Quote:
Originally Posted by James Critchley
It is an increase in total mass of the robot or mass distribution of the wheels that contributes to any performance degradation.
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YMMV, but I think it's clearer to explain it the following way:
The equation for vehicle acceleration in the PDF file attached to
this post can be re-arranged as follows:
a = (tau/r) / (I/r
2 + (1/4)*(M
v+4*M
w))
or, substituting K*M
w for I/r
2
a = (tau/r) / (K*M
w + (1/4)*(M
v+4*M
w))
Since tau/r remains unchanged when you change the wheel radius (if you change the gearing accordingly), what remains is
a) the total vehicle mass M
v+4*M
w, and
b) the mass of the wheel times the mass distribution factor of the wheel (K*M
w)
Since neither (a) nor (b) is likely to remain the same when you change wheel size, there will be a change in vehicle acceleration.
The equation also gives a way to estimate the change.