Sorry, Brian, I've just realised that your print-out has been
sitting on my desk submerged for a week, and that I hadn't
acknowledged your help. I don't have a means of displaying
DXF files (I did try to install one of the monthly-magazine disks release
of TurboCAD v4, but it trashed the computer)

I'll reply once I've had the chance to decode the calculations in
the spread sheet.
TA!

"Brian Drummond" wrote in message
...
On Thu, 10 Feb 2005 11:32:36 -0000, "Airy R.Bean"
wrote:

I've conceived of a way of producing the beam by milling from
a bar and then screwing in the bushes, but what I don't know
are the intricacies of the Watt's Parallel Motion.

It provides a 5th order approximation to a straight line.

Discussed on the Yahoo groups "MLProjects2" group around 5-12 January
2004, refer to their archive for more info.

Here's a spreadsheet and diagram which should help design an accurate
link motion to any scale you want, and plot the error (deviation from
straight line) on a chart. For a given stroke, the spreadsheet lets you
find the beam length (and exact geometry) to meet any given error
criterion you want.

http://www.shapes.demon.co.uk/files/Beamer-5.xls
http://www.shapes.demon.co.uk/files/wattlink4.dxf

How it works...

All the input settings are in column B3-B11 of spreadsheet Beamer-5.xls.
Points A, B etc are illustrated in the CAD sketch wattlink4.dxf.
Outputs C(x,y) and CD tell you the remaining dimensions for minimul
error, and Chart 1 plots the error itself.

(excerpt from above discussion)

Start by setting the beam length (radius), and desired stroke of the
engine (currently 1000 and 720mm) in B3 and B4. If you are happy with
the bridle and link rods (half the beam and stroke respectively), leave
them, though you can enter different numbers and it SHOULD design you a
consistent and accurate linkage.

Then note that the beam angle A'Stroke is output in H4. Using it, decide
where you want to put the four zeroes in B8-B11. For example, choose 21
and 10.5 degrees for B8,9, and -10.5 and -21 will appear in B10,B11.

It will calculate 4 positions for D corresponding to zero error at these
4 angles, and use these (which lie on a circle) to calculate the centre
and radius of the circle, which gives the position of C, and the length
of CD. NOTE that if the bridle is shorter than half the beam length, CD
will be longer - and vice-versa - and the error can still be very low.

(If B10,11 are not mirror images of B8,B9 then the four positions of D
may not lie on the same circle, and the calculated positions of C (in
columns N8-O11) will not be the same. This is a good check that the
model is working...)

The resulting error is calculated in O16 to O42, involving the Cosine
Law (thanks to Robert Smith for that one!) roughly as per his
spreadsheet, and plotted in Chart 1. (You can modify the range to
display using Chart/Source Data when the chart is displayed)


Try 21 and 13 degrees, for slightly lower error.

Or 21 and 0 degrees, it should re-create the motion according to Jeynes.
(oops! try 21 and 0.001 degrees :-)

Or set the stroke to 600mm, note the beam angle is now only 17.45
degrees, and choose 17 and 10 degrees for B8 and B9. The error is under
0.1 mm!

Enjoy...

- Brian