Compound Gears Explained: Calculate Gear Ratio

What is a Compound Gear Train? How are compound gears different from Idler gears? How do you calculate the gear ratio in a compound gear train?
By creating compound gear trains it is possible to produce enormous gear ratios that would be impossible to produce with just a simple gear set made up of two gears. In this video we take a look at compound gear trains. Calculating the gear ratio for a compound gear train is not hard but it is important to recognize that the two gears which share an intermediate shaft share angular quantities not tangential quantities. Even though there are four gears in a compound gear train, there are only two lines of action between the input and output shafts and really only two gear sets.
The subject of Compound Gears often come up in both high school and college physics and engineering classes. They are found in Project Lead the Way (PLTW), Principles of Engineering (POE) and AP Physics.

[@cupostuff9929]

Good video. I really liked how clearly you drew the connection between the math that was being done & what was actually occuring between the gears.

[@INTEGRALPHYSICS]

Thanks! I never seem to be able to remember 'magically appearing' equations alone, I find it always helps me to understand the mechanics/theory of what is going on behind the equations. Hopefully it helps you too.

[@Shabazza84]

Best explanation I've seen so far. Easy to understand.

[@INTEGRALPHYSICS]

Thank you!

[@josiemaylinn]

straight and right to the point, i couldn't recommend this guy enough

[@Ryan-dk9sn]

Thank you for this video! It's the best one I've found for explaining the gear ratio of a compound gear train.

[@INTEGRALPHYSICS]

Glad it was helpful!

[@sbugwama3633]

There's isn't any explanation better than this.

[@goodfriendscrappycars8877]

This was extremely helpful in helping me solve a manual transmission gear set curiosity!

[@INTEGRALPHYSICS]

Glad it helped!

[@wbriggs111]

Thanks, you hit the nail on the head.

[@INTEGRALPHYSICS]

Happy to help

[@spookydaily6590]

Showed this to my friend who called me a dumbass for making these as a fun side project. Thanks.

[@mwont]

Awesome explanation. Thank you.

[@INTEGRALPHYSICS]

Glad it was helpful!

[@erinbentson6682]

Thanks! This helped so much. I wish you were my teacher!

[@INTEGRALPHYSICS]

You are so welcome!

[@py-sk4dn]

This is one of the top best explanation on youtube

[@INTEGRALPHYSICS]

Thanks!

[@tusharsantoshraut8915]

agree

[@sebastian.B0]

Thank you! Have a wonderful life :)

[@BarryDunne1]

Great explanation for my brain

[@INTEGRALPHYSICS]

Glad it was helpful!

[@tusharsantoshraut8915]

Thanks. It helped a lot :)

[@INTEGRALPHYSICS]

Glad it helped.

[@thatspyguy839]

Excellent video.

[@INTEGRALPHYSICS]

Thanks!

[@segopocothabane4140]

Nice!

[@troyam6607]

is there a calculator for when you have a set of gears and you need to find the right combination when all you have is input turns and output turns? IE: milling machine table to dividing head via gearing; 1 turn of the table equates to 5mm direction dividing head is 40:1? all i have at the moment is 30 turns is the lead of the table so 64t driver and 48t driven will turn the dividing head 1 rotation

[@nickyg9012]

Amazing !!

[@INTEGRALPHYSICS]

Thanks!!

[@parkminjoon1028]

THANK YOU.

[@INTEGRALPHYSICS]

youre welcome

[@ptyptypty3]

nicely done! Your dedication to Detail is amazing. thanks for that effort. I do have a question, the Middle Gear can also be thought of as a Wheel And Axle machine. So, when considering the Forces at the Interfaces.. it seems like the Wheel And Axle Mech Advantage is ignored. I guess we'd have to look at the Torques... anyway.. nicely done.. :)

[@INTEGRALPHYSICS]

1. The input and output shafts/are wheels and axles. 2. All wheels and axles are levers. Redraw the middle gear as a lever with a short side and a long side and you have turned a compound gear train into a simple machine.

[@trentbjorkman3688]

Mr. Bentson at it again

[@INTEGRALPHYSICS]

Again? I never stopped.

[@jvids0119]

This is so poggers!

[@INTEGRALPHYSICS]

I had to urbandictionary poggers, cause I'm old.

[@markthurst9751]

Is it possible to calculate torque reduction in a compound gear train like this one? would the torque be reduced to a quarter of the input?

