An Omni Latitude Equatorial Table

Mel Bartels, February 2013

I'm fascinated by the equatorial table, or Poncet Platform, ever since it was invented in the late 1970's by Adrian Poncet. The platform's versatility has been proven by its use from small table top telescopes to giant telescopes - even an entire observatory building!

http://en.wikipedia.org/wiki/Poncet_Platform

While the polar alignment has not proven too difficult, the equatorial table suffers from a serious limitation: it's built to a specific latitude. Traveling north or south a few hundred miles to a major star party means uncomfortably tipping the platform up on edge. Is there anything that can be done about this limitation?

Jerry Oltion’s Trackball cleverly uses a single roller aligned parallel to the polar axis pressed against the bottom of the ballscope. A single tracking roller that is slid along a curved holder based on the site’s latitude

 http://www.sff.net/people/j.oltion/trackball.htm

Jerry’s mounting design could be trimmed down into a hemisphere, resulting in an equatorial table platform. For moderate latitudes the drive arm rises above the two rollers.

My idea is that the curved pads cut out from a hemisphere can be driven by two rollers working on two lines of latitude; each wheel rotates at its own unique constant rate. The drives rates depend on the site’s latitude. Changing latitude is a matter of resetting the wheels’ drive rates.

For example, let's say that the drive wheels' diameter is 1.5 inches [4cm] and that the virtual ball's diameter is 20 inches [51cm]. For the placement of the drive wheels and pads shown

the drive rates for a site of 45 degrees latitude are:
pole facing motor: 20 inches / 1.5 inches * sin(line of latitude of 75 deg) * 1.002737909 sidereal rate / 1440 minutes per day = 0.0090 rpm
side facing motor: 20 inches / 1.5 inches * sin(line of latitude of 35 deg) * 1.002737909 sidereal rate / 1440 minutes per day = 0.0053 rpm

and for a site of 30 degrees latitude are:
pole facing motor: 20 inches / 1.5 inches * sin(line of latitude of 90 deg) * 1.002737909 sidereal rate / 1440 minutes per day = 0.0093 rpm
side facing motor: 20 inches / 1.5 inches * sin(line of latitude of 45 deg) * 1.002737909 sidereal rate / 1440 minutes per day = 0.0066 rpm

Here you can see the concept. Note how the platforms for site latitude of 45 degrees and site latitude of 30 degrees are identical; the only difference being that the two drive motors operate at different rates causing the platform to track on different lines of latitude.
 

Here is what the platforms for latitudes of 45 and 30 degrees respectively look like at the end of an hour of tracking.
 

There is a slight difference in the platforms’ ending angle. The platform on the left tracked for site latitude of 45 degrees, which the platform on the right tracked tracked for a site latitude of 30 degrees.

The drive wheels will need to be made from hard plastic, possibly with a thin ribber O-ring to generate friction. The friction is needed to resist sliding as the telescope sitting on the platform is pushed about the sky.

The tradeoff for the omni-latitude table is two fold:
1. Two motors that rotate at constant rates, the rates varying per the site's latitude
2. The need to grind or sand the curved pads in two dimensions; many equatorial tables have their curved tracking surfaces ground in one dimension, this has to be expanded to two dimensions.

Sketchup model can be found here

 
Other inspirations include Alphonse Pouplier's "Robotic Astroscan" (see Sky and Telescope magazine, August 1993) where he uses two tracking wheels that sidereally track and provide goto motions for a ballscope. And Pierre LeMay’s dual tracking roller platform places both rollers at the same line of latitude. Conceptually it appears more in line with Jerry’s thinking than with the dual great circle tracker here. More can be found on Jerry Oltion's webpage noted above.

 
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