Re: Rack and Pinion

--- In CAD_CAM_EDM_DRO@yahoogroups.com, Stephen Wille Padnos
<spadnos@s...> wrote:

> turbulatordude wrote:
>
> >Hi all,
> >
> >I am probably missing something very simple in this.
> >
> >A spur gear has a unit value as the rack with a pitch diameter
> >value of 1 inch. ie: a 12 pitch rack matches a 12 tooth gear

when

> >the pitch diameter of the gear is 1 inch.
> >
> >This then means the linear movement equals Pi for one revolution

of

> >the gear.
> >
> >
> I'm not sure I agree with this statement.
> If you have a gear with 12 teeth, and that meshes with a 12 pitch

rack,

> then the pitch *circumference* is 1 inch - not the diameter.
> One revolution will be 12 teeth, or 1 inch.
> If that's correct, then the rest of your worries magically vanish :)
>

Unfortunatly, the whole gear thing starts with 1 inch diameter.

Unlike threaded rod, the pitch is not teeth per one linear inch, it
is teeth per dimetrical inch. A pitch diameter of 1 inch = Pi in
linear inches.

How many teeth can be cut into a 1 inch diameter gear ? if you can
cut 12 teeth in the 1 inch diameter gear, then the pitch is 12.

That also means that 1 inch diameter is 3.14159.... inches of linear
movement for each complete rotation of the gear on the rack. The
rack then would have 3.819718634 teeth per linear inch.

As for software compensation, a 200 step motor with 10x driver will
move 2,000 steps for 3.14159

3.1415926535898 inches per rotaton, 2,000 steps per rotation =
0.0015707963268 inches per step. I rounded off the decimals for
simplicity.

But, this means one 636 steps = 0.9990264638416 inches of movemnt
or 637 steps = 1.0005972601684 inches.

In the first case, the accumulated error over 48 inches is -0.04673
or in the second it is +0.02867

Adding a gear reduction with tiing belts can reduce this, but it is
still off over the table lenght. A second reduction offers a lower
error over the full table lenght.

But, theoretically, it is impossible to cut a part that has a
dimention of 1.00 inches, it will be wither a little high or a little
low.

Timing belts instead of rack, and also lead screws both offer integer
steps to attain one inch.

It just seems the rack and pinion offer a lower linear distance per
rotation.

A GT2 pulley is danr close to a XL pulley, one is 5mm the other 0.2"
either can be put into unit that are integers at some measured
distance and therefore will have no accumulated error over any
distance. But, with a 1/2" shaft, the XL and GT2 both come in over
28 teeth per revolution. for the XL, that is over 5 inches linear
for one revolution. 14 teeth engaged so one can drive the axis with
some decent power. less teeth means less engaged and that means
less potential power.

OK, I'll stop rambling.

Anyone know if I'm missing something ?

Dave