Rotary Cogwheel

All the historical information on this page comes from the fascinating "Rotary Global Fellowship" web site
http://www.rghf.org/
Specific history of the origin of a cart wheel morphing into a functional cogwheel can be found within the RGHF site at
http://www.rotaryfirst100.org/history/history/wheel/
The following is taken from
http://www.rotaryfirst100.org/history/history/wheel/index.htm
but anyone with any science or engineering background will realise, by the time they get to the end, that it has been written by someone from outside those disciplines:

"A wheel has been the symbol of Rotary since our earliest days. The first design was made by Chicago Rotarian Montague Bear, an engraver who drew a simple wagon wheel, with a few lines to show dust and motion. The wheel was said to illustrate "Civilization and Movement." Most of the early clubs had some form of wagon wheel on their publications and letterheads. Finally, in 1922, it was decided that all Rotary clubs should adopt a single design as the exclusive emblem of Rotarians. Thus, in 1923, the present gear wheel, with 24 cogs and six spokes was adopted by the "Rotary International Association." A group of engineers advised that the geared wheel was mechanically unsound and would not work without a "keyway" in the center of the gear to attach it to a power shaft. So, in 1923 the keyway was added and the design which we now know was formally adopted as the official Rotary International emblem. "

Fortunately there is a link on that page ("Why so many cogs?") to the page
http://www.rotaryfirst100.org/history/history/wheel/cogs.htm
which gives the following much more satisfactory explanation, attributed to "the Philadelphia club, and published by Rotary Club of Bay City, Texas, 2004."

" The Rotary gearwheel is one of the most familiar symbols in the world today. But for many years, there was no standard Rotary emblem. Rotary clubs designed their own.
In its early years, the Rotary Club of Chicago used a wagon wheel emblem, an idea attributed to Paul Harris, who reasoned that it symbolized civilization and movement. The appearance changed from time to time.
When an engraver joined the club, he offered to design a permanent emblem. Members rejected his first idea---a plain buggy wheel---as looking lifeless and meaningless. To give the appearance of action, the engraver added clouds of dust ahead of and behind the wheel. He also placed the words "Rotary Club" above it. One observant Rotarian pointed out that a wheel would not generate clouds of dust in front of it. He removed the offending cloud and that design remained the emblem for Chicago until about 1912.
At the 1911 national convention in Portland it was suggested that delegates adopt a standard emblem, based upon the wheel, which had become the generally accepted emblem of Rotary clubs. The Board of Directors appointed a committee to come up with a design. Everyone was amazed how quickly the committee acted. They were appointed in August and had the emblem ready in September. All they did was copy the emblem used by the Rotary Club of Philadelphia.
The Philadelphia club had been chartered in 1910 as the 19th club in the world. [Bay City was the 134th club in 1915] The Philadelphians thought that the Chicago wagon wheel design did not convey the Rotary idea very well. They added cogs to create a working wheel, symbolizing the members working together, literally interlocked with one another to achieve the organization's objectives. They used 19 cogs in honor of their club. The club started producing metal lapel pins in 1910 with this design for its members to wear on their coats. Today, the millions of pins worn by Rotarians around the world had their genesis in the minds of a club president and a jeweler in Philadelphia in 1910. ->>

The 1912 Rotary convention in Duluth approved the Philadelphia design for the whole organization. To ensure uniformity, the club's name was replaced by the association's name, Rotary International. It probably didn't hurt that the president of the Philadelphia club [who had designed that club's emblem] became president of the International Association of Rotary Clubs at the Duluth convention.     
Even after approval by the convention there was still a divergence in design of the emblem. Many local clubs still had their own wheel. Some wheels had 8 spokes, other had 10, some none at all. Some wheels had 16 gear cogs, some 20, some none. Even the Rotary staff at headquarters was confused. In April 1919, the Rotary wheel on the cover of The Rotarian magazine had 19 cogs. On the May issue's cover the wheel had 20 cogs. On the June cover it had 27 cogs.     
In 1918, a Rotarian engineer from Minnesota petitioned Rotary to amend the design of the wheel. He said that a cogwheel with 19 cogs would not work. He said that the emblem had square-cornered teeth of disproportionate size, that the cogs were irregularly spaced. This Rotarian, Oscar Bjorge, said the emblem was "an insult to engineering that only the brain of an artist could conceive." So he sketched a new wheel, with 6 spokes [symbolizing the 6 Objects of Rotary at that time] and 24 cogs or teeth. He also added a keyway, which locks a wheel to a hub, thus making it "a worker and not an idler."
In 1928, the exact specifications of this engineer were written into the Manual of Procedure, approved at the 1929 Dallas convention. The specifications have been unchanged ever since. The geared Rotary wheel appears today throughout the world on millions of lapel pins, flags, ties, jewelry of all sorts, etc. It has been pasted on billboards and postage stamps in more than 100 countries. The Rotary wheel started as an idea in the mind of founder Paul Harris nearly 100 years ago. It has remained in its present exact form for 75 years.  "

Oscar Bjorge is a Rotarian the Webmaster of this site would very much like to have met. What he clearly will have said is that the teeth need to be an involute shape, as shown here, chosen for the hugely beneficial reason that that shape ensures no sliding movement as each tooth moves in contact with another when 2 interlocking cogwheels rotate.
Provided here, in case by now you are wishing
you could remember just exactly what the
equations of an involute curve are :





(for a parametrically defined function f(t) , g(t) )
Finally, back in the days when many Rotarians were young, the world was a dreadfully sexist place. Therefore most female Rotarians will have been deprived by a childhood totally devoid of Meccano.
For their benefit, and nostalgia for everyone else, here is the Meccano worm & one of the pinions.


(Sorry about the unfortunate word "France" seen here. I nearly got my extensive set of Meccano down from the attic straight away and photographed some proper Liverpool cogs. Once I do, the image shown here (from a Google search) will be replaced !)