How does it work?
These type of mounts work with the simplicity of a universal joint. Hence the name of this type of mount. With these mounts you can move a telescope in a true equatorial way. To track a celestial body, the physical parts of this mount move in the same way as a universal joint would be required to do. The funny part: In order to this, the universal joint itself doesn't need to be physically there. We need to drive and control three axes in order to retrieve rotation of the telescope around a fourth axis: the polar axis. The only difference with an ordinary universal joint is that we use its properties inverted, on two occasions.
Take a universal joint in mind, or just grab the universal joint that came with your socket wrench set. The two axes are connected by a double pivoted anchor in the centre between the shafts. There is 90° of shift between the pivots. In the designs of our proposed mount you find the anchor in the form of the cradle on the outside of the shafts. And the shafts themselves.. One is obvious, it is the azimuthal axis. The other one is also there, it's the polar axis that belongs to your observatory position. For the principle of operation of your alt-alt-az mount it doesn't matter if there is a physical polar axis or not. For the proper equatorial rotation we just need to rotate all parts in the way that a universal joint needs to rotate to track the sky. Now things are getting less trivial.
Universal joints have the peculiarity that there are differences in angle velocity between the driven shaft and the loaded shaft. That is not different in our appliance. Jean-Victor Poncelet gave us the math that describes this well in 1854. (Besides, the IAU has named a moon crater and an asteroid after him.) The relation between angular velocities of the azimuthal - and polar axis can be depicted as the graph of a point on a rotating ellipse, just like the sine is the graph of a point on a rotating circle. The ellipse has the same shape that the surface of a fluid forms in a cylinder when you tilt this cylinder parallel with polar axis for your latitude.
We drive the azimuthal plane with the inverted speed in order to retrieve a unanimous rotating polar axis as the outgoing axis. And we also drive both the axes on the cradle in the proper way. Now we retrieve an equatorial rotation of the OTA, regardless if there is a physical polar axis or not.
So we need to drive these three axes all actively because there is no physical universal joint in the mount. I just left it out in these designs because it can be a source of mechanical trouble like friction, elasticity and vibrations, especially on lower latitudes. So the universal joint still exists, only virtually, in the realm of software and motor control.
And of course we still can choose to equip a mount like this with a real universal joint. We have actually built and tested a few already. The nice part, it works fully equatorial with just one motor. You can choose to drive the polar axis directly or to drive the azimuthal plane. They both were tested with a 10 inch Newton and a focus of 1200mm. It all performed good enough to take one minute integrations without guiding.
Can it be this simple as these pictures suggest?
Yes, really, indeed. Affirmative. The physical appearance really is as simple as can be. With appliance of the right math, software and electronics anyone can build and use constructions like these. It might be a little less simple to design the mount in such a way that it maintains balance with every combination of angles. But that can be done too, no rocket science required.
If it is this simple, why did no one think to build and control a mount like this before?
I really don't know. You should ask the other people. I 've played with universal joints and turned them in my hands like a mount years ago. I suspect many of you have done that too. Anyhow I stayed clueless how to solve things. What impeded me most to find a complete solution was my pretty firm believe that the existing equatorial or alt-az mounts could give fine solutions for the ususal demands. Why bother.. I would not have found the solution without the inspiration that I received from Theo Adolfs. He was the first that showed me an alt-alt-az mount that was equipped with a physical polar axis. He received a patent for that. Everybody could tell how to drive the polar axis, but that wasn't a satisfactory solution to drive this mount. For constructive reasons it would be preferable to drive the azimuthal plane with one motor, the other axes are forced by the mechanics of the physical universal joint to rotate with the right angles. But to drive the azimuthal axis in order to retrieve a unanimous rotation of the polar axis you need to control the speed in a non linear way. In seven years time the people that were consulted were clueless about how to drive the azimuthal axis with the right angular velocity. That didn't encourage much to think about driving the other axes as well. In the end of 2017 I was invited to take part in a business with the goal to develop the invention of Theo. It took me a week to find the math, and it took me a month to have a first version of a motor that ran with the right speed. It is a pity that this business opportunity didn't grew to a success. Still it was a valuable experience. And the best, as spin off, it seems like I 'm the first to have cracked these riddles. And the nice part, this solution can be applied to any alt-alt-az mount there is in the field. And you can apply it to any other mechanical system that is driven by universal joint in general.
Which disadvantages come with this design?
