What is the formula for plotting an accelerating involute curve?

In summary: Summary: The wiki page provides several formulas for specific types of curves, and you may need to do a parametric plot to plot them.
  • #1
homerwho
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TL;DR Summary
I once viewed an involute which the involute accelerated.
Can someone help me with a formula for an accelerating involute curve? I have found this wiki on involute
 
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  • #2
What do you mean by "accelerated"?

It looks like there is a lot of context missing.
 
  • #3
The circle of derivation is increasing as the "string" around that circle is enlarging
 
  • #4
homerwho said:
Summary: I once viewed an involute which the involute accelerated.

Can someone help me with a formula for an accelerating involute curve? I have found this wiki on involute
This wiki page you cited has a formula for a general curve, and several more for specific types of curves. Isn't one of these what you're looking for?
 
  • #5
possibly. that's why I posted in the math forum. I can't decipher from that what I would need to plot. Thanks
 
  • #6
homerwho said:
possibly. that's why I posted in the math forum. I can't decipher from that what I would need to plot. Thanks
For most of the formulas on the page you linked to, you need to do a parametric plot. For example, to plot ##x(t) = t + \sin(t), y(t) = 3 + \cos(t)## on the interval ##[0, 2\pi]##, you can do this in WolframAlpha:

parametric plot (t + sin t, 3 + cos t), t=0..2pi

Here's a link to the plot - https://www.wolframalpha.com/input/?i=parametric+plot+(t+++sin+t,+3+++cos+t),+t=0..2pi
 
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1. What is an accelerating involute?

An accelerating involute is a type of gear profile that is used in gear design to create smooth and efficient power transmission.

2. How does an accelerating involute work?

An accelerating involute works by gradually increasing the contact ratio between two gears as they rotate, resulting in a smoother transfer of power and less wear and tear on the gears.

3. What are the advantages of using an accelerating involute?

The main advantage of using an accelerating involute is that it reduces the impact and shock loads on the gears, resulting in longer gear life and improved efficiency.

4. How is an accelerating involute different from a standard involute?

An accelerating involute has a more gradual curve, which allows for a larger contact ratio and smoother power transfer compared to a standard involute, which has a more abrupt curve.

5. Are there any limitations to using an accelerating involute?

One limitation of using an accelerating involute is that it requires precise manufacturing and assembly to ensure proper functioning. Additionally, it may not be suitable for all types of gear applications.

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