Calculating curve for a machine

[Phillip81]

Mod note: Thread moved from the Precalc Homework section
1. Homework Statement
So I am designing a machine. the issue is I have to calculate like 8 things and the maths is floating in my head but I can't get there.

the requirements are that X axis squared + Y axis Squared = 75 Squared.
then project a line out another 75 from there to get the arc I am referring to. I have included 2 rough attempts at trying to find the arc but no maths involved.
now the vertical line will always be above the horizontal. but the horizontal can go + or - 75

Homework Equations

to equate the points pythagoras... to equate an arc from this... My brain is overloading

The Attempt at a Solution

I got some pics for ya

 

[Baluncore]

Welcome to pf.

There will be two points, one on the x and one on the y axis.
By Pythagoras, the line that joins those two points has a length of 75.
The angle of that line is not specified so consider the locus of all possible positions for that line.

If you extend that line by another 75 in the same direction, (say at the x end), the extension will trace the points P( –y, 2 * x ).

Google "ellipse mechanism"
https://en.wikipedia.org/wiki/Trammel_of_Archimedes

 

[Phillip81]

ok let's say I am a noob... like 1+1 = 7 type of noob. if I was to use resource like https://www.symbolab.com/solver/ellipse-equation-calculator/-y2x how would I get the same arc?

oh and thanks for the hi

 

[Baluncore]

You know that the extension is the same length as the hypotenuse line = 75.
The semi-major axis of the ellipse, a = 75+75 and the semi-minor axis, b = 75.
Find the general equation of an ellipse in Cartesian coordinates, in terms of x, y and a, b. wikipedia?
You can then write the equation of an ellipse from that information alone.
What would happen if the extension was a different proportion of the diagonal?

 

[Phillip81]

I realized this was in homework... but its not for a course or school. my bad if someone wants to move it I would appreciate it.

I have rethought the idea.now the vertical axis had to be stationary. this is because the home must always be the same in x y and z. Z is not moving so I only have x and y to move. as the pivot point is the middle point I will use the bottom point to move the item backwards and up. now I have a lot of maths to play with

 

[Baluncore]

You probably need to know about these copyright free books. http://www.gutenberg.org/
Where you will find ...

How to Draw a Straight Line: A Lecture on Linkages by A. B. Kempe.
http://www.gutenberg.org/ebooks/25155

See also;
http://web.mit.edu/2.75/fundamentals/FUNdaMENTALs Book pdf/FUNdaMENTALs Topic 4.PDF