Tag: mathematics

More Magic Designer Nonsense

This is what I simulated earlier – except drawn on a real Magic Designer. Something’s off with what I modelled …
All of these are drawn with the Magic Designer angle set to 57, which puts the crank discs exactly in phase. The blue circle in the middle is an exactly image of a crank disc, if perhaps a very dull plot.

Slightly imperfect Hoot-Nanny/Magic Designer simulation

round figure with three interlaced 6-fold curves picked out in red, green and blue
I even emulated the locating notches at the edge of the paper …

Simulated (and not quite right yet) output from a “HOOT-NANNY” or Magic Designer, a proto-Spirograph toy that drew six-sided curves on round paper sheets. It was made by Howard B. Jones and Co. of Chicago, IL and first sold in 1929. The company’s better known for producing Jones Plugs and Sockets, sometimes known as Cinch-Jones connectors. The “HOOT-NANNY” name was dropped when production moved to the Northern Signal Company of Saukville, WI.

My eBay-acquired Magic Designer is quite beaten up, and doesn’t always produce accurate results. Here’s how one should look, from the instruction pamphlet:

diagram of the Magic Designer toy: central turntable holding paper is rotated by crank at bottom right. On the left are two crank discs (upper and lower) each with a crank pin that can fit into holes along two arms. These arms are joined at a pivot, and in the centre of this pivot is a pencil. The upper crank disc can be moved in an arc relative to the lower disc. This is controlled by a locking shift lever on the right
I can’t shake the feeling this was originally something like an artillery ranging tool or suchlike

As far as I’ve been able to work out, the parameters of the machine are:

  • central turntable is 6″ in diameter, with 192 gear teeth around the edge;
  • each crank disc is 1″ diameter (32 teeth), with the crank pin at 3/8″ radius;
  • the shift lever has a 10-70 degree scale, which corresponds to moving the upper crank disc between 30-90 degrees of arc from the lower (fixed) crank disc;
  • the pencil arms have 18 holes labelled A to R, at 1/4″ spacing from 5.75 to 1.5″. The perpendicular distance from the pivot holes to the pencil is 5/16″. This small offset makes very little difference to the overall arm length.

If we model the toy with a fixed turntable:

  • the crank pins describe epitrochoids around the edge of the paper;
  • the pencil point traces the intersection of two circles of radius the lengths of the pencil arms, each centred on a crank pin.

Here’s a very simple model in Python that emits a hard-coded (but editable) pattern in HP-GL: Slightly imperfect Python simulation of the “HOOT-NANNY” (or Magic Designer) drawing toy (static local copy: hootnanny.zip). It doesn’t do anything with the fixed circle studs (yet)