SOME RP5 INFO & MEASUREMENTS
After some recent discussions and questions on the Pololu with regards to the RP5 and possible modifications
that could be made to it, myself included, I thought it would be a good idea if we could fill in the gaps on the
performance on this great little chassis. The RPM and gear ratio doesn’t come with a tech data provided.
After having taken it apart and put it together again, I can share with you some findings which might be
a useful reference.
The RP5 gear train has a series of gear pieces (4 to be exact) which act as speed reducers and torque boosters.
Without describing in words, I will shortly place a scanned in neat sketch of the arrangement, teeth count, arrangement, etc.
There are three gear pieces with 12 & 50 teeth ratios as you work your way through from the motor
output shaft to the output shaft driving the wheels. The 47mm diameter plastic wheel is wrapped around with a
6mm rubber tread making the ground contact diameter approx 51mm. This assumes a new un-worn tread.
All measurements were done with a fairly high precision digital precision vernier caliper and great care was taken to reduce
measurement and parallax (eye) errors.
The gear reduction ratio works out at about (72.3 : 1) or 0.013824 times the motor shaft angular velocity.
The next step is to determine how motor RPM at the output shaft. I dont know the answer to that one, however through gear ratios
and basic mechanics equations, It can be worked backwards also (maths is relatively simple).
[Motor RPM x (0.24)^3 = Output RPM] is the basic equation for translating RPM from one end of the gear train to the other. (12/50=0.24)
That is not all though, a conversion from RPM to RPS is then required,followed by a formula for changing from angular (omega) to (velocity) using
the ground contact radius of the wheel/tread (0.0255).
I think up to here most would probably agree with me.
The next step is not certain, and I will have to revise. If anyone has input, please share.
Taking the design speed of 15 cm/s as per the spec sheet, and the radius of the wheels, I arrived at a calculated 25,535 RPM
in order to get 15 cm/s by working the formulae backwards. I still have to confirm this as it seems high. A sensibility check on
most toy motors would see you can get up to 16,000 RPM for a 6 volt motor. Hmmm! 25,500RPM seems too high!
I have used the formula : arc lenth (L) = radius * theta (full wheel circumefrence is approx 16cm which is right)
The derivative version is: L_dot (velocity) = radius * theta_dot (or angular velocity) - 5.88 radians/second (for 352 RPM)
The problem is here I think! It could be that I forgot to divide by Pi somewhere.
Initially it was estimated at 11,000 RPM however this only produced 6.5cm. If were to base it on full revolution per second only at the
output shaft end, it would be 4341 RPM (2.5 cm/s). And if we were to assume 25,535 RPM (the calculated figure to give 15 cm/s) then that
would translate into 5.88 revs/sec at the output shaft end. Both values appear to be at the extremes.
Note: Motor is always assumed running at 100% speed.
Any comments or corrections would be appreciated.
Cheers,
Carl