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A pole is set in the middle of a fairly flat, square yard. A spool the width of the mower blade
(simple method) or reel with a timed "draw" calculated to the width of the mower blade(complicated method) will draw the self propelled mower toward the pole as the rope shortens as it wraps around the
reel, or as the reel pulls the mower towards the center pole in a calculated manner. This would operate much much like a control line model airplane which has its rudder set to make a turn towards the outside of the circle in order to maintain tension on the control line. The mower would be attached so that it would tend want to travel outside the circle, in order to keep the line taught at all times. Unless the mower were automated with more electronics, it would have be observed in order to switch the mower off when it reaches the end of the rope. An automatic switch could be fashioned to detected a loss of motion when the mower reached the end of the rope, in order to turn the mower off.
Obviously this mower will only cut a circle and will not cover the entire yard. Manual mowing and trimming will be needed to manicure the corners and edges after the automaton is finished.
2008 11 6: I had never heard of the Red Green show I just found segments on You Tube; I am an instant fan and would love to see this man at the Science Bar and he is the living breathing incarnation of halfbakery.com. Seldom do I watch TV but this CD will be on my Christmas list. Thanks to jutta for pointing this out.
Robot lawn mower
does the whole lawn, not just a circle in the middle [Bad Jim, Jun 25 2008]
Red Green Show, Episode 295, Season 15
I think this is what iron_horse was referring to. [jutta, Jun 26 2008]
(?) Red Green Show clips
HIllarious; Please bring him back if the show is no longer on the air [Sunstone, Nov 07 2008]
The maypole lawnmower is on the air
Not mine though, I don't have a yard. Awesome [Sunstone, Dec 24 2010]
A recent video on the latest maypole mower
If only the circle could be squared [Sunstone, Sep 01 2013]
Hack My Life TV Maypole mower
Episode E2 S13. The show is kinda like Red Green at a Maker Faire [Sunstone, May 11 2016]
||"Low tech don't mean no tech" (+)
||Minor correction: The spool would need a circumference equal to (preferably slightly less than) the diameter of the cutting blade.
A spool with diameter equal to the cutting blade will only allow the mower to cut 1/(pi) of your lawn.
||I don't see how you're gonna cut a square lawn, but [+]
||Baked, exactly as described, on an episode of the Red Greene Show.
||Nifty idea. Unfortunately one of the twenty people in the world who have seen the RedGreen show happened along to call it baked.
||//If only the circle could be squared// I was just watching a YT vid about a square-hole drilling mechanism for a hand-drill.