (i.e. wheels that are small and light) allow for your scrambler to go faster, but they will also have to spin faster and thus are very susceptible to axle friction. Many teams with tiny wheels failed to reach the wall simply because the cars, while launched at respectable speed, were bogged down by friction. Ways to reduce this friction will be discussed shortly. Teams with large wheeled scramblers enjoy lumbering, but roughly constant speeds. Once you accelerate the beast of a lawnmower wheel, it will not want to stop for a while. Note that the wheel radius is of a particular importance to one of the integrated mass scrambler types; that will be discussed later.
The second important aspect of a wheel in a scrambler is its traction. Traction is of supreme importance for the car's stability, and when the wheels are used as brakes, for its braking. The force of static friction that a wheel exerts on a ground can be approximated well by the following equation(note that static friction is used, the wheel is assumed not to be skidding, which would require us to use the kinetic friction):
Since this friction is always desired by the scrambler car (unless you specifically desire your scrambler to skid out of control at the drop of a hat) it appears that it can simply be increased by increasing the mass of the car. This is dubious for multiple reasons, first is that this mass increase will make the car slower, and secondly is that by the Newton's second law,
The equation (3) can be rewritten as this(assuming that the mass supported by the wheel is equal to the total mass of the car, a poor approximation as shall be seen later on):
<math>m a = m g k</math>
The m's cancel, and it is appears that the acceleration due to the force of friction is independent of the mass of the car! This is a naive understanding of the processes involved however. The equation (3) assumes that the wheel's geometry does not change when more weight is applied. This is true for rigid wheels, but for anything that is even mildly deformed it no longer applies. The deviation from ideal behavior is not that significant however, and thus the result from equation (5) is largely valid: the only way to increase the traction of the wheel is to increase its coefficient of friction. With the theory covered, let us now discuss the material considerations of the wheels.
http://scioly.org/wiki/index.php/Scrambler
- <math>E = 1/2 \left( m R^2 + I \right) {\omega}^2</math>
Note that radial velocity is easily related to the normal velocity of the wheel(and thus the car it is attached to by a simple equation:
- <math>v = \omega \times R</math>
It can be noted that the increase in mass, radius and rotational inertia all will lead to the wheel storing more energy in it that can be better used to accelerate the car. Note that the radius term is squared, so any increase in the wheels radius will severely impact its energy properties. Lastly, the inertial component is very often dependent on the squared radius of the wheel as well, further increasing the importance of the radius of the wheel.
Note, that nothing has been said whether having a large mass of the wheel is bad or good. This question cannot be answered decisively in either direction. Smaller mass wheels (i.e. wheels that are small and light) allow for your scrambler to go faster, but they will also have to spin faster and thus are very susceptible to axle friction. Many teams with tiny wheels failed to reach the wall simply because the cars, while launched at respectable speed, were bogged down by friction. Ways to reduce this friction will be discussed shortly. Teams with large wheeled scramblers enjoy lumbering, but roughly constant speeds. Once you accelerate the beast of a lawnmower wheel, it will not want to stop for a while. Note that the wheel radius is of a particular importance to one of the integrated mass scrambler types; that will be discussed later.
The second important aspect of a wheel in a scrambler is its traction. Traction is of supreme importance for the car's stability, and when the wheels are used as brakes, for its braking. The force of static friction that a wheel exerts on a ground can be approximated well by the following equation(note that static friction is used, the wheel is assumed not to be skidding, which would require us to use the kinetic friction):
- <math>F_f = m g k</math>
Since this friction is always desired by the scrambler car (unless you specifically desire your scrambler to skid out of control at the drop of a hat) it appears that it can simply be increased by increasing the mass of the car. This is dubious for multiple reasons, first is that this mass increase will make the car slower, and secondly is that by the Newton's second law,
- <math>F = m a</math>
The equation (3) can be rewritten as this(assuming that the mass supported by the wheel is equal to the total mass of the car, a poor approximation as shall be seen later on):
<math>m a = m g k</math>
- <math>a = gk</math>
The m's cancel, and it is appears that the acceleration due to the force of friction is independent of the mass of the car! This is a naive understanding of the processes involved however. The equation (3) assumes that the wheel's geometry does not change when more weight is applied. This is true for rigid wheels, but for anything that is even mildly deformed it no longer applies. The deviation from ideal behavior is not that significant however, and thus the result from equation (5) is largely valid: the only way to increase the traction of the wheel is to increase its coefficient of friction. With the theory covered, let us now discuss the material considerations of the wheels.
http://scioly.org/wiki/index.php/Scrambler
Material Considerations of the Wheel
Ready... Set... Go!
Designing & Building a Launching mechanism
How to propel our Wheeled Vehicle? Here are the SO construction guidelines...
"b. All energy used to propel the vehicle must be stored in a non-metallic elastic device. It may be left unattached until just prior to the run. Pre-loaded energy storage devices may be used to operate other vehicle functions (like the braking system) as long as they do not provide energy to propel the vehicle."
"g. Competitors must start the vehicle by using any part of an unsharpened #2 pencil with an unused eraser to actuate a trigger. The trigger must be designed so that its actuation is perpendicular (vertical) to the floor. A non-vertically actuated trigger is a construction violation. The vehicle must be able to remain at the starting postition without being touched until triggered."
"b. All energy used to propel the vehicle must be stored in a non-metallic elastic device. It may be left unattached until just prior to the run. Pre-loaded energy storage devices may be used to operate other vehicle functions (like the braking system) as long as they do not provide energy to propel the vehicle."
"g. Competitors must start the vehicle by using any part of an unsharpened #2 pencil with an unused eraser to actuate a trigger. The trigger must be designed so that its actuation is perpendicular (vertical) to the floor. A non-vertically actuated trigger is a construction violation. The vehicle must be able to remain at the starting postition without being touched until triggered."
rubber_band_power.pdf | |
File Size: | 201 kb |
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Brakes
http://scioly.org/wiki/index.php/Scrambler