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Intersections Calculate 2 circles / Analysis / Math

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Re: Intersections Calculate 2 circles / Analysis / Math

Look if the attached helps.

BTW, the error you get is because you have to use the vector index when you type theta[i, not the literal index you get with theta [ctrl -] i.

 

 

Re: Intersections Calculate 2 circles / Analysis / Math

Thanks, this is what i need, but now i dont understand were is the calculation on the sheet (equation f(x,y)....)?

 

Is it possible to get the x1/y1 and x2/y2 koordinates as a variable? Read it out of the matrix?

 

i have to calculate with this values in later calculations.

 

The reason, why i want to calculate this is, i have a hydraulic zylinder. This zylinder lifts a crucible. i need to know at which stroke in mm the corner of the crucible is in degrees.

 

so i need the x koordinates, and subract the x-value of the upper cycle from the x koordinate. then i can calculate with the corner functions the degree of the crucible.

 

is it possible to get a matrix or something else, to get a list with values for each millimeter for the stroke (0-440mm)?

 

Re: Intersections Calculate 2 circles / Analysis / Math

oh,

i found the calculation 🙂 i have to click the "+". I dont understand the first calculation. I think i have to study math for this, mechanical engineering isnt enough to understand this :-(.

Re: Intersections Calculate 2 circles / Analysis / Math

No need to study math.

kreis() simply creates a m N-sided polygon to approximate a circle and is only used for plotting.

It creates a (N+1) x 2 matrix with the coordinates of the points. first column x-coordinates, second column y-coordinates.

Its a utility routine you can use if you intend to plot a couple of circles and don't want to bother with any kind of equations.

 

Concerning the matrix you are looking for or the angle - I am pretty sure Mathcad can deliver what you need, but unfortunately I don't understand which values you would need. Not sure where the 440mm you mention do stem from.

 

When it comes to the coordinated of the points of intersection, you may either access them as matrix elements using matrix indices and of course you may also assign the values to dedicated variables, too.
See attached sheet.

Re: Intersections Calculate 2 circles / Analysis / Math

Reply to your PM below:

According to you handwritten notes in a former answer it looks like not the larger circle is your cylinder but your cylinder rather is a radius of that circle and the smaller circle is not the lever but rather the path of its end.

It looks to me like your are only interested in the upper left one of the two points of intersection, right? The one with the lower x-coordinate.

As the lever and the cylinder are connected, the cylinder must have a minimal length of about 7,38. Otherwise the two circles will not intersect.

So I wonder why you are talking of a range from 4 to 8?

See if the attachment is of help

 

 

---- snipp --------------------------------

ich versuche es hier mal auf deutsch, da englisch nicht so meine Sprache ist 🙂

 

Ich brauche im Endeffekt eine Tabelle, wo ich abhängig vom Hub des Zylinders (Zylinder ist der unter Kreis (0/0)einen den Winkel des Hebels errechnen kann (Hebel ist der obere Kreis), vllt kann man das auf dem Foto mit meinen händsichen Berechnungen erkennen.

 

Wenn ich den x Wert zum Hebel kenne, welcher constant ist (in dem Beispiel der Wert x = 7), dann kann ich mir den Winkel errechnen, dadruch, dass ich die 7 minus meinem x wert der koorinate nehme. dann bekomme ich eine seite des dreieckes, der Hebel ist immer konstant (3,25= Hypotenuse).

 

Ich denke auf dem Bild kann man die Problemstellung erkennen, ansonsten kann ich gerne eine Skizze machen.

 

Der Zylinder hat eine Länge von, sagen wir mal 8, dies ist der Radius = 8, ausgefahren. Fahre ich den Zylinder ein, dann hat er z.B. eine Länge von 4. somit brauch ich am besten eine Tabelle, die die Winkel von 4,01, 4,02.... bis 8,00 ausspuckt.

Re: Intersections Calculate 2 circles / Analysis / Math

Hey, thanks for your new version, it is getting more complicated, but this is what i need. The r_start is 1108 and the r_end is 1548. The calculation of the lever angle begins at r_start (zylinder lenght) = 1108, (in my CAD-Modell the angle then is approximately 14.6 degrees. I have to confess, that i dont fully grasp this sheet, i thought that the calculation is easier. 😞

 

yes the larger cycle is the Zylinder, i posted a sketch with the real values. the values of 4+4 and 3.25 are values which makes it for me easy to check my calculation and to ensure my way is the correct one.

 

Yes you are right i am only interestet in the left (lower x) intersection and the x-value of it. The max value of zylinder is 1108mm+440mm.

 

Marc

Re: Intersections Calculate 2 circles / Analysis / Math

There might possibly be shorter approaches to your task but I don't consider the sheet complex or complicated (you can completely delete the first page) and it should work with the real values you have as well, I hope.

Re: Intersections Calculate 2 circles / Analysis / Math

Hey,

so, i got the solution for my problem.

Now i have to implement a table where the values from 0 to 440 are shown.

 

@Werner_E can you tell me, what you did on top of the sheet kreis(xm,ym,r):=.......  ?

 

Thanks for help.

 

Marc

Re: Intersections Calculate 2 circles / Analysis / Math

Thanks to Werner_E for your very good Mathcad sheets. 

Now I can use your Mathcad sheet and it is very helpful to understand the usage of Mathcad functions.

Tokoro.

 

Thanks_for_Werner_E.png

Re: Intersections Calculate 2 circles / Analysis / Math


@Marc2610 wrote:

Hey,

so, i got the solution for my problem.

Now i have to implement a table where the values from 0 to 440 are shown.

 

@Werner_E can you tell me, what you did on top of the sheet kreis(xm,ym,r):=.......  ?

 

I think I explained that shortly in an answer above or in my PM.

"kreis" is a function which takes the coordinates of the venter of a circle and its radius as arguments and returns a 2-column matrix containing the coordinates of 96 points of that circle. This structure is only used for plotting. You can see in the plots that I place the first column at the abscissa (x-coordinates) and the second column at the ordinate (y-coordinates).

The first pair is [NaN NaN] which was chosen for two reasons:

1) Its easier to program if we can already start with a two column matrix

2) Its possible to stack multiple matrices representing different circles and plot them with one command (but all in the same color).

So again - "kreis" is only used at the first page of the sheet as its the easiest way for me to plot one or more circles.

For the calculation of the points of intersection or the table you were looking for its not needed at all.