[@INTEGRALPHYSICS]

Once you have the gear ratio, calculate torque just like you would with a simple gear combination. Ignoring losses, GR of 10 means 10x the torque, regardless of how that gear ratio was produced.

[@markthurst9751]

@@INTEGRALPHYSICS thank you.

[@LouisG-gw4no]

Great video. Is it possible to ask for further instruction on this topic?

[@INTEGRALPHYSICS]

Yes, absolutely. Whats your question?

[@LouisG-gw4no]

I'm not understanding if there's any mechanical advantage, loss, or neither in a double rack and pinion gear system where primary rack has 20 teeth, meshing w a pinion gear that has 10 teeth. That pinion is a compound gear which shares an axel with a 20 tooth gear, which drives the secondary rack gear of 40 teeth. How much force out will I get per force in?

[@LouisG-gw4no]

I'm not understanding if there's any mechanical advantage, loss, or neither in a double rack and pinion gear system where primary rack has 20 teeth, meshing w a pinion gear that has 10 teeth. That pinion is a compound gear which shares an axel with a 20 tooth gear, which drives the secondary rack gear of 40 teeth. How much force out of the second rack will I get per force in to the primary rack?

[@INTEGRALPHYSICS]

primary rack moves one tooth, 10t pinon moves one tooth... the 20t on the same axle as the 10t moves 2 teeth (same angular rotation as the 10t, different tangential distance), the secondary rack moves 2t. 1t in, 2t out. IMA = 1/2. Conversely, if the 10t and 20t were meshed together and not on a common axle the 20t and secondary rack would each move 1t. IMA = 1/1

[@JohnDoe-ot8le]

Thank you, I have a question, compound gears have the same speed (rpm) so normally they have the same Torque, However torque is related to distance as per T= Fxm (Torque equals to force x distance) here distance is the radius of the gear. So normally as per the definition of Torque they shouldn't have the same Torque as they have different distances away from the center of rotation. Any explanation? Thank you.

[@INTEGRALPHYSICS]

All gears that mesh have the same TANGENTIAL speed (measured as a linear speed at the edge of the gear) and force (measured in Newtons or lb). All gears that are fixed to the same shaft have the same ANGULAR speed ( measured in rpm) and torque (measured in Nm or inlb). The two gears on the intermediate shaft have the same torque, but because they have different radii they produce different forces against the gears with which they mesh. Hence mechanical advantage.

[@JohnDoe-ot8le]

@@INTEGRALPHYSICS I have a drill press with a motor connected to a step cone pulley (pulley with different groove diameter), obviously the pulley grooves rotate at the same speed. so according to the coumpound gears explanation they have the same torque. Is this correct!? Isn't it more difficult for the motor to move when the belt is connected to the bigger diameter groove than to the smaller one logically. Am I missing something? Thank you.

[@INTEGRALPHYSICS]

The belt and pulley on a drill press which connect the motor to the chuck shaft can be viewed as a set of simple gears connected via a belt, not compound gears. This means they share tangential values such as speed and force, via the belt, however the step cones have different diameters there fore they have different torques. Belts & pulleys are on my to-do list for videos. Hopefully in the next month here I can get something out for you... In the mean time check out the Simple Gears vid, the calculations and concepts from which can translate to your drill press (sans belt).

[@JohnDoe-ot8le]

@@INTEGRALPHYSICS Thank you, looking forward for your videos.

[@dave9343]

Hi Guys, I am working on a design that requires Indexing Gears. And so, I need to know how fast can an Indexing Gear spins. And where would I be able to find detailed information on this type of gear. Thanks very much everyone.

[@sirazulislam1362]

I have a question, How to select Covering machine gear stretch wise. 1.Take up gear. 2. Drafting gear 3. Feed gear. please formula? Thank you

[@INTEGRALPHYSICS]

I'm afraid I do not understand the question.

[@realstatistician]

Wouldn’t it be more straightforward to flip the ratios? Then you’ll get that rotating the first shaft 1 time rotates the last shaft 4 times.

[@INTEGRALPHYSICS]

I agree that sometimes GR would be easier if it was inversed. However it mirrors what we see with mechanical advantage, meaning a GR>1 translates to an increase in torque.

[@jackconley5629]

I would like to ask a question on Compound gear trains in private

[@caelinbuenger7095]

Your students are lucky

[@INTEGRALPHYSICS]

That's precisely what I keep telling them!

[@2.5cogs]

Ron swanson