Well, I don't normally post here - I especially don't make threads very frequently... but I was curious if anyone was interested in working on an idea I had, it's a pretty fun one, I think. I make no claim as a mathematician.
So here's the idea - I want to generate a cog (gear) using gscript or gscript2. I'm not especially interested in programming it, I mostly need help with the actual equation.
The equation I've made so far is pretty simple. I'll define the terms I've used before I go into details on the actual equation.
1.) Valley
2.) Peak
3.) Slope
If the diagram isn't clear enough I'll explain it in words. The gear obviously has a highest point for each little point - I've called this part the peak
(2). Then there is a slope on either side of the peak which I called the slope
(3). At the bottom of the slope there is a valley between each peak, the base of this I've called the valley
(1).
Though my diagram doesn't display the angle which the valley would assume, there is one there - I didn't want to make the effort to show one, if I could not show one precisely
The gear is based around a circle - the radius of the circle is the key point in this equation (or atleast I believe as much). As you will likely know, if you are to complete this equation, the radius is what forms the circumference.
Based entirely on the radius we can generate the value of the circumference. Assuming that we want 8 "peaks" on the cog we will also want 8 valleys, so if A is to represent the ammount of peaks, it could be said that we want 2A (for the valleys and peaks both share the same width).
Now, assuming we've got as far as to take Peaks & Valleys multiplied by the number of peaks ( (A2)(8) ) we must have a width - the width of the peak represents a percentage of the entire circumference. We can't simply devide the circumference by 8 and then work out the width of our peaks/valleys because there would be no room for for the slopes as represented in the diagram as
(3).
Slope will be multiplied by the ammount of peaks and then multiplied by two, because each peak must have two slopes leading up to it. If the slope is represented as B, we would have ( ((B)(8))(2) ). The slopes, after being calculated also represent a portion of the circumference.
Now is the tricky part...
Or atleast for me - the Valleys, Peaks, and slopes must ALL be angled according to the arch which the circle assumes. If you don't understand what I mean, I will explain further.
As we know, gears assume a circular shape so that they meet their partner and either be pushed or pulled by them - regardless - they must be circular or they wouldn't gears (we won't go into the other mechanics which work with gears, let's concentrate on this subject). The gear's valleys are angled in such a way so that the entire section (valley, slope, peak, slope, valley) will, when repeated, wrap around the entire gear.
This is difficult for me for many reasons, I'll begin with the fact that I am so weak in math that I was in foundation courses throughout my entire highschool education (I'm an artist, give me a break).
This is where I need help. I can generate the slopes, valleys, peaks and all that fun stuff based on the radius - but I cannot, for the life of me, devise a way to find the slop of each valley! And this is where you come in.
Based on the information, or atleast the premise I've presented, I'm looking for someone to help me make a formula for generating gears in a programming enviroment.
I'm sure some of you will find this a very simple task, what with the very essence of some of your brains being cogs - so with that said, I hope I've made myself clear enough for you to either gain some interest in the subject, or to take pity upon me and show me the final work (and formula).
Thanks!
11-16-2005, 10:11 PM
Linear Mode
