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10-Marble

## How to solve this function

In this gear design work, I want to find a suitable x1 and x2 to make the sliding rate of each gear equal or close to equal

now I was stuck here, do you mind telling me which place is wrong and how to solve this question?

1 ACCEPTED SOLUTION

Accepted Solutions
24-Ruby V
(To:Jacky.Dong)

I have no solution for your problem, juts a few remarks:

you have five equations but just two variables you allow to be changed. This can't work.

I guess that you would also like d.a1,da2,alpha.a1 and alpha.a2 to be changed. If thats true, you also have to include them in the "find" command even though you may not be interested in their value.

Now we have six variables for Prime to play with but only five equations. Normally this means that you can expect an infinite number of possible solutions and you could add additional constraints like x.1>0mm or the like.

But in case of your system, Prime can find no solution at all. Thats the first moment you may ant to re-check your variables and equations - maybe the problem really has no solution the way you had set it up.

If a system has no solution its always worth a try to replace "find" with "minerr". That way Prime will try to find the best variable combination where the overall errors are minimal. If we do so in your example, the 'solutions' for all six variables are non-real! This also may explain why "find" fails because "find" will only look for real values if you provide a real valued guess.

But I guess that you are not interested in non-real results anyway and expect real values and maybe also positive values as result.

I can think of two possible reasons for the behaviour:

a.) There exist real and positive solutions, but your guess values are way off and so Primes algorithm can't find them. In this case you would have to provide more realistic guesses for all six variables.

b) Your system really can't be solved because some of your equations/constraints are wrong and demand the impossible. In this case you would have to re-check your setup. your equations and see if they really describe the underlying geometry and if there really is a solution to be expected.

6 REPLIES 6
24-Ruby V
(To:Jacky.Dong)

I have no solution for your problem, juts a few remarks:

you have five equations but just two variables you allow to be changed. This can't work.

I guess that you would also like d.a1,da2,alpha.a1 and alpha.a2 to be changed. If thats true, you also have to include them in the "find" command even though you may not be interested in their value.

Now we have six variables for Prime to play with but only five equations. Normally this means that you can expect an infinite number of possible solutions and you could add additional constraints like x.1>0mm or the like.

But in case of your system, Prime can find no solution at all. Thats the first moment you may ant to re-check your variables and equations - maybe the problem really has no solution the way you had set it up.

If a system has no solution its always worth a try to replace "find" with "minerr". That way Prime will try to find the best variable combination where the overall errors are minimal. If we do so in your example, the 'solutions' for all six variables are non-real! This also may explain why "find" fails because "find" will only look for real values if you provide a real valued guess.

But I guess that you are not interested in non-real results anyway and expect real values and maybe also positive values as result.

I can think of two possible reasons for the behaviour:

a.) There exist real and positive solutions, but your guess values are way off and so Primes algorithm can't find them. In this case you would have to provide more realistic guesses for all six variables.

b) Your system really can't be solved because some of your equations/constraints are wrong and demand the impossible. In this case you would have to re-check your setup. your equations and see if they really describe the underlying geometry and if there really is a solution to be expected.

10-Marble
(To:Werner_E)

Hello Werner

Thank you for your answer and advice, I think you are right, I have updated the Mathcad sheet with the Chord position root-finding method.

and I just want to say this is what I wanted at the beginning,

anyway, do you know how to program the iteration?

20-Turquoise
(To:Jacky.Dong)

10-Marble
(To:ttokoro)

hello 🙂

Thanks a lot. Respect!!!!👍

24-Ruby V
(To:Jacky.Dong)

@Jacky.Dong wrote:

Hello Werner

Thank you for your answer and advice, I think you are right, I have updated the Mathcad sheet with the Chord position root-finding method.

and I just want to say this is what I wanted at the beginning,

anyway, do you know how to program the iteration?

Do you really need a program which does the iteration step by step as shown in your sheet - maybe also returning all the intermediate results?

Or are you just looking for the numeric result? In this case you should use Primes built-in facilities for solving an equation.

The one which I would prefer was already shown by @ttokoro , the "root" function used by providing a range (a to b).

Another way to use the root function is by providing a guess value:

As an alternative you could use a solve block with "find":

Another option (which I would not suggest using) is to use the symbolics

But to get this result, two things have to be done first:

1) turn on the option for "units/constants in symbolics" in the calculation options
2) Define

somewhere at the top of the sheet.
Reason for both steps is that the symbolics does not know anything about units and treats them as unknown variables.

I won't suggest using the symbolics if you are just looking for numeric results.

10-Marble
(To:Werner_E)

yes, I just looking for numeric results, @ttokoro 's method is enough for me. thank you very much😉

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