Many hand made dispensers use 28BYJ-48 motors. Those are very cheap, but not enough small and not convenient to mount. We need something better:

• More compact.
• Precise enougth.

Let's estimate desired gearbox ratio.

All small 10-15mm steppers usually have 18° step (20 steps per turn). Gearbox can be:

• Plastic. Usually up to 1:50
• Metal. Up to 1:295 (sometime up to 1:600)

Other data:

• Pusher uses M3 shaft with 0.5mm pitch.
• Inner dia of 10cc medical syringe is about 15mm (a bit more for pneumatic syringe, but not principal now
• Volume of paste for 0603 resistor pad is ¹/₁₂ - ¹/₁₆ mm³.
• Let's say we need to dispense one 0603 portion with precision about 10%.

Desired portion size per single motor step is 0.006 mm³.

Let's calculate, what stepper with plastic gearbox 1:50 can give us:

(3.14 * 15² / 4) * 0.5 / 50 / 20 => 0.09

 0.09 mm³ is very bad. It's 1.5x more than portion size and 15x more than desired precision. What can we do?

• Use metal gearboxes with better ratio
• Decrease syringe dia (use 3cc or even 1cc)

1cc syringe has dia about 5mm. Portion per step will decrease in 9x. Better, but not perfect. Let's use metal gearbox 1:295.

Estimate for 3cc syringe (9mm inner dia):

(3.14 * 9² / 4) * 0.5 / 295 / 20 => 0.005

Estimate for 1cc syringe (5mm inner dia):

(3.14 * 5² / 4) * 0.5 / 295 / 20 => 0.001

In total:

• 3cc syringe & 1:295 gearbox - 0.005 mm³ per step, very good for 0603 components. With some reserve for smaller pads.
• 1cc syringe & 1:295 gearbox - 0.001 mm³ per step, should be enough for all.

Of cause, we could use dynamic model (quick step forward and back) and cheat with paste viscosity. But that's much more complicated and result will depend on paste temperature. Also, it's not good idea to use micro stepping, because it's not precise with cheap motors and consumes more power.

Conclusion

• Mini steppers with metal gearboxes are preferable over plastic ones.
• 3cc & 1cc syringes are most optimal for soldering paste.
• 10cc syringes still may be interesting for fluxes and glues.

That's all with boring maths, next time I'll try to post some pictures :)