A transmission system exercise

In summary, the problem involves a transmission system with a 38-tooth chainring and a 14-tooth sprocket, with a distance of 170 mm between the crank and the pedal. The pedal is overloaded with 60 kg and pedalled at a speed of 70 min-1. The solution involves calculating the force applied to the pedal, input torque, gear ratio, output torque, and output speed using equations for force, torque, and gear ratio. Suggestions for improvement include providing a more complete problem statement, including a diagram, and asking for additional variables such as the force of the pavement on the tire. The calculation for the problem is correct.
  • #1
Guillem_dlc
184
15

Homework Statement


We have a transmission system (plate-pinion), with a 38-tooth chainring and a 14-tooth sprocket. The distance between the crank (between the chainring and the pedal) is 170 mm and the pedal is overloaded with 60 kg and pedalled at a speed of 70 min-1.

Homework Equations


P = mg; Γ = Fd

The Attempt at a Solution


Data:
Z1=38
Z2=14
m=60 kg
g = 9,81 m/s2
d = 170 mm = 0,17 m
ω1 = 70 min-1 = 7,33 rad/s

The first step is to calculate the force (weight) applied to the pedal:
P = m·g → P = 60·9,81=588,6 N

Once we know the force, we have to calculate the input torque (Γ1):
Γ1 = F·d → Γ1 = 588,6 · 0,17 = 100,062 N·m

The next step is to calculate the gear ratio (i) using the number of teeth, and once calculated we can obtain the output torque (Γ2) and output speed (ω2):
i1→2=(Z1) / (Z2) → i1→2=38/14 = 2,71

i1→2=(Γ1) / (Γ2) → Γ2 = (Γ1) / (i1→2 → Γ2=(100,062) / (2,71) = 36,86 N·m

i1→2=(ω2) / (ω1)→ω2=ω1·i1→2→ω2=7,33·2,71=19,89 rad/s

Is the exercise well done? What could I add because the resolution was more physically correct? Any suggestions or ideas?
 
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  • #2
In the problem, we have to Find the speed and output torque.
 
  • #3
I think a more complete problem statement would be a good place to start. It is not clear how the components of the system are related to each other, or what a correct answer would look like. A good diagram of the system would help a lot. Also, you could tell the student what to solve for. Why stop with the output torque and angular rate of the sprocket? Why not make it a two-part problem and ask for the force of the pavement on the tire?
 
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  • #4
tnich said:
I think a more complete problem statement would be a good place to start. It is not clear how the components of the system are related to each other, or what a correct answer would look like. A good diagram of the system would help a lot. Also, you could tell the student what to solve for. Why stop with the output torque and angular rate of the sprocket? Why not make it a two-part problem and ask for the force of the pavement on the tire?
Thanks! I'm going to add what you are saying!
 
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  • #5
tnich said:
I think a more complete problem statement would be a good place to start. It is not clear how the components of the system are related to each other, or what a correct answer would look like. A good diagram of the system would help a lot. Also, you could tell the student what to solve for. Why stop with the output torque and angular rate of the sprocket? Why not make it a two-part problem and ask for the force of the pavement on the tire?

The force of the pavement on the tire would be equal to the friction force?
 
  • #6
Guillem_dlc said:
The force of the pavement on the tire would be equal to the friction force?
The force of the pavement on the tire parallel to the pavement surface would be the frictional force.
 
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  • #7
The chainring wheel power has to be the same as sprocket power. Then Tq1*V1=Tq2*V2.
One rotation of 38 Teeth wheel1=38/14 rotations of the 14 teeth wheel2.
Then V2/V1=38/14 and and Tq2/Tq1=14/38 as you said.
So your calculation is correct.
 

1. What is a transmission system exercise?

A transmission system exercise is a type of physical activity that focuses on strengthening and improving the function of the body's transmission system, which includes the cardiovascular and respiratory systems. It typically involves activities such as running, cycling, or swimming, and is often used as a way to improve overall fitness and endurance.

2. What are the benefits of a transmission system exercise?

There are many benefits to regularly engaging in a transmission system exercise, including improved cardiovascular and respiratory health, increased endurance and stamina, and reduced risk of chronic diseases such as heart disease and diabetes. It can also improve mood and mental well-being, and help with weight management.

3. How often should I do a transmission system exercise?

The frequency of transmission system exercises will depend on individual fitness levels and goals. However, it is generally recommended to engage in at least 30 minutes of moderate to vigorous activity 3-5 times per week. It is important to listen to your body and gradually increase the intensity and duration of the exercise over time.

4. Can anyone do a transmission system exercise?

Most people can safely engage in a transmission system exercise, but it is always recommended to consult with a healthcare professional before starting a new exercise routine. People with certain medical conditions may need to modify the intensity or type of exercise they do, and it is important to listen to your body and make adjustments as needed.

5. Are there any safety precautions to keep in mind while doing a transmission system exercise?

Yes, it is important to stay hydrated and properly warm up and cool down before and after the exercise. It is also important to listen to your body and stop if you experience any pain or discomfort. Wearing appropriate clothing and footwear, and exercising in well-lit and safe environments can also help prevent injuries. If using equipment, make sure to use it properly and follow safety guidelines.

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