Equation to be found

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1

 Hello everyone,

 

I am faced with a mathematical problem, I need to find an equation of a point as a function of a value (see attached sketch)

The sketch represents a radius under the head of a screw, and my goal is to find mathematically the point indicated for machine programming. We can see a circle with radius 0.1 that corresponds to my tool, which originates from the projection of these two sides.

My radius under the head is cut into three rays, which have junction points constrained at 7° (the three rays as well as the two smooth parts are all tangent). I also have as the starting point of the radius, the positioning formula which is the x-ray (7/5.5). In the end, only my radius value (the middle one) can be changed. The tool is tangent to the radius and coincides with respect to the point where the rays meet. My goal is to find the coordinates of the origin of my tool with an equation where only the value of the radius can be modified into X and Y (Two equations at once).

I also attach the 3D sketch if ever

Thank you in advance for your answers.


capture.png
2

Sketch attached

 


probleme_mathematique.sldprt
3

Hello

Have you looked at it by decomposing into several triangles in order to solve the problem by simple trigonometry calculations   ?

Cdt

Fred

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4

I tried but I can't get a concrete result, when I increment the radius, the position of the origin point does not increase linearly. Until today it was used a calculation with a ratio, however when you vary the radius too much, you are in a mess. I can't translate the tangency between the radius of the tool and the profile of the radius into an equation (since it's never in the same place depending on the radius chosen).

5

Hello Kilian

What good are your 7°?

I don't see why you're looking for the bottom equation that doesn't correspond to anything functional.

Can you tell us more about it if not difficult to help you

It's curious because if your tool moves from bottom to top it means that you have a variable inclination of your tool head.

You should tell us how your  tool moves

Plush

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6

After several tests, I realized that making a single radius we obtained false results on the parts aesthetically and even in terms of value. I came to the conclusion that by cutting my radius into three with the two larger end spokes, I got a perfect result. The 7° is therefore imposed on myself to constrain my radius junction points. What I'm looking for is the trajectory points of my tool in relation to my profile. I don't want to go into too much detail so as not to lose you, I'm just trying to find a calculation with an unknown value that corresponds to my radius that I want in the end (which corresponds to the radius of the middle).

To date I have made good progress, I try to break it down into a triangle as Fred had indicated.

Attached is a small diagram to understand how the system works. 


capture.png
7

It's okay I made it, thank you for your help

8

Great kilian

Don't forget to close by indicating the best answer.

Have a good week :-)

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9

@ Killian it's not nice and not very constructive 

to name you the best answer since it does not give any solution to the problem stated 

How do you expect another participant to solve  your problem with this answer

@+ -1

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10

Hello

"It's okay I made it, thank you for your help"

Yes, but if you could elaborate on it, we might be interested.

may the force be with you.

 

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11

Hello

I found values on my sketch which was fixed whatever the radius imposed, then I started from the center of my imposed radius (R0.6 for the capture)

I first looked for point A on the capture (I don't care about my wheel radiated at 0.1). I used the thalli theorem with the angle of 18.35° fixed to it, as well as the ratio of 0.0379.... * Radius that is also fixed. So I deduce my position in Y from the point A or I add the value of 0.00501 which is also the same according to any value of the Radius

 Y position:  (( R * 0.03792708333) + ( R – (-R * Cos(18.35136876)))) + 0.00508564

For my position in X, since I have my position from point A to Y as well as the angle at 7°, I also use the thalli theorem. So I find a value of the point A in X or I add a fixed value of 0.0685

X position: (( R * 0.03792708333) + ( R - ( R * Cos(18.35136876)))) / Tan(7) + 0.06851565

The two sides are symmetrical, you just have to reverse to get the right equations, it's a bit laborious but it works (I took a lot of digits after the decimal point for my fixed values in order to have the fairest possible result at the end).

 


capture.png
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