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I tried asking this on other SE forum but i think this is the correct one:

Basically our teacher has sent us quite a lot of exercises but I can't get past this one which says: a pulley cone consists of 3 pulleys of 150, 250 and 350 mm of diameter that link an identical but inverted cone. Determine the three possible transmission ratios. Our teacher doesn't explain very well and I don't know where to search. If someone knows something about this, anything would be helpful.

PD: if you think I didn't tried to solve it, in all the book there's no information about this type of mechanism and we don't see our teacher until the day we need to bring the homework. There's no more info. in the exercise sorry.

(ignore, i messed up the question here)Edit: by the way what I'm trying to look for here is for a formula about the transmission ratio, but I can't understand how to do the formula with this specific mechanism because I don't see how to get the speed of the pulleys, here's an example given by the book.

example of formula about the answer

Edit 2: i finally came up with this answer: This question defines a system of adjustable speed pulleys, of this type of mechanisms what we can see as a ratio is that the bigger the gear we choose the pulley will go slower, this means that if we choose the gears that are parallel to each other the speed will always be the same because we will always have gears that are proportional to each other. 350mm -> 150mm 250mm -> 250mm 150mm -> 350mm

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  • $\begingroup$ Your question title says "bevel gear". Your question body says "pulley system". Which is it? Hit the Edit link to fix it. Tip: capitalise your sentences properly. It leaves an impression one way or another. $\endgroup$
    – Transistor
    Apr 17, 2022 at 22:22
  • $\begingroup$ i meant that the pulley system includes bevel gears $\endgroup$ Apr 17, 2022 at 22:49
  • $\begingroup$ Well then the question in your post is not giving the full information. It doesn't mention gears. You need to fix that. Edit and use the > quotation markdown syntax to post the exact wording of the original question. We can't guess. $\endgroup$
    – Transistor
    Apr 17, 2022 at 22:51
  • $\begingroup$ Your update still hasn't posted the actual question. Please fix it. $\endgroup$
    – Transistor
    Apr 17, 2022 at 23:11
  • $\begingroup$ nvm i'll close it because i think it's not even understandable at this point sorry if i lost people time it wasn't my intention i just didn't find a way to do it and this was my last chance of not having to put on the question: i don't understand $\endgroup$ Apr 18, 2022 at 9:36

1 Answer 1

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Your question is describing an adjustable speed pulley system. These are commonly found in bench drill presses. (See the link below.)

enter image description here

Figure 1. A 5-speed adjustable speed pulley system. Image source: Toolbox Buzz.

Since the centres of the shafts are fixed and the length of the belt is fixed this arrangement requires that the path of the belt on each "level" of the system must be a constant (because the belt isn't elastic). Therefore, as you increase the pulley circumference on one shaft you must decrease it on the other to keep the path length constant.

Question to get you thinking:

  • If the motor is on the left and the drill chuck on the right, will moving the belt up increase or decrease the speed of the drill?

With this information you should be able to solve the problem. Update your question with the answer or method and we'll give you some feedback.

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  • $\begingroup$ the supposed answer I should be giving is 3 formulas, something like: diameter1 x speed1 = diameter2 x speed2 (rpm) so i probably didn't understand your answer correctly or i might messed up the question $\endgroup$ Apr 17, 2022 at 22:52
  • $\begingroup$ If the belt is on 150 mm drive pulley how far will the belt move in one revolution of the drive? What pulley will it be on the other side? What angle will that pulley turn for one revolution of the drive pulley? Your question doesn't ask for speed. It asks for ratios. You still haven't posted the actual question. $\endgroup$
    – Transistor
    Apr 17, 2022 at 23:10
  • $\begingroup$ it's highly probable that as i'm spanish and my english isn't very good the question isn't correctly explained, but thank you a lot for the answer because at least now i can put something in the question $\endgroup$ Apr 18, 2022 at 9:39

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