Re: 2 dimensional engineering problem

• To: mathgroup at smc.vnet.net
• Subject: [mg112209] Re: 2 dimensional engineering problem
• From: Joseph Gwinn <joegwinn at comcast.net>
• Date: Sat, 4 Sep 2010 04:03:20 -0400 (EDT)
• References: <i5l9qg\$7ge\$1@smc.vnet.net> <i5ngc9\$2mc\$1@smc.vnet.net> <i5qhc7\$pet\$1@smc.vnet.net>

```In article <i5qhc7\$pet\$1 at smc.vnet.net>,
Dave Francis <suilvenassociates at googlemail.com> wrote:

> On 2 Sep, 07:31, Joseph Gwinn <joegw... at comcast.net> wrote:
> > In article <i5l9qg\$7g... at smc.vnet.net>,
> >  Dave Francis <suilvenassocia... at googlemail.com> wrote:
> >
> >
> >
> >
> >
> > > Hi all,
> >
> > > I have a friend in a manufacturing business who, I think, needs
> > > Mathematica to solve a problem. Could anyone here tell me if the
> > > following is possible and perhaps if they would be interested in
> > > taking on the project for a fee?
> >
> > > Here's the problem... It is purely 2 dimensional cam-follower type
> > > puzzle.
> >
> > > Imagine a cartoon heart shape rotating about a fixed point at its
> > > centre (x).  As the heart shape rotates, a small diameter wheel, which
> > > is attached to an arm of fixed length pivoted at point y, follows the
> > > circumference of the heart (like a cam follower). The distance xy is
> > > greater than the greatest radius of the heart shape. Point y lies at
> > > 12 o'clock to point x and the wheel touches the heart at about 10
> > > o'clock.
> > > The arm which is pivoted at point y has a 90 degree bend at that point
> > > and this shorter arm caries another wheel at its end (z). This arm
> > > extends downwards from point y at about 4 o'clock.
> > > My friend needs to define a shape that also rotates about x at the
> > > same speed as the heart shape, and is always in contact with the
> > > second wheel on the arm at point z.
> > > The heart shape, or, of course, any closed loop shape, would be
> > > defined by a set of x,y coordinates or polar coors wrt x. The new
> > > shape would need to be defined in the same way.
> > > NB Please don't be misled by the "heart", the profile is such that the
> > > wheel that follows it, only touches the shape at a single point at any
> > > time - so pure cam-following.
> >
> > > I would love to dive into Mathematica and try this for myself, but
> > > time does not allow that I'm afraid.
> >
> > > TIA  Dave Francis
> >
> > This is a classic problem in the design of cams, the cartoon heart being
> > the cam and the little wheel (roller) being the cam follower.
> >
> > One can certainly use Mathematica for cam design, but unless your friend
> > understands the mathematics of cam design, or wants to learn, he may be
> > happier with commercial cam-design software.
> >
> > Joe Gwinn
>
> Joe,
>
> Thanks for the  advice. Not so simple then? He's using SolidWorks to
> create models and tooling for the original shape, but he can find
> nothing in that product nor advice in its user community to help with
> this problem. He's no dunce so the Mathematica route might suit him
> (and it interests me too) so can you point us to some references that
> might get us started?

There are many sources, far too many to list.  Google yields thousands of hits.
I would sniff around and seen what textbooks are being used for Mechanical
Engineering students.  As with any book, some authors are better than others, so
I always look for books that are in their 2nd or 3rd edition, on the theory that
they would not get that far if badly written.

Joe Gwinn

```

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