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A Math Condundrum

Perhaps we're over complicating this with details. A simpler rule of thumb would be that if the motive force is X and moves distance Y you can't lift anything heavier than X more than distance Y. You can move things heavier but that reduces distance and you can move things further but that reduces the supported weight. So for a 50lb actuator that moves 24" the most it can move is 50lbs for 24".

The reason the screw works so well is that you're moving a longer distance for a given input force.

Note that that isn't taking into account any system losses, which will vary wildly depending on the build.
 
Got that part.

Distance can be increased with the stacked scissors mechanics. Yes?

Weight moved can be increased or decreased with a rope and pulley process. Yes?

And, speed can be increased or decreased with the size of pulleys in relationship with one another. Yes?

Finally, dual scissors are cool and add to stability. True!

Ah, Rube Goldberg may still be alive and well!
 
Carol Reed said:
Distance can be increased with the stacked scissors mechanics. Yes?
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Yes but at a reduction in force.

Carol Reed said:
Weight moved can be increased or decreased with a rope and pulley process. Yes?
Click to expand...
Yes but you have to have the motivating bit (your arms :D) move further for a given distance moved proportional to the weight increase

Carol Reed said:
And, speed can be increased or decreased with the size of pulleys in relationship with one another. Yes?
Click to expand...

Yes but speed increase is directly proportional to requiring more force. Move faster, move less weight (and vice versa as I'm finding to be true on oh so many levels as the years pass).

As they say.. TANSTAAFL - There Ain't No Such Thing As A Free Lunch.

Carol Reed said:
Finally, dual scissors are cool and add to stability. True!
Click to expand...

Most definitely true! Double on the cool part :) I could plausibly see some setup where they were only used for stabilization, hmmm...
 
OK, Ryan. Help my pea brain here with regard to the scissors physics. What do you mean by a reduction in force? Does the effort to lift change the mass to be lifted? Is there a correlation between the number of crosses and lifting capability? There are levers involved, and fulcrums, so how does this play between load and effort?

And I don't quite understand how distance is multiplied by stacked crosses of the scissors lift. If one cross lifts 10", do 2 stacked crosses lift 20"? That would make sense.

Back to my Popsicle sticks.
 
Carol Reed said:
OK, Ryan. Help my pea brain here with regard to the scissors physics. What do you mean by a reduction in force? Does the effort to lift change the mass to be lifted? Is there a correlation between the number of crosses and lifting capability? There are levers involved, and fulcrums, so how does this play between load and effort?
Click to expand...

I'm having a hard time figuring the multiple crosses bit myself. As I have it figured (mildly dubious, but I think its close..) if you have multiple crosses on same level you can pretty much ignore them for the force calculations and treat them the same as one X (they'll add more overhead but not really change the base physics). So if you figured out a design that lifted a certain amount with a single X then added another side to it for stability, it should be about the same required force as if it was still the single X.

For the stacked X's I meant that the delivered lifting force proportional to the motive force is reduced by the number of stacked crosses. So if you have one level that will require force Y to move the load, two levels is 2*Y, three levels is 3*Y and so on. This makes sense in the whole "if you move further for a given motive force then you have less delivered force roughly proportional to how much further you moved" baseline rule of thumb.

Carol Reed said:
And I don't quite understand how distance is multiplied by stacked crosses of the scissors lift. If one cross lifts 10", do 2 stacked crosses lift 20"? That would make sense.
Click to expand...

Yeah its pretty much 1:1 - which is why the force delivered versus the force required difference is also right about 1:1 (takes 2x the force to move the same load 2x the distance).
 
So, effort still has to equal load.

The number of crosses increases lift at the cost of decreased load capability due to increased resistances of the interacting mechanics.

Speed is not changed due to the number of crosses.

Now, ropes and pulleys.

The effort is reduced by the number of ropes, not including the effort rope. The speed of the lift is inversely affected. If the effort speed of a 4 rope system is 1"/sec., the load speed is 1/4 of that. Yes?

And the load is 4 times the effort, not accounting for resistance?

And, dual scissors are still way cool.
 
I think we should keep this as simple as possible. As a certain chief engineer once said, the more you over think the plumbing, the easier it is to stop up the drain. 3 pulleys, and a length of rope. Pull rope, platform goes up.
 
Yep yep.

