# Belt length comp for 3 leadscrews and stepper motor

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### Dan Newman

Dec 7, 2014, 12:53:11 AM12/7/14
to
[Edited 7 Dec 2014: revised sketch/image to clarify gap, G.]

Needed to compute the belt length for a three leadscrew + driver motor setup.

While I did this for the leadscrews at the vertices of an equilateral triangle,
it's trivial to generalize the math to other configurations (e.g., the 3*l1 term
becomes l1 + l2 + l3).

The diameters of the pulleys and idlers ideally should be pitch diameters: the
diameter of the belt center line when mounted on the pulley or idler.  SDP/SI
provides that diameter with their pulley specs.  Likely other major suppliers
as well.

Dan
Scan.jpeg

### Dan Newman

Dec 7, 2014, 1:33:05 AM12/7/14
P.S. Add a fourth leadscrew, locate the leadscrews at the vertices of a square, and you have the configuration used on the Cupcake.

### Ryan Carlyle

Dec 7, 2014, 11:45:44 AM12/7/14
G is the axis-axis distance between the two small idlers?

### Dan Newman

Dec 7, 2014, 12:09:33 PM12/7/14
On 07/12/2014, 8:45 AM, Ryan Carlyle wrote:
> G is the axis-axis distance between the two small idlers?

Yes. On the side, I've set

G = D1 + 2 * (D2/2) = D1 + D2

However, it's not necessary to use that particular spacing.

And, of course,

l2 > D1/2 + D2/2

otherwise the two will interfere with one another.

Dan

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### Vernon Barry

Dec 7, 2014, 3:59:15 PM12/7/14

Double V arrangement for maximum belt wrap on every pulley and still only uses 2 idlers.

608 skate bearing idlers.

Motor and overall arrangement.

Moving stage plate detail from the bottom side.

### Ryan Carlyle

Dec 7, 2014, 5:37:30 PM12/7/14