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'[OT] Puzzle for R.McMahon and others.'
2006\09\27@113519 by

In the OT spirit, and just for fun (and to waste away some time...),
here's a little challenge that will exercise your mind.

Pretend there is a "Grandfather" clock (standard clock face, no second
hand). There is a piece of string tied from the end of the hour hand to
the end of the minute hand. The length of this string is greater than
the sum of the hour and minute hand  lengths. Suspended from this
string, on a pulley, is a weight. This weight can move freely along the
string and will need to as the time changes on the clock face.

Given that:
the length of the String is 's' (not counting the string required to tie
the actual knots)
the length of the hour hand is 'h'
the length of the minute hand is 'm'
s >= h + m
the co-ordinate system will be an x-y system in the same units as the
various lengths above, with the origin centered on the center of the
clock face.
the pulley that the weight hangs from is assumed to have *no* diameter.

what will be the position (x,y) of the *pulley* at time 't' on the clock.

Rolf.

P.S. No prize, but I am scurrying off to remember how to solve this
one..... ;-)

I must be a mathmatician.  I understand how I should solve the
problem, and that there /is/ an answer.  So now I'm no longer as
interested in it as I was while reading it.  Mostly I'm avoiding it
because I realize it would take me a good bit of time I can't use
right now.  If I were to solve it, I'd be particularily interested in
seeing if there's a unique or unusual relationship between H, M, and
S.  If not then you have to include a lot of variables in the end
equation, which could be quite cumbersome.  Can it be simplified if we
assume M = 2H, for instance.

Let me know... :-)

What I'm more interested in now is - what could such a mechanism
possibly have use as?

On 9/27/06, Rolf <learrrogers.com> wrote:
{Quote hidden}

> -

On Wed, 27 Sep 2006 11:50:45 -0400, M. Adam Davis wrote:

> I must be a mathmatician.  I understand how I should solve the
> problem, and that there /is/ an answer.  So now I'm no longer as
> interested in it as I was while reading it.

Funny that - I feel the same way about it, but I put it down to my being an engineer!  :-)  I feel the same way about Sudoku - I can see that it needs
a series of strategies to work out particular parts of it, and if I had to I'd write a program to solve it, but as for doing them all myself, life's too short!

Probably explains why my ratio of finished to in-progress projects is so low.  Is there a completer-finisher in the house?  :-)

>...
> What I'm more interested in now is - what could such a mechanism
> possibly have use as?

What would interest me is how you build it such that the string doesn't get tangled around the hands and their spindles fairly soon in the run.
Probably have to have the spindles coming in from opposite sides, with the string in the gap in the middle - not like a clock at all, in fact.  Next!

Cheers,

Howard Winter
St.Albans, England

> In the OT spirit, and just for fun (and to waste away some time...),
> here's a little challenge that will exercise your mind.
>
> Pretend there is a "Grandfather" clock (standard clock face, no
> second
> hand). ...

Looks almost fun, but I've not got the time to pursue at present -
although shouldn't (yeah right) take very long.

Hand end positions are given by h.sin(hour x 30), h cos(hour x 30) and
m sin(minute x 6), ...
Then ...

What say I stop there before I get too engrossed and ... :-)

Pulley needs a "swivel" as the rope will twist whenever minute hand
tip passes the vertical line through the hour hand tip.

Russell

On Sep 28, 2006, at 8:46 AM, Russell McMahon wrote:

> Hand end positions are given by h.sin(hour x 30), h cos(hour x 30) and
> m sin(minute x 6), ...
> Then ...
>
> What say I stop there before I get too engrossed and ... :-)

Reminds me of hektor, a can of spray paint on two strings.
http://www.hektor.ch/

My favorite video: www.hektor.ch/Videos/Beautifull-Place.mov/

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