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I'm trying to build a lightweight antenna tracker with two servos. For mechanical reasons, I'm first mounting servo1 on a base so that it tilts forward/backwards, then mount servo2 on it twisted 90˚so it can tilt left/right.

I can basically use the first servo to select a from the great circles that go through azimuth=0˚ and alt=0˚ and az=180˚ and alt=0˚, and use hte 2nd servo to move on the chosen great circle. This way, I should be able to point at the entire upper hemisphere even though I might need to reposition the antenna when crossing the midline (the servos only have 180 degrees of movement.)

I'm trying to find the function that maps az/alt to the tilt/tilt servo angles. I suspect that should be similar to how equatorial telescope mounts work, but I couldn't find a good reference on how to do it - neither do I trust my own math.

I found this astronomy lecture notes vaguely helpful: http://ircamera.as.arizona.edu/Astr_518/ametry.pdf especially page 22/23 on the ecliptic coordinate system, but I think the problem solved here is slightly different.

This seems a standard kinematics problem, it bothers me I can't figure it out or even find online resources. I'd be super thankful for any pointers. Happy to give more details on the servo setup.

Klapaucius Klapaucius
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1 Answers1

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I think I figured this out on math.stackexchange.com:

https://math.stackexchange.com/questions/3799191/direct-conversion-from-az-el-to-ecliptic-coordinates

Short answer (for python, consider parameter order for atan2 in your language):

$\epsilon=\atan2(\sin\delta, \cos\delta\cdot\sin\alpha)$

$\lambda = \arccos(\cos\alpha\cdot\cos\delta)$

where $\alpha$ is azimuth, $\delta$ is elevation or altitude, $epsilon$ is the angle for the first and $lambda$ the angle for the 2nd servo. This seems to work for all values of $\alpha$ and for values in $[0,\pi/2]$ for $\delta$.

Klapaucius Klapaucius
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