# CNC Milling Machines for CAM

### Problems:

• Backlash Must be eliminated in hardware. Backlash compinsation is not applicable in Mills.
Peter Van Hoof says: "You set up your x-y table in front of the milling bit lined up exactly where you want it the bit turns as seen from above clockwise (just like an electric drill) the last adjustment to line the piece to be milled you moved it a little to the left you now move the piece forward against the bit the spinning bit excerts a force to the left on the piece being milled and because the backlash is left at the wrong side of the piece it will jump making measurments inaccurate and potentially creating a dangerous situation."

• Non-Linearity
Denny Esterline says: "Hardware store rod does have a nonliniarity problem. Rods I've measured are between -10 and +30 thou per "inch" of turns. The driver board I designed stores calibration constants in eeprom and compensates every half inch. With this method I was able to achive absolute positional accuracy of less than five thou."

### Alternatives:

http://freeandeasy.sourceforge.net/ A very inexpensive design for a computer controlled milling table. Not X-Y but has the same effect. A rotating base with an offset rotating table.

Main Arc Rotation= theta = 2*arcsin(sqrt(x^2+y^2)/2/R)
Table Rotation= phi =arctan2(y,x)+(theta+pi)/2
where R is the radius of the Main Arc

The second solution is found by changing the sign on theta, and the sign on the pi in the second formula. (In practice that sign may need changing anyway - it depends which direction is considered "positive" for the relevant rotations...)

When x==y==0 the second formula breaks down completely - you can spin the table to any angle you like, it just isn`t going to make anydifference.

As for how you generate a set of stepped angles for the machine, I think it works as follows...

• a) Break the path you want to traverse into Bezier curves (they are easy to subdivide)
• b) The two end-points will have two values for theta and two values for phi, which presumably you will step between in the same period of time. What you need to know is: are any of the points on this curve too far away for comfort from the original Bezier? (You may be very lucky and have a circle centred on the centre of the table!)
• c) Doing b) properly seems pretty difficult to me. So it`s a darn site easier to do a subdivision if theta or phi differ by more than 1. Eventually they will differ by either 0 or 1, in which case you step the motors to the correct place (with the drill-head up, if further awaythan 1).

As an algorithm you get:

```  DrawBezier(Bezier B)
(theta1,phi1)=Angles(B.start)
(theta2,phi2)=Angles(B.end)
If abs(theta1-theta2)>1 or abs(phi1-phi2)>1 then
(BLeft,BRight)=SplitBezier(B)
DrawBezier(BLeft)
DrawBezier(BRight)
else
if abs(currenttheta-theta1)>1 or abs(currentphi-phi1)>1
lift the drill
endif
move drill to (theta1,phi1)
drop the drill if lifted
move drill to (theta2,phi2)
endif
```

It`s important that the point called B.start is part of BLeft (and consequently that B.end is part of BRight)

http://www.tinaja.com/flut01.html "Flutterwumpers are low cost machines that spit or chomp. Such as printed circuit drills, sign routers, animation stands, CAD/CAM mills, plotters, Santa Claus machines, etc. A new approach to designing these machines involves both the PIC microprocessor and the PostScript computer language. This library shelf holds tutorials, resources, and application notes you can use to build yourself a flutterwumper. Such as a \$100 printed circuit drill or a \$200 Santa Claus machine.

Also:

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