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### Author Topic: mistake in meachnics gear tutorial?  (Read 1593 times)

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#### cervantes • Beginner
• • Posts: 6
• Helpful? 0 ##### mistake in meachnics gear tutorial?
« on: March 15, 2016, 01:12:17 PM »
Hi

I just started to read whole website.
On page: http://www.societyofrobots.com/mechanics_gears.shtml I think there is a mistake.
In section Compound Gears there is a formula for torque gear calculation:

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In this example, what minimum torque does the motor need to pull the weight up?

writing down the equations:
torque_motor * radius_gear1 = torque_gear2 * radius_gear2
torque_gear2 * radius_gear2 = torque_gear3 * radius_gear3
torque_gear3 * radius_gear3 = weight * radius_gear3

simplifying, we get:
torque_motor * radius_gear1 = weight * radius_gear3

so therefore the minimum required motor torque is
torque_motor = weight * radius_gear3 / radius_gear1
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BUT THE UNITS are not ok...? how can moment can be compare to load (mass)?....
can someone verify my opinion?

#### bdeuell

• Robot Overlord
•    • Posts: 189
• Helpful? 15 ##### Re: mistake in meachnics gear tutorial?
« Reply #1 on: March 15, 2016, 08:25:41 PM »
you are correct there are several errors, below are what the equations should be.

writing down the equations:
torque_motor / radius_gear1 = torque_gear2 / radius_gear2
torque_gear2  = torque_gear3
torque_gear3 / radius_gear3 = weight

simplifying, we get:
torque_motor / radius_gear1 = weight * radius_gear3 / radius_gear2

so therefore the minimum required motor torque is
torque_motor = weight * radius_gear3 / radius_gear2 * radius_gear1

as radius_gear3 = r and radius_gear2 = r you can further reduce the equation to
torque_motor = weight * radius_gear1

Also weight has the units of force not mass.

#### cervantes • Beginner
• • Posts: 6
• Helpful? 0 ##### Re: mistake in meachnics gear tutorial?
« Reply #2 on: March 15, 2016, 08:57:46 PM »
thank you!

sorry for this kind of question but is the second part (about velocity) correct ? (I haven't analyzed it yet)

#### bdeuell

• Robot Overlord
•    • Posts: 189
• Helpful? 15 ##### Re: mistake in meachnics gear tutorial?
« Reply #3 on: March 15, 2016, 09:14:32 PM »
i took a quick glance through the velocity equations and i didn't see any errors.

#### cervantes • Beginner
• • Posts: 6
• Helpful? 0 ##### Re: mistake in meachnics gear tutorial?
« Reply #4 on: March 16, 2016, 12:52:52 PM »
thanks

I am little in doubt regarding torque calcuation
I follow with your solution trying to apply it to situation presented in attachment

I also received result the same as it was in first case however it is a little bit changed:

torque_motor/radius_gear1=torque_gear2/radius_gear2
torque_gear2/radius_gear2=torque_gear3/radius_gear3
torque_gear3/radius_gear3=torque_gear4/radius_gear4
torque_gear4/radius_gear4=weight -> torque_gear4=weight*radius_gear4

torque_gear3/radius_gear3=(weight*radius_gear4)/radius_gear4 -> torque_gear3/radius_gear3=weight -> torque_gear3=weight*radius_gear3

torque_gear2/radius_gear2=(weight*radius_gear3)/radius_gear3 -> torque_gear2/radius_gear2=weight - > torque_gear2=weight*radius_gear2

torque_motor/radius_gear1=(weight*radius_gear2)/radius_gear2 - > torque_motor/radius_gear1=weight
so.... torque_motor=weight*radius_gear1  ALSO?

That's why I am not sure if I did it correctly or in the fact website example is 100% correctly solved?

Sorry for my curiosity but I like to investigate things which are not fully yet cleared to me, thank you for your help

#### bdeuell

• Robot Overlord
•    • Posts: 189
• Helpful? 15 ##### Re: mistake in meachnics gear tutorial?
« Reply #5 on: March 16, 2016, 05:09:58 PM »
for your example

gear 2 and pulley 3 are attached with a shaft so the torques will be equal

torque_gear2=torque_gear3

#### cervantes • Beginner
• • Posts: 6
• Helpful? 0 ##### Re: mistake in meachnics gear tutorial?
« Reply #6 on: March 17, 2016, 11:45:03 AM »

can you check it ? torque_motor/radius_gear1=torque_gear2/radius_gear2
torque_gear3/radius_gear3=torque_gear4/radius_gear4
torque_gear4/radius_gear4=weight -> torque_gear4=weight*radius_gear4

torque_gear3/radius_gear3=(weight*radius_gear4)/radius_gear4 -> torque_gear3/radius_gear3=weight -> torque_gear3(or torque_gear2)=weight*radius_gear3

torque_motor/radius_gear1=(weight*radius_gear3)/radius_gear2 - > torque_motor=((weight*radius_gear3)*radius_gear1)/radius_gear2

#### cervantes • Beginner
• • Posts: 6
• Helpful? 0 ##### Re: mistake in meachnics gear tutorial?
« Reply #7 on: March 17, 2016, 12:16:55 PM »
for your example

gear 2 and pulley 3 are attached with a shaft so the torques will be equal

torque_gear2=torque_gear3

hmmm.. but radiuses are different... it shall affect the Force value isn't it?
can not understand it correctly :/

#### bdeuell

• Robot Overlord
•    • Posts: 189
• Helpful? 15 ##### Re: mistake in meachnics gear tutorial?
« Reply #8 on: March 17, 2016, 02:02:05 PM »

can you check it ? torque_motor/radius_gear1=torque_gear2/radius_gear2
torque_gear3/radius_gear3=torque_gear4/radius_gear4
torque_gear4/radius_gear4=weight -> torque_gear4=weight*radius_gear4

torque_gear3/radius_gear3=(weight*radius_gear4)/radius_gear4 -> torque_gear3/radius_gear3=weight -> torque_gear3(or torque_gear2)=weight*radius_gear3

torque_motor/radius_gear1=(weight*radius_gear3)/radius_gear2 - > torque_motor=((weight*radius_gear3)*radius_gear1)/radius_gear2

looks correct to me

for your example

gear 2 and pulley 3 are attached with a shaft so the torques will be equal

torque_gear2=torque_gear3

hmmm.. but radiuses are different... it shall affect the Force value isn't it?
can not understand it correctly :/

when you are driving a pulley or gear at the outer diameter (technically the pitch diameter) you set the tangential forces equal to each other (Force=Torque/radius)

when a pulley or gear is connected with a shaft the torques will be equal

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