Physics question from non-Physics guy

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In summary: I assume you're still looking for a ratio between the angular motion of the pinion and the linear motion of the rack. You might be able to find this equation by looking at the wiki page for rack and pinion.
  • #1
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Homework Statement


I've never studied Physics, and I've run into a Physics question while writing a code for a 3D plugin. I'm making a routine which automatically creates gear trains. I've covered spur, helical and bevel gear ratios and everything works nicely, However, I've run into a brick wall with rack & pinion gears.

I know just enough to assume that this is a question of finding a ratio between the angular motion of the pinion and the linear motion of the rack. I also suspect that the angular increments have to be in radians rather than degrees. Can anyone tell me if there's a basic equation tranlating motion between these that I can incorporate into my code? Many thanks in advance.



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The Attempt at a Solution


 
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  • #2
This isn't something I know offhand, but it doesn't seem too complicated(I went to the wiki page for rack and pinion to see what it looked like and am basing this off that cute .gif >_>)

Well I assume you know the rpm of the round gear, so you can find its angular velocity(w) in radians/second (and you sounded familiar with radians so I won't go into that)

So w=v/r, where r is the radius of the round gear, and v is its tangential velocity on the edge. I believe that v will be the velocity with which the flat gear is moving

If w is in radians/second and r is in meters, v will be in meters/second

Edit: So what exactly are you looking for? The ratio of angular velocity of the round gear to linear motion of the flat gear is w/v=1/r, I think. If that's what you're looking for
 
  • #3
Thank you, blochwave. You've certainly pointed me in the right direction. In terms of what I'm specifically after, I want the the 3D user to create a pinion gear and rack (the plugin I'm writing spaces the cogs correctly), then (a) when the pinion is rotated the rack will move the appropriate distance, and (b) when the rack is move laterally the pinion will rotate the appropriate amount.
 
  • #4
Oh ok, so I gave you stuff involving velocities and you want distance

When talking about "distance" with the pinion(whoo my vocab expanded)you'd say "it rotates x radians" and this would certainly most conveniently be expressed in radians because...

the length of the arc is going to be the angle in radians multipled by the radius of the circle(such is basically the definition of a radian)

So basically http://en.wikipedia.org/wiki/Image:Radian_cropped_color.svg

That's a picture of the definition of a radian, in general s=r*theta where theta is the angle in radians, r is the radius of the circle in whatever unit of distance, and s is the length of that arc in the same units of distance(you might ask how distance*radians=distance, but radians is a "dimensionless unit")

That length of arc I believe corresponds directly to the distance moved by the rack(so if the distance is d, s=d)

So you say "my pinion of radius = 2 meters(huge I know) rotates 90 degrees, how far does a point on the rack get displaced?(ie how far does it move)"

so 90 degrees=pi/2 radians, pi/2*2meters=pi meters, so the rack moved about 3.14 meters

What if the rack moves like 4 meters? so d=s=theta*r, so 4 meters=theta*2 meters

theta = 2 radians, which you can convert to degrees
 
  • #5
Great! Thanks, blochwave. For some reason I wasn't notified of your latest post.
 

1. What is the difference between speed and velocity?

Speed refers to the rate at which an object moves, while velocity takes into account both the speed and direction of an object's motion. In other words, velocity is a vector quantity that includes both magnitude (speed) and direction.

2. Can you explain the concept of acceleration?

Acceleration is the rate of change of an object's velocity over time. It can be positive (speeding up), negative (slowing down), or zero (constant velocity). The formula for acceleration is change in velocity divided by change in time.

3. How does gravity work?

Gravity is a force of attraction between two objects with mass. The more mass an object has, the stronger its gravitational pull. This force is described by Newton's Law of Universal Gravitation, which states that the force is directly proportional to the product of the masses and inversely proportional to the square of the distance between them.

4. What is the difference between weight and mass?

Mass refers to the amount of matter in an object, while weight is a measure of the force of gravity on an object. Mass is constant, but weight can vary depending on the strength of the gravitational pull. On Earth, mass and weight are often used interchangeably because the gravitational pull is relatively constant.

5. Can you explain the concept of energy?

Energy is the ability to do work or cause change. There are many different forms of energy, including kinetic (motion), potential (stored), thermal (heat), and chemical (stored in bonds between atoms). The Law of Conservation of Energy states that energy cannot be created or destroyed, only converted from one form to another.

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