Very cool idea! However, you'd have to control the speed & angle very carefully to allow the shape to fall to one side or the other at the appropriate time. You might also have to engineer non-homogeneity into the mass to give you some more degrees of freedom. Of course, if you also allow for internal mechanisms, where weights can move around within while "rolling" without, the possibilities seem endless. If you also give some of the internal parts the ability to start with a spin, then gyroscopic mechanisms can also be employed. There are already simple "walking" robots with no moving parts that can maneuver themselves down an inclined plane, so these ideas would subsume those robots. At 12:00 PM 4/22/2010, Allan Wechsler wrote:

This business of weird rolling shapes got me musing. One could design a "ball" that, released from rest in the proper orientation on a sufficiently flat surface, would roll along a predetermined path. In principle, if one were parsimonious enough with potential energy, the path could be arbitrarily ornate, though the object would roll very slowly along it.

So, in practice, how complicated a path could be programmed into, say, a machined steel roller? Could a skilled machinist create a "signature" roller that wrote the machinist's name?

On Thu, Apr 22, 2010 at 2:38 PM, <rcs@xmission.com> wrote:

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[another SBG contribution trapped by the mystery mail filter -- rich] -----------

Date: Wed, 21 Apr 2010 15:46:57 -0700 Subject: Re: [math-fun] Trying to recall funny shape From: "Stephen B. Gray" <stevebg@roadrunner.com> To: math-fun@mailman.xmission.com

On 4/21/2010 12:50 PM, Dan Asimov wrote:

I recently read of an odd solid shape, with I think an odd name,

...

that has recently been defined. It may be this:

Take a solid cylinder whose diameter equals its height, cut it in half along a square, rotate one half 90 degrees, and glue the halves back together again.

Does this shape have a name, or is there something similar that does? Apparently it has very interesting rolling behavior.

--Dan

It's called a gefubuwichmuttle. Next question?

-Anonymous