Question About the effect of gearbox ratios

Hi!

While pondering which gear ratio I should use for my upcoming compact 2DOF rig, I was thinking about the relationship between motor torque, gear ratio, CTC distance, resulting force, linear speed and travel.

I came to the somewhat odd conclusion that high ratio (low rpm) should generally be preferred. I want to discuss this with you guys, to uncover potential mistakes on my side.

Scenario A
Ratio: 25:1
Rotational Speed: 120 1/min = 2 1/s
Torque at gearbox output: 10 Nm
CTC: 50 mm = 0,050 m
Force = Torque / CTC = 200 N
Linear Speed = CTC*2*Pi*<rotational Speed> = 0,628 m/s = 628 mm/s
Used angle of rotation: 80 degree
Travel = CTC * <used Angle> / 180 * Pi = 0,070 m = 70 mm

Let's assume the 200 N of force and 628 mm/s linear speed are satisfying for the application.

Now let's switch the Gearbox for a 50:1 model. Because we just doubled the torque (assuming no increase in gearbox loss), we can also double CTC in order to keep the resulting force constant. Let's have a look at the resulting linear speed and travel.

Scenario B
Ratio: 50:1
Rotational Speed: 60 1/min = 1 1/s
Torque at gearbox output: 20 Nm
CTC: 100 mm = 0,100 m
Force = Torque / CTC = 200 N
Linear Speed = CTC*2*Pi*<rotational Speed> = 0,628 m/s = 628 mm/s
Used angle of rotation: 80 degree
Travel = CTC * <used Angle> / 180 * Pi = 0,140 m = 140 mm

The increased CTC compensates the reduction in rotational speed, so that the same linear speed is achieved.

But the travel has doubled! So I can get more roll or pitch angle out of my rig.

According to these calculations, one should always choose the gearbox with the highest available ratio (as long as the resulting CTC stays within practical limits).

So what do you guys think? Is there a flaw in my reasoning?

Best regards,
Sebastian

So increased gearbox ratio gives us bigger travel at the price of increased losses and more effective backlash. Sounds plausible and I'll keep that in mind.

While worm drives are not very efficient, I think that the difference in efficiency of a 50:1 and a 25:1 gearbox for the same motor won't be that big. So I guess the force generated of a 50:1 gearbox with 100 mm CTC won't be that different than that of a 25:1 gearbox with 50 mm CTC. I doubt this effect would be very noticeable.

Backlash is different though. First, a 50:1 gearbox might have slightly bigger backlash than 25:1. But then the effective backlash at the end of the lever is really doubled if you double CTC. Which is hard to counter from a designer's perspective.

I've read some posts on this forum of people talking about gearbox ratios and some seem to think the choice of ratio would affect linear speed or force. But I think the calculations shown above show otherwise (if the CTC is adjusted accordingly).