new help with a 3D printer Design flaw!

Okay so I designed and made my own large format 3d printer . While considering the cons of a large printer. One being the added mass to the moving parts and how that will limit the top speeds achievable during a print . Another is time to complete a large print. my printer has a printable work area of around 410x940x500mm Large is probably an understatement.What I decided on was a heavy duty frame and z axis structure and mechanism to keep everything rigged while under the huge force invoked with a sudden change of direction while at high speeds. I made this main structure of steel and aluminum , While keeping the gantry and extruder as nimble as possible. I Made it with carbon fiber and 4 aluminum bearing blocks that have been lightened by shaving and drilling of excess weight . Since it will be doing like 98% of the all moving during a print. The scissor lift mechanism was born and although different than any printer I have seen . And it posses some new issues it also fits my design criteria beautifully. this design would also allow me to offload the Y axis and its hardware from the gantry or carriage and moving mass. Together with a bowden extruder all would help make the carriage very nimble. another advantage is my work bed will be stable and more consistently level Than say a bed that’s counter levered out from a single support point. requiring constant leveling of the bed before every print. one more plus is it can be stored in a compact space like under a bed. Now fast-forward to today and_** the machine was made several moons and 4 Ramps boards latter**_. and let me tell you its capable of moving the head at blinding speeds with accuracy some other issues i have been dealing with in order to move that fast while printing are tip temperature stability and power consumption short comings.
The cons of my scissor lift design are not immediately apartment nevertheless were considered and ruled out as an easy code fix .
The truth is I have no Idea how to go about doing this . You see the problem with a scissor lift is the resulting travel (or displacement ) of the bed from the actual z motor travel is a variable curve . or the layer increment amount gets smaller with every new layer. The ratio between the two is only equal when the total height of the machine(or scissor lift part) is equal to the total width of the machine. this is true only when one stage of the scissor lift is used with a second stage lift amount would double and multiply by the no. of stages but irreverent in my case only one stage . As it is now my printer starts with a layer height that’s too thick and gradually gets closer to the correct height then continues to shrink every time a little less than the previous layer.

I know its a simple Math equation to solve for, The Pythagorean theorem can be employed here but have no clue where , how , or why to code it.
So please if there any code Wizards out there that can help . Please help me to make my machine have the glory it deserves

Anybody Please any advice is welcome just point me in the right direction
Is my problem too complicated or isolated has no one ever tried what I’m attempting?
Any word of advice is welcome ! :geek:

Just put a vertical Z axis on both sides of the scissor. Make it so your can slide the top to the left and the bottom to the right and lockable in the center.that way your z travel is linear and you keep the ability to stow your printer. Stowing procedure would be go to max z travel un latch the z axis mounting points and lower it down

That is an interesting build, I would imagine there is a lot to tweak to remove unwanted play from the scissor. You must clearly have a bunch of mechanical skills to do that build, why not put them to use and build a drive with a cam ? The cam could be shaped to make the move from the motors point of view linear. It would probably also reduce the load on the motor when the scissor is at its lowest point.

If two same shaped disks on a shaft driven by your stepper would push against some form of rollers at the point where the scissor slides on the machine base that could give you what you need without the need of changing software. That is if you can figure out the math on how to shape the disks.