Some notes on a clock design

National Institute of Standards and Technology (NIST)
The Time

It all started with gears! I have an interest in gears. Most clocks require gears, so why not build a clock? This was also an experiment in rapid model design that turned out to be not so rapid. I plan to build a clock from acrylic plastic. I have been using a LASER cutter to cut 1/4 Plexiglas. This first batch of gears was cut at Freedom Arts & Manufacturing a LASER cutting service. The following picture shows a cutting plan for the LASER cuttter to follow. Note that the voids that form the spokes of the largest gear are 16 tooth gears. This saves materials and makes an interesting spoke design. The figure at the lower right is an experimental escapement design that failed.

A pendulum timed clock also requires an escapement. This is a simple component, but with many subtleties. An entire book has been written on the subject and can be ordered from Mark Headrick's Horology site.

Philippe de La Hire was one of the first to suggest the epicycloidal profile for gear teeth. I find this form more pleasing than a traditional involute spur gear. I may use this form my clock design.

left analysis by de Vinci
right analysis by La Hire

Modern cycloidal gear form

On the right is a nine tooth cycloidal gear designed for me by Bob Kunkel of Roberts Engineering and Design in Albertville, Alabama. Bob also designed all my other gears. Great job!

Gear ratios are chosen to convert the time counted by the escape wheel into minutes and hours. For a 30 tooth, 60 second escape wheel a 60:1 ratio is needed to count 60 minutes for one hour. Then to count 12 hours, a 12:1 ratio is needed. Below, the 9:78 and 13:90 gear train produces a 60:1 ratio. Note that the intermediate ratios are not integer values. It may seem more intuitive to choose a train with a 15:1 followed by a 4:1 to get 60:1, but a gear train with non-integer ratios will produce more even wear on the teeth over the lifetime of the clock. I wrote a program to search all gear combinations over a given set of restrictions to produce the values shown below. It took less than 60 seconds to search about 2 million combinations and was written in Java.

This is the most current schematic of the clock. The pendulum is not shown. Gears are represented by pitch circles.

An older version -- unfortunately, the direct 720:1 gear ratio would result in a large gear size of almost 20 meters (for a metric module 4 tooth size). Maybe someday... Other alternatives would be a longer pendulum period.

Experimental Escapement

Sorry about the poor quality pictures, but all I had handy was a toy Polaroid camera. These scans came from pictures about the size of a postage stamp.

This is a Pin Wheel Escapement. See Mark Headrick's Pin Wheel Escapement animation page.

The wood fall-weight is directly connected to a spindle behind the escape wheel. There is no gearing. The faces of the palettes are lubricated with powdered graphite.

Interesting links

The Clocks Site A great site by Carlo G. Croce

Timezone Good escapement info

glass clock

Melchester skeleton clock

Delightful Machines articles on mechanical movements


Antikythera Mechanism
Antikythera Mechanism II
Delightful Machines Horology

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