For ropes and pulleys the force is proportional to the "number of ropes between pulleys" and the speed is inversely proportional in the same amount. So yes if there are 4 ropes between pulleys the effort is roughly 1/4 the load and the effort speed is 4x the load speed.

effort = load / (efficiency * number of ropes)

I'm not sure what average efficiency is on pulleys, but the system loss will be roughly proportional to the number of ropes between pulleys in the system as well.. so more pulleys more loss. Poking around I'm seeing measured loss of 2.5% - 10% per rope-between-pulleys depending on how effective the pulley is so for 4 ropes you'll have a 10-40% system loss. So assuming 30% if you wanted to lift 100lbs you have 100/(.7 * 4) or about 35lbs worth of force.

https://www.engineeringtoolbox.com/pulleys-d_1297.html
 
"So assuming 30% if you wanted to lift 100lbs you have 100/(.7 * 4) or about 35lbs worth of force."

Translation? The 35lbs of force for resistance is subtracted from the available effort force, leaving the load force muchly reduced?
 
Carol Reed said:
"So assuming 30% if you wanted to lift 100lbs you have 100/(.7 * 4) or about 35lbs worth of force."

Translation? The 35lbs of force for resistance is subtracted from the available effort force, leaving the load force muchly reduced?
Click to expand...

You need 100lbs of delivered force so if you naively had a 4x reduction with 4 rope connections that would be 100/4 or 25lbs of force needed on the input side. If we figure each pulley adds around 6% overhead (for a somewhat arbitrary ballpark number which is likely a smidge high) that means we have 4*0.06 or around 24% loss.. I rounded that up to 30% because.. I'm lazy.. and figured that works out to about 70% efficiency (1-0.3=0.7) in a 4 rope system so 25lbs /.7 = 35lbs. or put another way 100lbs of force / (70% efficiency * 4 ropes) = roughly 35lbs of required input force.

Once we get all done with this I'll be part way through remembering some algebra :rolleyes: :D
 
Side note, I picked 100lbs as a purely arbitrary round number as well, figured it would be at least moderately close with a smidge of margin for a well built platform plus the groceries and a bit extra but might well be off in the weeds with that as well.
 
Since you brought up naivety :rolleyes: (guilty!), this has been a very interesting exercise and I am probably not finished with it yet.

I also am concurrently looking at other solutions. Thought I'd pause an d inventory the alligators in this here pond.

Goal: electrically lift 100 pounds of groceries, etc. from my waist height from ground level to my waist height at the top of my stairs. Secondary goal: use as much stuff as I already have and spend as little as needed. There are other considerations, one of which is to have it look relatively unobtrusive so the HOA doesn't go into cardiac arrest and render my journey mute and a waste.

Limitations: No ceiling to attach to.

Going out to make some real world measurements and get serious here.

Ryan, you are a saint. Thanks of helping me noodle through the options. My high school algebra is only dimly remembered. Seems I have gotten through 75 years without needing it much!
 
Carol Reed said:
Ryan, you are a saint. Thanks of helping me noodle through the options. My high school algebra is only dimly remembered. Seems I have gotten through 75 years without needing it much!
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I had a hard time resisting the challenge :D Its certainly been stretching my memory muscles more than a little, mostly I'm hoping i have it mostly correct (I think I'm passing the eyeball spit test at this point...).
 
An interesting thread Carol. Given your concern about the HOA, I was wondering if there could be another method that didn't involve building a stand alone structure.
If there is a railing beside the stairs, could it be strengthened enough to hold a couple of guides that would support a folding platform?
The platform could be lifted with an electric winch. Hopefully gravity would pull it down.
Given that railings are usually about 3' high, it should be possible to have a 30" x 30" platform. If it was collapsible, it would not be visible when not in use.
 
Thank, Paul. I haven't thrown in the towel yet.I have taken the railings off th stairs because they were the flimsiest railing I have ever tried to hang unto. I put a grab bar up on the house side instead.

The thought was to build a rail system that incorporated a lift. The linear actuator I have is not up to the task. Looking at other options.
 
I don't remember if this is an outside door or inside of a garage, but either way, how about a nice double railing on one side with a four wheels, could have short sides so things stay put on the ride. Nice cheap ac winch from HF and get to the top and pull it up with winch. Set the rail height so the box is comfortable to load at bottom of stairs and at top of stairs to unload. Level at each end, weight helps pull it back down as you either free spool the winch or let the winch let it back down in reverse. Solves a lot of issues. With a remote, you could even sit on the box and ride up to the porch on bad days!!!!!

Examples of wheels: https://www.amazon.com/Flanged-Track-Wheels/b?ie=UTF8&node=16413381
 
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