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 IceInSpace Geometry/maths question (re tangent errors).
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#1
11-07-2007, 02:28 PM
 eqcradle Registered User Join Date: Apr 2007 Posts: 31
Geometry/maths question (re tangent errors).

I've been out of high school too long to answer this one ...

This page does a good job of explaining the tangent error that you get when using a threaded rod to drive a barndoor mount (and the resulting tracking inaccuracy):
http://www.mikeoates.org/mas/projects/scotch/

What I'm wondering is whether a threaded rod with a universal joint or CV joint in the middle of it might solve the tracking error. Eg, each half of the rod would remain at 90 degrees to its arm, and both ends would be rotating in a threaded nut mounted in each arm. Maybe the rods could be joined in the middle by something other than a universal joint. As the arms separate, the universal joint should stay half way between them, with the angle between the 2 halves of the rod gradually approaching 90 (from starting at 180 degrees).

So, the question is: would this give the desired constant angular rate of change between the 2 arms??
#2
11-07-2007, 02:53 PM
 janoskiss (Steve H) Registered User Join Date: Jan 2005 Location: Sale, VIC Posts: 6,033
Quote:
 Originally Posted by eqcradle So, the question is: would this give the desired constant angular rate of change between the 2 arms??
No. You need a circular arc or electronic error correction to get constant angular speed.
#3
11-07-2007, 02:54 PM
 erick (Eric) Starcatcher Join Date: Dec 2006 Location: Gerringong Posts: 8,521
Have you read up on a curved-bolt tracker? Supposed to have lower errors, but design is different - nut has to turn rather than the bolt. Question whether curved bolt would support the weight as well if this is to support your dob?
#4
11-07-2007, 03:14 PM
 eqcradle Registered User Join Date: Apr 2007 Posts: 31
Erick: yep, I've seen the curved rod idea - it's quite clever. And yes, i do have a Dob in mind - ;-).

Janoskiss: I can understand why the two examples on the linked page wouldn't work, but can you explain specifically why this one wouldn't?

This idea doesn't seem to suffer either of the stated problems of the two types listed on the linked page. It seems to me that the end of each arm would be driven at a constant rate relative to its tangent (ie. perpendicularly). So, why doesn't that give a constant rate of angular change?
#5
11-07-2007, 03:30 PM
 janoskiss (Steve H) Registered User Join Date: Jan 2005 Location: Sale, VIC Posts: 6,033
I'm not sure I follow you. How is this angle: "the angle between the 2 halves of the rod gradually approaching 90 (from starting at 180 degrees).", going to be fixed for a given arm length? I cannot even picture what you mean, given that "each half of the rod would remain at 90 degrees to its arm"...
#6
11-07-2007, 04:18 PM
 middy Registered User Join Date: Feb 2006 Location: Brisbane Posts: 631
Hmmm I can picture what you are saying and I have to say that is a very interesting concept and one that has occupied my mind for the last hour here at work.

I haven't done any calculations but after thinking about it I decided that you would only reduce the error by half. This is because you are effectively butting together two right angled triangles with the threaded rod in each only having to turn at half the normal speed to maintain the required rate. (Gosh I wish I had a picture my brain is hurting again. )

Imagine the case where you split the rod into smaller sections with more universal joints connecting them. The tangential error will get less and less until the case where you have an infinite number of sections of threaded rod (this is exactly what a curved threaded rod is) which will then have zero tangential error.

Phew I need a lie down!!
#7
11-07-2007, 05:12 PM
 eqcradle Registered User Join Date: Apr 2007 Posts: 31
Hopefully the attached pic will help...

As the rod is turned, the angle between the arms will increase. The universal joint itself should remain in the centre as the arms separate.

So, if the rod is being turned at a constant rate, then the end of each arm should also be driven at a constant rate. And because the rods are at 90 degrees to the ends of the arms, then the ends of the arms are always driven (at a constant rate) relative to each arm's tangent. That's why I thought it might work.

The angle I referred to earlier was the angle that the universal joint makes between the 2 halves of the threaded rod. At first the 2 halves of the rod would be relatively straight, but as the arms separate, the angle between the rods would gradually reduce from 180 towards 90 degrees.

