Ballscrew position in a scissor mechanism

[Dave7000]

TL;DR Summary

Spindle position in scissor mechanism to achieve uniform movement.

Hello, regards to all.

I am designing a CNC machine where the table will work as a Z axis.
I have found a complication when trying to save space under the table, to avoid set the ballscrew upright I have decided to make a scissor mechanism but I have noticed that when the ballscrew travel 10mm, the table does not.
I placed the ballscrew in several positions, not in the center of the legs pin or totally horizontal to achieve the same travel between ballscrew and table height, or some fraction as half or 1/4 something that can be fixed later with the machine controller.
At first I thought it could be a mathematical problem of triangles. I'm not so sure anymore. After days trying I ask for help in this forum to save the scissor desing.
Can anybody help me?

 

[BvU]

Hello Dave, !

It's one and all Pythagoras.

If I sketch your jack, you see that for height h, $$h = h_1 + h_2 = \sqrt{B^2 - (S/2)^2 } + \sqrt{A^2 - (S/2)^2 }$$ with A and B the leg lengths and S the screw length. So your driving algorithm has to do some math to convert S to h

 

[Dave7000]

Greetings and thanks for the answer.

In this way I have calculated the measurement of leg A to obtain the desired height but when I move the spindle 10mm for example, the height does not move 10mm exactly.
Any idea to calculate the measure of the leg A so that when moving the ballscrew S it matches with the total height H travel?

 

[Baluncore]

The scissor is not a linear function in width:height, so you must design a reciprocal scissor that lies flat, driven cross-ways by the screw, that then controls the vertical scissor separation. That will perform the anti-function and so cancel the curved response, giving linear vertical movement tracking the screw.

That correction linkage is really just a 3/4 partial scissor. But you must also control the table x, y position and rotation about z, plus keep the table level, and at the height z. How you do that will decide the design of the simplest correction linkage you can use.

 

[Dave7000]

I also came to the conclusion of the antifunction, I did some mirror tests with two overlapping mechanisms but I don't understand how they should be joined.
Can you draw an example?

 

[Baluncore]

One 4 link diamond in a vertical plane, another in a horizontal plane, sharing mid points where they might be joined by pins.
You need to integrate the scissors while controlling all the other free dimensions. You have not identified the other controls. That will determine the solution.

 

[BvU]

So your driving algorithm has to do some math to convert S to h

@Dave7000 : what is driving the screw ?

 

[Dave7000]

The screw is driven by a stepper motor.
The motor controller cannot make that kind of algorithm. Even if this could do it, it would lose a lot of intermediate precision and would have to work with many microsteps.

 

[Dave7000]

One 4 link diamond in a vertical plane, another in a horizontal plane, sharing mid points where they might be joined by pins.
You need to integrate the scissors while controlling all the other free dimensions. You have not identified the other controls. That will determine the solution.

View attachment 250550

I tried this without success.
I am focused on getting the inversion of the angle made by the triangle, I suppose that in this way what one adds the other subtracts while still moving up. I keep trying to connect the two triangles, any help is welcome.

 

[BvU]

The screw is driven by a stepper motor.
The motor controller cannot make that kind of algorithm. Even if this could do it, it would lose a lot of intermediate precision and would have to work with many microsteps.

Is that a feeling or the outcome of a calculation ?
I fail to see how a complicated mechanical solution can achieve an apparently extremely high resolution.

Did you study a linear alternative with three or four parallel vertical screws ?

 

[Dave7000]

Is that a feeling or the outcome of a calculation ?
I fail to see how a complicated mechanical solution can achieve an apparently extremely high resolution.

Did you study a linear alternative with three or four parallel vertical screws ?

It is closer to a feeling.
The alternative you propose is not possible since it would mean redesigning everything, more costs and two motors moving the same axis, which I don't like very much.

 

[Baluncore]

I tried this without success.

It works. What did you try? Did you make all links the same length?

... and two motors moving the same axis, which I don't like very much.

Two ball screws would be connected by a stepped belt with one motor and one controller.

 

[Baluncore]

With a link length of 1.000
For screw length, s = 0.5 to 1.5
width of diamond, w = 2 * √( 1 - ( s/2 )² )
height of diamond, h = 2 * √( 1 - ( w/2 )² )
Symmetry makes the function it's own anti-function.

screw width height
0.500 1.936 0.500
0.600 1.908 0.600
0.700 1.873 0.700
0.800 1.833 0.800
0.900 1.786 0.900
1.000 1.732 1.000
1.100 1.670 1.100
1.200 1.600 1.200
1.300 1.520 1.300
1.400 1.428 1.400
1.500 1.323 1.500

 

[Dave7000]

With a link length of 1.000
For screw length, s = 0.5 to 1.5
width of diamond, w = 2 * √( 1 - ( s/2 )² )
height of diamond, h = 2 * √( 1 - ( w/2 )² )
Symmetry makes the function it's own anti-function.

screw width height
0.500 1.936 0.500
0.600 1.908 0.600
0.700 1.873 0.700
0.800 1.833 0.800
0.900 1.786 0.900
1.000 1.732 1.000
1.100 1.670 1.100
1.200 1.600 1.200
1.300 1.520 1.300
1.400 1.428 1.400
1.500 1.323 1.500

I think you are miscalculating. Have you tried it on a model with a CAD program?

Thanks for the options but I think I'll place the ballscrew vertically under the table, it is simpler and less expensive to do. All the bad things will be that I can't add a drawer to save tools.

 

[BvU]

Huh ? I thought the table was to go up and down, not that it has to spin around ??
And if it has to move and still be accurate, cross your fingers !

 

[Dave7000]

Sorry, I forgot to say that it has 4 linear guides near the vertices of the table to avoid twists or turns. It is a machine within a frame and the guides are fixed to the structure.
As for the precision, I don't think there is another better way because it moves directly, even if the ballscrew has any backlash the weight of the table will relieve it.
Later I will post some photos to show it. Now I am finishing the bridge and the X axis. When I return to the table I will try the scissors for the last time, if not it stays that way.