2" shaft mounting Pt.41: Balance in all things.

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The declination axis of a German Equatorial Mounting [GEM] acts much like a seesaw. Add a heavy OTA on one end of the Dec shaft and it must be balanced by matching counterweights. If the Dec shaft is longer on one side than the other than the counterweight required will be changed in the ratio of the difference in lengths. [Or moment arms as they are known in basic physics.] This simple arrangement allows an equally simple moment calculation. Moment being Mass [weight] x Distance [moment arm] from the pivot [or fulcrum.]  The lever is assumed to be horizontal for simplicity.

The moment should preferably expressed in similar units. Metric: Kg x cm [kg/cm] or Imperial:  Lbs x inches [lb/inches] are matching units. Kg and inches only makes life slightly more complicated if one forgets and swaps units mid-calculation. Otherwise Kg/inches is just as valid as Lb/cm. Those brought up on Newtons can use those. I wasn't and still prefer the simplicity of familiar units of length and weight.

Note how I have deliberately offset the center of the PA axis [Dec axis fulcrum] relative to the declination axis length. This helps to reduce the degree of OTA overhang beyond the nearest Dec bearing. As does placing the declination wormwheel on the far end of the Dec shaft from the OTA. 

The OTA extends beyond the saddle by about half the ring diameter + any thickness in the ring fixing boss. I'm calling that 13cm from the center of gravity of the saddle with the Tollok bush attached.

I have marked the image with the actual dimensions.  The 45cm dimension [on the right] is the distance from the PA axis to the center of the bare Declination shaft. Provided the weights are evenly arranged the center of the weight cluster can be considered as the center of gravity of all the weights. This is the length of the moment arm of all the weights for our balance calculations. 

On the other side of the declination 'seesaw' we have the OTA. Its center of gravity is roughly the middle of the main tube for our purposes. This distance is 37cm in our example.

37:45 = .82. So we can lighten the counterweights relative to the OTA's weight by multiplying by .82.  If the OTA weighs 50lbs then we can use 0.82 x 50 = 41lbs. Which is about 20kg. This is the total weight of counterweights required to balance the OTA. This assumes that all of the CWTs are of equal size and weight. A larger or heavier weight will alter the balance depending on its placement along the Dec axis. As will altering the position of multiple weights of course.

Placing the wormwheel at the saddle/OTA end of the declination shaft pushes the moment arm outwards at that end  by 45mm. This results in an almost equal balance occurring between the OTA and its vital counterweights.

By sheer coincidence weight lifters have adopted so-called 'Olympic' standards for their weight disks and bars. They have settled on 50mm as the hole size in the heavy disks but the lifting bar is not remotely that size. It was decided to reduce twist [torque] in the bar by fitting captive bearing sleeves at each end of the bar. This reduces the risk of damage to the lifter's wrists as the disks can now spin freely as they are lifted.

My lathe is limited in a maximum diameter of work-piece of about 7" [18cm] for turning. Fortunately  I now no longer have to find smaller diameter weight disks for counterweights to bore them out. I just choose from the Olympic standard disks knowing they will slide onto my 50mm declination axis without effort. I have just ordered five, plain cast iron, 5kg weight disks with a 50mm bore. With 130mm available shaft length their 25mm thickness is perfect to leave a little extra room for a collar.

The advantage of plain disks is that they look the part on a telescope mounting. Many weight lifting disks have handles and grips for easier handling. Which complexity would look rather strange. 5kg disks are relatively easy to handle compared with [say] 10kg and above. A total of 25kg should offer a slight excess of counterbalancing. A permanently set up mounting could [should] have an independent, quickly adjustable weight running along the declination housing to offer adjustable bias when heavier or lighter components are added to the OTA. For years I have been struggling with undersized mountings. This includes the Fullerscopes MkIV. Friction within the plain [bronze Oilite sleeve] bearings rises rapidly with increasing OTA weight. The ability to add extras to the OTA or mounting has been very limited.

Click on any image for an enlargement.

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