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|MMD Tech SpoolF pulleyDesign
by Robbie Rhodes
My 1913 Cremona A-roll piano arrived with a 3/8" leather belt installed on the cone pulley transmission, which is much too big -- it barely stays in the intended grooves. As far as I can determine by measurements and conversations with other Cremona owners, the cone pulleys were designed for 1/4" round leather belting. Someday I want to make new cone pulleys to get a wider range of speed control, such as Tempo 65 to Tempo 95. As it is now the A-roll won't move fast enough for some tunes.
The sketch above shows the geometry of a round belt riding in a standard Vee groove of 60 degrees total angle. I assume that when the belt deforms slightly (it becomes slightly egg-shaped) that the contact point doesn't change significantly. The simple formula that results says that the outside diameter (OD) equals the pitch diameter (PD) + 1.5 times the diameter of the round belt. Conversely, one can measure the outside diameter to determine the pitch diameter.
I measured the pitch diameter of each groove of the small pulley shown above by inserting 1/4" shafting (actually 1/4' drill bits) and holding them parallel which I measured the outside diameter (OD) with vernier calipers. I also measured the larger pulley which drives the takeup spool. I recorded this data:
Cone pulley with 1/4" round belt:
"A" 4.25 3.88
For fastest play speed the belt rides in grooves G and A; the pitch
diameter ratio A/G is 3.88/2.31 = 1.68
The ratio of these two numbers is the total speed range ratio: 2.32/1.68 = 1.38 which is, for example, the ratio of Tempo 55 to Tempo 76.
[to be continued]
9 January 2003
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