Why is the velocity ratio inverted for gears compared to wheels?

[Crissy]

Hi, if the velocity ratio is equal to the distance traveled by the effort divided by the distance traveled by the load, in a gears and wheels system, do you invert that in the case or gears? Making it number of teeth on driven gear divided by number of teeth on driving gear? Thanks

 

[sophiecentaur]

Hi, if the velocity ratio is equal to the distance traveled by the effort divided by the distance traveled by the load, in a gears and wheels system, do you invert that in the case or gears? Making it number of teeth on driven gear divided by number of teeth on driving gear? Thanks

It's exactly the same but you need to read the small print about what VR really means. The velocity ratio is the diameter (or number of teeth) of the input wheel divided by the diameter of the output wheel. That follows the definition. You cannot compare it with the way VR is calculated for levers because, with rigid levers it's the angle change that stays the same but, for gears in mesh, it's the tangential distance.

It will always be lower than the Mechanical advantage due to dead weight and friction etc.

 

[Crissy]

Thanks for ur reply. So how come in book it inverts it? I dnt quite understand

 

[sophiecentaur]

Thanks for ur reply. So how come in book it inverts it? I dnt quite understand

I can't read what the book actually says - it's too blurry with no contrast. But I think, if you read the book carefully (as I cannot) then you should find the distance moved by the Input and output teeth is the same but the input torque is Input Force_in times its radius and the output torque is Force_out times its radius. If you are still confused then, rather than trying to make sense of the book, work it out independently. Unless the book is actually wrong (never impossible to find a typo) your final result will agree with it.
Apply the 'does to make sense?' test against your experience of gears.

PS Read my earlier post again and digest the message; it shows how one could get things back to front.