Not really.   Imagine the crown wheel made on a wooden drum with a metal tire just like a wheel.  Now say you want 13 teeth on your gear that are 1 inch in length.  The circumference is 2 X Pi X r = Pi X D = 13  That works out to be a 4.138 diameter crown gear.  -Probably too small so maybe 51 in teeth.  51 / Pi = 16.234.  In other words adjust the size of teeth and number of teeth to get a convent size size gear and number of teeth you want.
  A second method involves figuring out the circumference as above for the exact diameter crown gear you want.  Lay out a line that is the length of the circumference.  Lets say you want a 16 inch crown gear with 23 teeth.  Pi X 16 = 50.265.   This is how long the strip of metal needs to be. (you will obviously need to add seam allowance for overlap for riveting or welding or however you will fasten the ends together to make a loop.)  To lay out the position of the gear teeth you will need a measuring rod marked out with 23 spaces on it.  These spaces will need to be a little bigger than the gear teeth -say 1/4 in or so but they must all be the same.  Lets call these units quinches so we can talk more easily about them.  Now put a square at the end of your last tooth on your strip your laying out your teeth on.  Put the 0 position of the measuring stick you have made that is marked out in quinches at the beginning of the first tooth. raise the opposite end of the quince ruler until the 23 mark intersects the edge of the square.  That is to say you have created a right triangle where the base is 50.265 inches long, the hypotenuse is 23 quinches long, and the height is what ever was necessary to make it a right triangle.  You now can mark the beginning of every gear by drawing a vertical line that is at a right angle to the base from each quinch mark.  This is a way to divide any line into any number of equal pieces.

I bet you can tell I once had a real drafting class that used a penile and straight edge!



On 8/1/2013 10:54 AM, <Franz Johann Gottskrieger> wrote:
[log in to unmask]" type="cite">
Oh, and for the record, the non radial pin design has the distinct disadvantage of requiring an ODD number of gear teeth in the crown to function. That was their hold up as well. How do you use a compass to construct an odd number of evenly spaced teeth around the circumference of a circle?  It's not just the period manufacturing tools that restrict, but the period design tools as well.

Franz



On Aug 1, 2013, at 4:25 AM, Jerry Harder <[log in to unmask]> wrote:

SOOO....   Having reached a dead end and posted to the net I then found the word 'strob'  That opened up everything and I found the sources you mentioned and of course have figured out that both forms of the verge and foliot  design are period, and both appropriate to be hanging around in the great machine with the crown wheel version being the most appropriate (later version) but the double pinwheel ie strob version being easier to build (out of wood at least). But when did I ever take the easy way out. 

So which one do you have half built?  You are ahead of me on this, right?

On 8/1/2013 2:58 AM, john heitman wrote:
[log in to unmask]" type="cite">
not only is that type period, it is recognized as frontrunner for the first truly mechanical only movement.

The man who was to be come Pope Sylvester II had what is acknowledged as the first completely mechanical clock in 996 CE, and it supposedly had this radial pin design.  But that is all buried in my notes as to the quote source.

However, to give you the reference you are desperately seeking:

1327 CE - Richard of Wallingford ("Tractus Horologii Astonomici") wrote on a tower clock he built for the Abbey St. Albans that it had a "strobe escapement", two wheels on the same axle with alternating radial teeth/ verge suspended BETWEEN them, with a short cross piece oscillating as the wheels rotated past. (no currently known period examples exist, primarily because they lost as much as several hours a day, and were quickly changed over in the 1600s to the vertical pendulum because those lose only minutes a day.

Part of the problem is that a) the first treatise on clock making wasn't until 1364 when the son of a clockmaker expounded upon his father's work, and b) as stated above, they were all changed over to the vertical pendulum in the 1600s.

So,Good Master, since I seem to have gotten you hooked,  your other research terms should include "escapements" and, oddly, "engines".

The best site I found, however, was .www.my-time-machines.net/speech_final_web.pdf.  Full out presentation on the subject. I can give you more if you like, but that is the mother lode.

franz



On Thu, Aug 1, 2013 at 1:41 AM, Miklos.Farma <[log in to unmask]> wrote:
You want to read this book:

Shaping the Day: A History of Timekeeping in England and Wales 1300-1800, by Paul Glennie and Nigel Thrift

http://www.amazon.com/Shaping-Day-History-Timekeeping-1300-1800/dp/0199278202/ref=wl_it_dp_o_pd_S_nC?ie=UTF8&colid=36NTMMOPUZONZ&coliid=I2OPPLIHIHO3IA

It has a rather large section on the verge and foiliot designs, and a number of very good sources.

Miklos


On 8/1/2013 12:58 AM, Jerry Harder wrote:
I have been doing some research on clock escapements.  Turns out pendulum escapements aren't period by about 65 years.  Verge and foliot with a crown wheel where the pallets engage with opposite sides of the crown wheel are.  There are some verge and foiliot escapement designs which have 2 gears with pins that replace the crown wheel and the pallets both engage the top of these two pin gears.  I am looking to prove or disprove weather this type is also period.  Any help would be appreciated.  A simple search on firefox gives a great overview on wickipedia, and  www.youtube.com/watch?v=7HgAtCn3VUU shows the two pin-wheeled type.