One of the reasons that inside out toothed belts don't work well is because of 
the rounded shape of the teeth.  In the case of gears both the root pitch of 
the gear and the distance between teeth doesn't change as it turns.  

The belt goes around the pulley and at the back ends the shape of the belt 
teeth are smoothly and tightly coupled to the shape of the teeth. 

Because nothing changes on normal gears you also need that set of 7 or 8 
involute cutters have ever so slightly different shapes so a 20T mates well 
with a 60T.  But with harmonic drives the shape of the tooth profile changes as 
the flex gear changes radius mating with fixed gear that does not.

That's why the triangle shape that Sam used is better than an involute or round 
tooth rubber belt.

My FHA-25 is rated for 60 RPM (max 80) and has a reduction ratio of 50.  The AC 
servo controlled by the STMBL drive runs the motor up to 3000 RPM which means 
it's spinning that elliptical gear at 3000 RPM.

So there must be 100 teeth on the cup gear and 102 teeth on the spline gear 
which results in that 50:1.  I've not taken mine apart but I'll guess it's 
about 100mm?  So the pitch is about 1mm.  I think.  Much less than the 3D 
printed one which is closer to 4mm but then 37 teeth in about the same 100mm.

Do correct me if I've got this wrong.

John


          

> -----Original Message-----
> From: Stuart Stevenson [mailto:stus...@gmail.com]
> Sent: November-30-21 5:29 PM
> To: Enhanced Machine Controller (EMC)
> Subject: Re: [Emc-users] Harmonic Drive
> 
> Isn't the purpose of an involute surface the minimization of sliding two
> surfaces? I would think an attempt would be made in the harmonic mesh.
> 
> On Wed, Dec 1, 2021 at 12:09 AM andy pugh <bodge...@gmail.com> wrote:
> 
> > On Tue, 30 Nov 2021 at 23:07, Stuart Stevenson <stus...@gmail.com> wrote:
> >
> > > Is the tooth shape an attempt to mesh in an involute fashion?
> >
> > No, because the motion of the teeth relative to each other is very
> > much unlike meshing gears, and so involute is inappropriate.
> >
> > --
> > atp
> > "A motorcycle is a bicycle with a pandemonium attachment and is
> > designed for the especial use of mechanical geniuses, daredevils and
> > lunatics."
> > � George Fitch, Atlanta Constitution Newspaper, 1912
> >
> >
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> >
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