I’m working on an elevator that is similar to the thrifty elevator and I want to get a good visualization of the rigging in cad but I am not sure how the rigging for the final/carriage stage works, can anyone clarify how the stages scale relative to the other stages and why?

If you’re really using the Thrifty Elevator as your model, then take a look at pages 35-37 of the Thrifty Elevator assembly guide. Those show pretty clear images of the cascade rigging for the carriage. It’s really pretty simple: the ends of the lines attach (by cam blocks for tension adjustment) to the top and bottom rails of the carriage, they run over pulleys on the top and bottom rails of the second stage, and attach to retention plates on the upper cross-rail of the base stage. That way, as the second stage is pulled up, the lines also pull up on the carriage and raise it proportionally to the second stage.

So I understand that part, but what proportion is it going at, so if i was to change the carriage size while keeping everything else the same, would the amount the elevator could extend change?

The proportion of carriage travel to second stage travel is basically 1 to 1. For every inch the second stage rises, you get the same for the carriage. There’s not really a good way to change that.
Changing the carriage size really won’t change the extension by much. That’s going to be limited by the size of the second stage and the overlap you need with the base stage for stability. In theory you could get a little more height for a mechanism on the carriage by making the carriage vertically shorter, since that would mean it could rise higher than if it was longer, but the shorter you make it the less reliable it will become due to the distance between the bearing blocks it runs on getting shorter too. If you get them too close together, any slight misalignment due to things like uneven weight distribution or differences in line tension become exaggerated. So making a really short carriage may look tempting, but there are definite limits to doing this and having the elevator not bind itself up in action.
Of course, you can also get more height just by increasing the size of the elevator overall, but I’m thinking you wouldn’t be asking this question if you thought that was a viable option.

So, when the second stage is extended all the way, can I be sure that the carriage is on the end of its range of motion and when it is retracted, can I be sure that it is on the beginning of its travel, regardless of the ratio of the sizes of the second stage and the carriage to each other?

Well, yes and no, since the travel of the carriage is determined by distance traveled by the second stage. The way to ensure you have the maximum travel of the carriage is to make it the same size top to bottom as the overlap between the base and second stages. For example, if you have a second stage that’s 3’ tall, but you have a 1’ overlap with the base stage, then you get 2’ of travel for the second stage and making your carriage 10" tall (assuming the top and bottom members of the second stage are 1" each) would get you maximum travel of the carriage. You can get more travel by reducing the overlap and the carriage size. If you took the same elevator and cut it to a 6" overlap, you’d get 2 1/2’ of travel and could cut the carriage size to 4" tall, which would gain you height for the mechanism but at the expense of stability. But you could not get the same effect by keeping the carriage at 10", since it would hit the top of it’s travel before the second stage did (i.e., at 2’ of travel.)

Challenge accepted

To move the carriage half as fast as the second stage, just add a pulley on the carriage and fix the rope back to the top of the carriage:

To move the carriage twice as fast as the second stage, you need to add a floating pulley. The line pulls the floating pulley up, and the rope going around the pulley is anchored to the carriage and the second stage.

Assuming you have proper tension in your system, both are fairly easy and straight forward to implement, although I don’t see much reason why you would do it in this context. In the first one, the carriage moves slower, but it means you need less force to lift it. You’ll see it in situations where you need to lift something heavy, but don’t really care about how much rope you need to pull in. The second you move faster, but you need more force to lift it. I can’t think of a situation off the top of my head where that would be particularly useful, but I’m sure it’s there somewhere!

Note that both of these arrangements change the total distance travelled for the elevator system - you won’t be able to reach as high. In the first, the carriage will only be halfway up when the second stage reaches its limit. In the second, the second stage will only be halfway up when the carriage reaches its limit.

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And this was why I said there wasn’t a good way to change that rather than saying there was no way to change that. The whole context of the answer was in regard to trying to get more height out of the same size elevator. Thus I disregarded solutions that would get less height for a mechanism as not being a good way to change that. It certainly wasn’t that I didn’t know you could use mechanical advantage to change the travel ratio between carriage and second stage, it was just that these were not useful solutions in this circumstance.

I must have missed where that was a stated goal in this particular thread…

and both ways kinda sorta defeat the entire purpose of putting a second stage on an elevator so like yeah

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