Differential hoist Model A Engine Lift Puzzle

[Tom Wesenberg]

Here's a picture of a differential hoist like the one I have.
The top pulley has 13 chain link pockets on the large side of the pulley, and 12 pockets on the smaller side.
Each link is 1" apart.
How many inches of chain do I have to pull down to raise my Model A engine 1"?.

Differential Hoist z.jpg

[2manycars]

Too early in the morning for math questions.

[tbirdtbird]

Yikes I haven't seen or used a chain fall in a good many years. Greatest thing ever invented.
yes it is too early for math.
I am gonna guess 12 or 13. The smaller side I believe is the driving side,and the larger side is the driven side, so in my morning stupor I am gonna go with 12
It also could be the sum, at 25.
Tom,we know you worked at a GM dealership, did you have a side career writing brain teasers for magazines, or better yet, in high school we took those aptitude tests that showed 29 gears all combined and you had to tell which way the last gear turned....you wrote those,i bet!

[DaWizard]

4in of chain to raise 1in.

Now, how long do we need to wait for the answer?

[BILL WILLIAMSON]

My COFFEE hasn't "KICKED" in YET!!!
Bill Groggy

[Bob C]

I have one that has 11 and 12 pockets and it took 21" of chain to raise the hook 1".

Bob

[Mitch]

It looks like it can use some Kroil:

[CarlG]

A bunch.

[WMWS]

My grandson says 26 inches would move the hook 1 inch.

[Tom Wesenberg]

My grandson says 26 inches would move the hook 1 inch.

You're grandson is correct. Since only every other link fits into a pocket on the pulley, there are 26 links around the large pulley, and 24 links on the smaller side of the pulley. Each link is one inch, so pulling the chain over the large pulley will pull 26 links to make one revolution, and one revolution will feed down 24 links, so the net gain in raising is 2 links. However the bottom pulley is supported by the chain on each side of the pulley, so the 2 links removed by the larger pulley will be split on each side of the bottom pulley, for a net raise of one link, which equals one inch.

[Tom Wesenberg]

Someone needs to send in a correction to what is on Wikipedia. I'll copy and paste a part of the page.

Calculation of mechanical advantage[edit]


In the above graphic, the four segments of the chain are labelled W, X, Y and Z. The magnitudes of their corresponding forces are F_W, F_X, F_Y and F_Z, respectively.

Assuming that the chain is massless, F_X = 0 because segment X is not supporting any weight.

Taking the system at equilibrium, F_W and F_Y are equal — if they were not, the lower pulley would freely turn until they were.

Next, the downward force acting on the lower pulley equal the upward forces acting on it, so F_L = F_W + F_Y, or 2 F_W because F_W = F_Y.
Additionally, there is no net torque or moment around the compound pulley, so the clockwise torque is equal to the anticlockwise torque: F_WR + F_Xr = F_Yr + F_ZR .
Substituting F_X and F_Y from the above equations, F_WR + 0 = F_Wr + F_ZR .
Rearranging gives F_W = F_Z ·

R/R − r

.
As F_W =

F _L/2

,

F _L/2

= F_Z ·

R/R − r

.
Finally, the mechanical advantage,

F _L/F _Z

=

2 R/R − r

or

2/1 −

r/R

.
Differential Hoist 3.jpg
Here is where I say they are wrong. Lets say the load is 200 lbs., then the chain on each side of the violet pulley would be supporting 100 lbs. Now, lets say the green part of the top pulley is 12" and the blue part is 6". The green would want to turn clockwise with 100 foot pounds of force, but the blue would want to turn the opposite direction with 50 foot pounds of force, so the pulley would spin clockwise and lower the load until the chain no longer had loose links. This is assuming the hand isn't holding the chain.

Here's the link to the full Wikipedia page:

https://en.wikipedia.org/wiki/Differential_pulley

[DaWizard]

Sorry, but the left side of the Blue pulley would actually have the same load (100#) that the left side of your Violet pulley left side. The same as the right side of the Green pulley and Violet pulley right side.

[Tom Wesenberg]

Sorry, but the left side of the Blue pulley would actually have the same load (100#) that the left side of your Violet pulley left side. The same as the right side of the Green pulley and Violet pulley right side.

But the torque is only half on the blue pulley as the green pulley because it is applied at half the distance.

[tbirdtbird]

Tom, I haven't had a chain fall in my hands in 30 yrs. On a real chain fall, are not the two pulleys (green and blue) turning in the same direction? I thought they were married to each other

[Mitch]

I think someone is pulling my chain

[Tom Wesenberg]

Tom, I haven't had a chain fall in my hands in 30 yrs. On a real chain fall, are not the two pulleys (green and blue) turning in the same direction? I thought they were married to each other

Yes, they are one cast part, so they do turn in the same direction.

I was hoping to hear from Vince and Mike K. on this. I still think Wikipedia needs a correction.

[Tom Wesenberg]

Now, for the second part of the puzzle, how many inches need to be pulled to lower the engine 1"?

[Rowdy]

Tom, I have a couple of hoists just like that one. Nice to see another one still out there in usable condition. Too bad my home made A-frame is a POS. Not built by me but was something Dad drug home from an auction when I was in highschool. It was in the shop when the tornado took the shop and my first Model A in 1988. A-frame and hoist survived, Model A didn't.

The answer to the question is 5.78 inches. Rod

[DaWizard]

Now, for the second part of the puzzle, how many inches need to be pulled to lower the engine 1"?

HAHAHA!!! Caught that one right off. Trick question, IF you use the hand shown in the diagram and PULL, it will NOT lower the engine, it will raise it!!

[Tom Wesenberg]

HAHAHA!!! Caught that one right off. Trick question, IF you use the hand shown in the diagram and PULL, it will NOT lower the engine, it will raise it!!

No, forget the hand, which is shown raising the load. You need to grab the other loose side of the chain and pull to lower the load, and believe it or not, it's not the same length as raising the load. You'll have to study the original picture and reason it out. Remember, the pulleys only have pockets for every other link.

[DaWizard]

Then, pulling from the other side my guess without google is 6.5in.

[Tom Wesenberg]

I might as well give the answer. To lower the engine one inch (one chain link) you will pull on the chain that goes over the smaller pulley with 24 links per revolution, so the answer is 24 inches to lower the engine one inch.

To raise the engine one inch, you will pull on the chain that goes over the larger pulley with 26 links per revolution. So, it's 26 inches to raise the engine 1", but 24 inches to lower the engine 1".

If this doesn't seem to make sense, just consider that the slack part of the chain gets shorter as the engine is lowered, and of course the chain supporting the load gets longer.

[Tom Wesenberg]

It looks like it can use some Kroil:

I took that picture from an ebay listing because it had the pulleys and chain so nicely layed out to show how it operates. I couldn't find mine to take a picture, but while looking on ebay I saw this mint looking chain hoist, so I bought it. I haven't seen one with a chain with no rust, and one that also has good original paint on it. It came in the mail today, and is the nicest one I've ever seen.

Years ago at an antique shop I saw a differential hoist that was so used the pockets were worn out on the top pulley.
Sure hard to imaging one getting that much use.

Differential Hoist b.jpg

Differential Hoist c.jpg