it’s a mass of equasions, and the problem with the stock design is that there
are just too many variables
you have
- the space between the motors
- the space from the top of the work area to the motors
- the space between the chains where they attach to the sled (note that this is
where the chains pivot, not the end of the chain inside the bracket)
- how much chain you loose from the calibrated ‘end of the chain’ and where the
chain pivots
- the distance down from the line connecting the chain mounts to the center of
the bit
- the distance down from the bit to the center of gravity of the sled.
if any of these measurements are off by a few mm, you see noticable errors in
your accuracy.
This is because you have the question of what angles you have in many places.
Depending on the left-right position of the sled, and the values of 3-6, the
sled tilts different amounts left to right. and depending on this angle, the bit
cuts in a different place. This angle also affects the angle of the chains, and
depending on the angles of the chains, they wrap around the sprockets a
different amount, which changes where they stop being a circle and become a
straight line.
This calculation is so messy that we don’t actually know how to calculate it by
putting in either the chain lengths or the desired X/Y coordinates and get back
the other set. Instead we have to guess, and see how far off we are, tweak our
guess and try again. By default we do this up to 5000 times (down from 50,000 in
earlier versions) and it’s not uncommon for us to run into the condition where
we give up.
the triangular kinematics is far simpler
- the space between the motors
- the space from the top of the work area to the motors
- the distance to add to the chain to get from the calibrated ‘end of the
chain’ to the center of the bit.
this still has the problem of chain wrap around the sprockets, but other than
that, this is simple trig.
we can measure #1 fairly accurately, the chain has very little stretch, and not
much sag, so we can start from a (fairly) known position, run the chain out
until it reaches the other motor in a (fairly) known position, and pull the
chain tight. Since we know how far the motors have rotated in this whole
process, the amount of chain between the two motors is known pretty accurately.
We may be able to improve this measurement if we can more accurately position
the motors to start with (manually setting one prong on the sprocket ‘straight
up’ when you are measuring to an accuracy of 0.044 degrees isn’t that accurate),
and if we measure the sag of the chain (impossible to do with the stock frame,
not hard with the alternate ‘top beam’ approach)
making sure the frame isn’t flexing while the chain is pulled tight is also
important.
#2 doesn’t really matter that much, it’s an offset value, if it’s wrong, the
work area is a little higher or lower than you think it is.
#3 is the only remaining thing, and this is here the linkage vs ring debate
starts.
A. Which is easier to mount accurately (so that the chain motion is truely
centered on the bit)
B. Which has less error in use (chain rollers not moving plus tolerances in the
rollers/bearings) vs slop in linkages). Both have the question of flex in the
materials and wear on whatever joints there are.
C. Which makes it easier to define the amount to add to the chain.
I like!