<p>Following the video, the shape of the cam is a polar plot of the equation of time, with an offset to keep the values positive.  You can use any of the trigonometric approximations to the equation of time to plot this, with your choice of offset (presumably a smaller offset makes more deeply indented cam that is hard to follow, but a larger offset makes a cog that is easy to follow, but heavier and takes up more space. So the exact shape is a practical and engineering decision.</p>
<p>You can plot the polar curve with your favourite graph plotter. Here is a <a href="https://www.geogebra.org/classic/ztjkwmuh" rel="nofollow noreferrer">quick mockup with geogebra</a> and a simple formula adapted from wikipedia,
<span class="math-container">$$r = c -0.7659\sin(6.24+0.0172 d)+0.9863\sin(2( 6.24+0.0172 d)+3.5932)$$</span></p>
<p><a href="https://i.sstatic.net/20NyRl.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/20NyRl.png" alt="enter image description here" /></a></p>
<p>In which <span class="math-container">$c$</span> is the offset to keep the radius positive and <span class="math-container">$d$</span> is days of the (Julian) year <span class="math-container">$0\le d&lt;365.35$</span>.</p>
<p>How that shape is then used to adjust a clockwork mechanism is hinted at by the video, but well beyond my knowledge of clocks (and isn't an astronomical question)</p>

CC BY-SA 4.0
2024-03-28T18:48:45.430Z
one thing I notice is that this is plotted anticlockwise (positive increasing angle) but the clock, or course, works clockwise, so their cam is like the mirror image of this.
James K
CC BY-SA 4.0
2024-03-29T20:54:46.743Z
Hi James, thank you for taking the time to provide an answer to my post. I apologize for not having made it more specific. But I'm glad you immediately knew what information to provide. This is going to help a lot. Thanks again. If you or anyone else is interested to see what this is about, follow on Instagram @noob_watchmaker.
noob_watchmaker
CC BY-SA 4.0
2024-03-28T13:04:53.330Z
2024-03-28T13:10:43.217Z
2024-03-28T13:10:43.217Z
James K
<p>I'd like to use <a href="https://en.wikipedia.org/wiki/SolidWorks" rel="nofollow noreferrer">Solidworks</a> to create a cam (peanut looking) for computing the equation of time in a pocket watch. Would appreciate any point to the right direction or advice.</p>
<p><a href="https://www.youtube.com/watch?v=fhiSGg06uRU" rel="nofollow noreferrer">Audemars Piguet EoT</a><a href="https://i.sstatic.net/Re0eG.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/Re0eG.png" alt="Inner workings of the same watch" /></a></p>

CC BY-SA 4.0
2024-03-28T04:08:59.390Z
I'm not sure: what is the Astronomy part of the question? How does the Image illustrate your question or Problem? What did you try?
planetmaker
CC BY-SA 4.0
2024-03-28T06:49:06.480Z
Not sure what your actual goal is here.  The equation of time is used to correct a sundial to give clock time, but if you have a pocketwatch, you already know clock-time.
James K
CC BY-SA 4.0
2024-03-28T10:15:16.073Z
@JamesK Presumably, the OP's goal is to make a watch that has a dial showing solar time (or just the EoT correction). FWIW, in the early days of mechanical clocks, the EoT was used to correct clock time to "proper" sundial time.
PM 2Ring
CC BY-SA 4.0
2024-03-28T10:23:25.103Z
There are equations for computing the EoT, with various levels of accuracy. I have [EoT code in Python](https://astronomy.stackexchange.com/a/49546/16685) (and much simpler code [here](https://astronomy.stackexchange.com/a/39685/16685)), but I have no idea how to turn that into clockwork mechanism.
PM 2Ring
CC BY-SA 4.0
2024-03-28T13:00:35.340Z
You might try reaching out to the author of this post if he doesn't see this: https://astronomy.stackexchange.com/questions/57180/how-can-i-build-a-gear-based-mechanism-to-calculate-solstices-equinoxes-and-cr
Greg Miller
<the-sun><the-moon><orbital-mechanics><time>
How can I plot a rotary cam for the equation of time?
noob_watchmaker
# How can I plot a rotary cam for the equation of time?

(Asked by: username_0 on 2024-03-28)

I'd like to use [Solidworks](https://en.wikipedia.org/wiki/SolidWorks) to create a cam (peanut looking) for computing the equation of time in a pocket watch. Would appreciate any point to the right direction or advice.

[Audemars Piguet EoT](https://www.youtube.com/watch?v=fhiSGg06uRU)[![Inner workings of the same watch](https://i.sstatic.net/Re0eG.png)](https://i.sstatic.net/Re0eG.png)

**Tags:** the-sun, the-moon, orbital-mechanics, time
> **Comments:**
> **username_1**: I'm not sure: what is the Astronomy part of the question? How does the Image illustrate your question or Problem? What did you try?  
> **username_2**: Not sure what your actual goal is here.  The equation of time is used to correct a sundial to give clock time, but if you have a pocketwatch, you already know clock-time.  
> **username_3**: @JamesK Presumably, the OP's goal is to make a watch that has a dial showing solar time (or just the EoT correction). FWIW, in the early days of mechanical clocks, the EoT was used to correct clock time to "proper" sundial time.  
> **username_3**: There are equations for computing the EoT, with various levels of accuracy. I have [EoT code in Python](https://astronomy.stackexchange.com/a/49546/16685) (and much simpler code [here](https://astronomy.stackexchange.com/a/39685/16685)), but I have no idea how to turn that into clockwork mechanism.  
> **username_4**: You might try reaching out to the author of this post if he doesn't see this: https://astronomy.stackexchange.com/questions/57180/how-can-i-build-a-gear-based-mechanism-to-calculate-solstices-equinoxes-and-cr  

---

## 1 answers

### Answer by username_2 on 2024-03-28. Score: 4 | Accepted answer

Following the video, the shape of the cam is a polar plot of the equation of time, with an offset to keep the values positive. You can use any of the trigonometric approximations to the equation of time to plot this, with your choice of offset (presumably a smaller offset makes more deeply indented cam that is hard to follow, but a larger offset makes a cog that is easy to follow, but heavier and takes up more space. So the exact shape is a practical and engineering decision.

You can plot the polar curve with your favourite graph plotter. Here is a [quick mockup with geogebra](https://www.geogebra.org/classic/ztjkwmuh) and a simple formula adapted from wikipedia,
$$r = c -0.7659\sin(6.24+0.0172 d)+0.9863\sin(2( 6.24+0.0172 d)+3.5932)$$

[![enter image description here](https://i.sstatic.net/20NyRl.png)](https://i.sstatic.net/20NyRl.png)

In which $c$ is the offset to keep the radius positive and $d$ is days of the (Julian) year $0\le d<365.35$.

How that shape is then used to adjust a clockwork mechanism is hinted at by the video, but well beyond my knowledge of clocks (and isn't an astronomical question)

> **Comments:**
> **username_2**: one thing I notice is that this is plotted anticlockwise (positive increasing angle) but the clock, or course, works clockwise, so their cam is like the mirror image of this.  
> **username_0**: Hi James, thank you for taking the time to provide an answer to my post. I apologize for not having made it more specific. But I'm glad you immediately knew what information to provide. This is going to help a lot. Thanks again. If you or anyone else is interested to see what this is about, follow on Instagram @noob_watchmaker.  

---

