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wheels moving and stuff

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Fermat
If the point is on the rim of the wheel, then the locus of its travel will be a cycloid - looks a bit like the arches of a bridge. See here
You can get the parametric eqns for cycloidal travel here


Why does it do that? :confused:
Reply 21
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Fermat
8
Mysticmin
Why does it do that? :confused:


???

Do you mean "why does it trace out that curve?"
Fermat
???

Do you mean "why does it trace out that curve?"


yup, sorry, my brain is not quite accepting why it should trace out a path of adjacent semi circles, could you please explain why? :smile:
Reply 23
Avatar for fishpaste
fishpaste
OP
Fermat
If the point is on the rim of the wheel, then the locus of its travel will be a cycloid - looks a bit like the arches of a bridge. See here
You can get the parametric eqns for cycloidal travel here


Ahhh cheers. Looks like I wasn't *that* far from the truth. *feeling rather impressed with self* "I DO have a brain!"
Reply 24
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john !!
14
Mysticmin
yup, sorry, my brain is not quite accepting why it should trace out a path of adjacent semi circles, could you please explain why? :smile:


Get a plate, put a ruler vertical, and put your finger on the same point, start off with your finger toughing the table and plate then move the plate. your finger will not go backwards at all - that is where I went wrong. The function is many - one mapping, so the point on the wheel does not change horizontal direction.
Reply 25
Avatar for Fermat
Fermat
8
Mysticmin
yup, sorry, my brain is not quite accepting why it should trace out a path of adjacent semi circles, could you please explain why? :smile:

It's a lot easier if you can see an animation of it!
Those aren't really semi-circles - or were you just calling them that? - they are cycloidal paths.
Try to imagine a wheel rolling along a plane. There's a hole drilled into it just on the perimeter of the wheel.
The wheel starts off with the hole touching the plane.
As the wheel rotates, moves along, the hole will move,vertically, up and down as well as horizontally.
Darnn! I can't describe it any better than that - sorry. I'll look on the net and see if I can find an animation.
Fermat
It's a lot easier if you can see an animation of it!
Those aren't really semi-circles - or were you just calling them that? - they are cycloidal paths.
Try to imagine a wheel rolling along a plane. There's a hole drilled into it just on the perimeter of the wheel.
The wheel starts off with the hole touching the plane.
As the wheel rotates, moves along, the hole will move,vertically, up and down as well as horizontally.
Darnn! I can't describe it any better than that - sorry. I'll look on the net and see if I can find an animation.


no wait, I think I may get it...the hole starts off at zero displacement (touching the plane), by the time the wheel has completed one revolution, the hole has moved up to max vertical displacement and back to zero displacement again? hence no spiral (so much for having spatial reasoning!)

Edit: Sorry Fishpaste...
Reply 27
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Fermat
8
Found the animation :smile:
http://astro.temple.edu/~dhill001/cycloid-demo/
Fermat


Cheers :smile:
Reply 29
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Fermat
8
Mysticmin
no wait, I think I may get it...the hole starts off at zero displacement (touching the plane), by the time the wheel has completed one revolution, the hole has moved up to max vertical displacement and back to zero displacement again? hence no spiral (so much for having spatial reasoning!)

You an get a spiral depending upon where the hole is wrt the plane.
Suppose you have a railway engine wheel. Such a wheel has a flange on it. The wheel runs on the track, but the edge of the flange can be below the top of the track. Now drill the hole in the perimeter of the flange.
When the railay engine wheel rotates, the flange hole will (eventually) travel below the surface of the tarck and the hole will travel in a spiral like someone else posted earlier on and cut back on itself.
Reply 30
Avatar for fishpaste
fishpaste
OP
Hey um can somebody tell me what intrinsic coordinates are and when they're used? They're not on my alevel syllabus but if they were to come up in STEP I don't want to be tackling a question on them and not realising it.
Reply 31
Avatar for Fermat
Fermat
8
fishpaste
Hey um can somebody tell me what intrinsic coordinates are and when they're used? They're not on my alevel syllabus but if they were to come up in STEP I don't want to be tackling a question on them and not realising it.

Have a look on this post here

Edit: Thanks for the rep - just gotta 'nuther gem :biggrin:
Is this from the 1997 STEP III paper? If you ask me its a bit of a poor question because if you happen to know the parametric equations for the cycloid it can be done in about 5 mins, however deriving these equations from scratch in an exam would be very hard - so depending on luck this question could either be very hard or very easy.

About intrinsic coordinates, they describe the 'intrinsic' nature of a curve. Which is its curvature (how bendy it is) its arc length (the length of the curve from an arbritrarily chosen point) and psi, the angle a tangent makes with the horizontal. In this sense they are not described with respect to fixed axes, so describe a family of curves, and when converting to cartesian you use some initial conditions to locate the with respect to the axes

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