# A transmission system exercise

• Guillem_dlc

## 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.

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)→ω21·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?

## Answers and Replies

In the problem, we have to Find the speed and output torque.

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?

berkeman
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!

tnich and berkeman
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?

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.

PeterO
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.