THE THEORY OF MECCANO GEARS

Part 2: Helical Gears

Appendix

Following publication of my article “The Theory of Meccano Gears – Part 2 – Helical Gears”, in which I suggested the pitch of Meccano helical gears is 35DP; the question has been raised regarding Exacto’s helical gears being 34DP?

I had realised this during compilation of my article, and spent a great deal of time studying the two proportions in seeking the most likely answer. The logic I used in justifying 35DP is as follows.

Using The expression for calculating the Centre Distance based on the number of teeth (T+t), the helix angle (σ) and an assumed diametral pitch (DP):

CD = (T+t)/2/cos σ/DP

the 14/35 tooth pair at 35DP yields a CD of 0.989949 in. (10 thou’ short of 1.0”). The same pair at 34DP yields a CD of 1.01909 in (19 thou’ greater than 1.0”). if integer diametral pitch values were chosen, then 35DP would be the most likely.

Alternatively, transposing the formula to calculate the DP from the known tooth numbers, helix angle (45deg.) and centre distance (1 inch) yields the fractional DP 34.64823. Rounding this to the nearest integer also gives 35DP.

Of course, any fractional/decimal value of pitch could have been used, but at the time that these gears were introduced by Meccano Liverpool, the decision would have been most likely based upon available tooling and the practice of adopting ‘standard’ (integer) proportions for gear manufacture.

An in-depth study of both pitch possibilities using my gear design programme showed that these gears could be made to either pitch, 35DP with a small amount of positive profile shift or 34DP with a greater amount of negative profile shift. Gears made to both options would be virtually indistinguishable using hand measuring tools, and certainly interchangeable.

So, why are Exacto gears 34DP? It could be that Exacto was very forward thinking (or Meccano was all those years ago) in planning to extend the range. If we could create a wish list of additions to the helical range, it would surely include the following:-

• A helical pair to mesh at ½” centres.
• Opposite hand (LH) helical gears for meshing on parallel axes.
• A wider range of ratio availability.

The first two possibilities would be satisfied by a left and right hand 12 tooth pair – exactly what Exacto have done, as well as to add considerably to the range of sizes, ratios and combinations available.

Using the transposed expression DP = (T+t)/2/ cos σ /CD, the Exacto 12 tooth pair yield a pitch diameter of 12/cos45/0.5 = 33.9411255 (Near enough to 34DP!).

I would be happy to accept either scenario; perhaps someone else can shed more light on the history?

Feedback: Please direct any queries or comments to the "Other / General Resources / Prototype Information & Research" section of the Meccanoscene public forum.

PS: Shortly after compiling these notes, I enquired of Exacto and received the following response:

“Dear Alan,

Thank you for your e-mail.

Meccano Liverpool helical gears were DP35. This is confirmed by the Encyclopedia of Meccano Parts compiled by Don Blakeborough . As far as I know, the use of DP34 was decided by the late Alberto Richini, founder of Exacto. Exacto helical gears have always been DP34. Find attached our technical data sheet please.

Regards, Juan Carlos Rovetta."

QED!

@Alan Wenbourne (January 2010)