Middy: Does your analysis require .... calculus?! Are there any high-schoolers around here? I really don't want to dig out the old text books....
Attached Thumbnails
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#8
11-07-2007, 06:05 PM
 eqcradle Registered User Join Date: Apr 2007 Posts: 31
I think Middy's way of thinking about it was right. It's just like 2 of the 1st example on the linked page back-to-back. And it's actually fairly easy to work out when you think about it that way. No calculus required, just the tan button on the calculator. I'm not sure it actually improves the error at all. Oh well ...

Last edited by eqcradle; 11-07-2007 at 06:17 PM.
#9
11-07-2007, 06:36 PM
 sheeny (Al) Spam Hunter Join Date: Jun 2005 Location: Oberon NSW Posts: 13,674
Quote:
 Originally Posted by erick Have you read up on a curved-bolt tracker? Supposed to have lower errors, but design is different - nut has to turn rather than the bolt. Question whether curved bolt would support the weight as well if this is to support your dob?
A curved bolt is the most elegant way to go for a barndoor, but it might be interesting for a dob, as you say!

I could calculate what size rod would be necessary from a strength point of view if I knew the weight of the dob, radius the screw was to act at, and the maximum angle the barndoor was to operate through... but... I'm not sure what criteria to use for deflection. So while I'm confident I could design something strong enough (without going overboard) I'm not sure if it would be any good because it may deflect too much at high tilt angles...

Al.
#10
11-07-2007, 06:38 PM
 sheeny (Al) Spam Hunter Join Date: Jun 2005 Location: Oberon NSW Posts: 13,674
Quote:
 Originally Posted by middy Hmmm I can picture what you are saying and I have to say that is a very interesting concept and one that has occupied my mind for the last hour here at work. I haven't done any calculations but after thinking about it I decided that you would only reduce the error by half. This is because you are effectively butting together two right angled triangles with the threaded rod in each only having to turn at half the normal speed to maintain the required rate. (Gosh I wish I had a picture my brain is hurting again. ) Imagine the case where you split the rod into smaller sections with more universal joints connecting them. The tangential error will get less and less until the case where you have an infinite number of sections of threaded rod (this is exactly what a curved threaded rod is) which will then have zero tangential error. Phew I need a lie down!!
You're on the right rack, Middy!

The error would be reduced to the tangent of half the angle of tilt of the barndoor, so it would be a bit better than 1/2 the straight screw error.

Al.
#11
11-07-2007, 06:43 PM
 sheeny (Al) Spam Hunter Join Date: Jun 2005 Location: Oberon NSW Posts: 13,674
Quote:
 Originally Posted by eqcradle I think Middy's way of thinking about it was right. It's just like 2 of the 1st example on the linked page back-to-back. And it's actually fairly easy to work out when you think about it that way. No calculus required, just the tan button on the calculator. I'm not sure it actually improves the error at all. Oh well ...
Yup! You're on the money with the calc.

It does improve the error, but I don't think the improvement is worthwhile given the extra complexity.

It's an interesting problem, but I suspect an EQ platform is probably a better solution... any differential deflection as the barndoor tilts is not a factor with the EQ platform.

Al.
#12
11-07-2007, 11:28 PM
 netwolf Registered User Join Date: Jan 2005 Posts: 2,934
Hmm sounds like Zeno's Arrow Pardox. Arrow must travel half the distance before it can reach the target, and half again and again on infinitum.
Giving 1 - 1/2^n < 1 making continuous motion impossible. Thats why we have infinity to link the Discrete and the continuous without it everything falls apart. As middy rightly pointed out ultimately the limit would give you a perfect arc and zero error. or 1/2^n as n approaches infinity becomes zero. Aristotle responded to this paradox with similar argument in his aptly titled book Physics. Its not Calculus (Newton) its older than that.

Regards
#13
01-08-2007, 08:02 PM
 eqcradle Registered User Join Date: Apr 2007 Posts: 31

The WP page describes a linkage which translates circular motion to linear motion (and vice versa). Note in particular the last sentence of the Geometry section:
"On the other hand, if point B were constrained to move along a line (not passing through O), then point D would necessarily have to move along a circle (passing through O)."

So, picture the blue line in the 2nd diagram going through B, not D. If B is driven along the blue line (which is a threaded rod), then D should move along a circular path I think.

So my question is: if B is driven at a constant rate, does D move at a constant *angular* rate? I'm guessing it probably doesn't, but it if did it might be a good system for a barn door mount.
#14
02-08-2007, 02:04 AM
 netwolf Registered User Join Date: Jan 2005 Posts: 2,934
http://hometown.aol.com/davetrott/page17.htm

Regards

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