In case you want to use the mount for visual observations, you most likely are going to use a Newton telescope. It can be cumbersome to do visual observations near the zenith with for example a SCT on this mount, unless you put it on a pier and have a zenith prism at hand.
A design that follows the rule of an intrinsically balanced mount will get relatively large for all telescopes that have large distances from the rear of the OTA to the declination axis. It will not be the ideal mount for most refractors.
If you are close to the equator you can experience trouble in accuracy and speed limitations.
What if my observation position is close to the equator?
There are rather simple solutions in the case your observatory position is close to the equator (say latitudes < 15°). In those cases you may run into trouble with this mount in alt-alt-az mode as originally proposed. The reason is that a low latitude results in very low or very high azimuthal motor speeds while tracking, depending on the hour angle were your telescope points to. There will be even a (pretty small) range of latitudes around the equator were the motor simply can't be fast enough to track the stars, a similar reason why ordinary alt-az mounts can't track near the zenith. We 've got three ways to deal with this inconvenience.
1. The simplest way to solve for a low latitude is to operate the mount in 'transverse alt-alt-az' mode. In that situation we change the functionalities of two axes and drive it with slightly different math. The mount still operates as a universal joint, the only difference is that we change the drive patterns for the azimuthal axis and the horseshoe axis. We can drive the horseshoe axis with the altered graph of the azimuthal axis and have the azimuth axis move as if it is the horseshoe axis, again with the altered graph. In the case of circumpolar tracking this leads to a discontinuation below and above the pole (meridian flip) to give the horseshoe axis the opportunity to return to the start position.
2. Another solution can be to put it on a wedge in order to give the azimuthal plane deliberately a well known angle with the horizon. We orient the wedge in such a way that it maximizes the latitude error, so the highest part to the equator, the lowest to the pole. The wedge doesn't need to have a large angle, it is likely that 15° is enough. Now we can operate the mount as if it has the latitude of the summation of the actual latitude and the angle of the wedge. The nice part is that the mount doesn't require meridian flips that came with the previous solution, a disadvantage is that the mount is tilted.
3. And another simple solution: put the mount on a wedge with the angle of your latitude and operate this mount in equatorial mode. Now we stop driving the former azimuthal plane and drive the horseshoe axis as the polar axis and we drive the fork axis as the declination axis. The system remains to be all sky, but it will be at the cost of two nice properties. We will have a form of meridian flip when we track a circumpolar object at east and west. The good thing is that the OTA/camera doesn't turn 180°. So it is not a flip in the literal sense, it is just that there is a discontinuity while tracking on those occasions. The other nice property that is lost is that the centre of gravity no longer is precisely above the centre of the pier.
OK, I'm convinced. How can I order one?
Good question! At the moment, you have to build it yourself. I 've solved the math for you and you can have a good understanding of the working principles from these pages. I hope I inspire you to do build a mount like this and that you share your experience with others. Or find people who can build it for you and have them share the experience. Anyhow, much has to be done when it comes to physical design, electronics and software. I 'm going to build a few to test. If you want to join me on this journey of discovery and are willing to contribute in some way, check out the contribute and contact pages.
What can I do to build the smallest mount?
To start you design you need to determine the distance from the rear end of the OTA to the centre of gravity at the declination axis. The shorter this distance, the smaller things can be. A relative heavy primary mirror and cell are beneficial.
If you don't plan to use a mobile setup with full coverage of all latitudes on earth you can save on the diameter of the horseshoes. Still you have a full sky coverage and equatorial tracking as properties. Tracking of objects that aren't in the ecliptic now must be done in the conventional way as other mounts do. That used to be not a big problem. The fun part of full size universal mounts is that they almost (depends on orbit inclination with equator and your place on Earth) always can track non-ecliptic objects without loss of orientation (polarization), this property may be lost (depends on trajectory) with smaller versions.
If you are so smart, why aren't you rich?
Thank you for your concern! Maybe because you didn't send money (yet)? I chose not to file for a patent, anyhow in this occasion. I took to the risk of being remembered for stupidity or better as someone who helped to solve things instead of being remembered as someone who is suing companies or individuals for patent breach. If you want to express gratitude to me or Theo Adolfs, or just save us from poverty, the simplest way is to send some money. That will help to keep this a community project and drives further development!
BANK: Triodos Bank, BIC: TRIONL2U
IBAN: NL38 TRIO 0198 0153 48