Re: 2 dimensional engineering problem

• To: mathgroup at smc.vnet.net
• Subject: [mg112151] Re: 2 dimensional engineering problem
• From: Joseph Gwinn <joegwinn at comcast.net>
• Date: Thu, 2 Sep 2010 02:31:44 -0400 (EDT)
• References: <i5l9qg\$7ge\$1@smc.vnet.net>

```In article <i5l9qg\$7ge\$1 at smc.vnet.net>,
Dave Francis <suilvenassociates 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

```

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