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.Crissy said:
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 Forcein times its radius and the output torque is Forceout 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.Crissy said:
The velocity ratio in gears and wheel systems refers to the ratio of the rotational speed of the input gear or wheel to that of the output gear or wheel. It is important because it determines the mechanical advantage of the system, which affects the amount of force and torque that can be transmitted between the gears or wheels.
The velocity ratio is calculated by dividing the number of teeth on the output gear or wheel by the number of teeth on the input gear or wheel. For example, if the output gear has 20 teeth and the input gear has 10 teeth, the velocity ratio would be 20/10, or 2.
Yes, the velocity ratio can be changed by using gears or wheels with different numbers of teeth. This is known as gear reduction or gear amplification, depending on whether the output gear has fewer or more teeth than the input gear, respectively.
The size of the gears or wheels does not affect the velocity ratio, as long as the number of teeth remains constant. However, larger gears or wheels may be able to transmit more force and torque due to their larger surface area.
Yes, there are limitations to the velocity ratio in gears and wheel systems. For example, if the velocity ratio is too high, the gears or wheels may become less efficient and start to slip or wear down quickly. Additionally, the size and strength of the gears or wheels may also limit the maximum velocity ratio that can be achieved.
