2 dimensional engineering problem

• To: mathgroup at smc.vnet.net
• Subject: [mg112130] 2 dimensional engineering problem
• From: Dave Francis <suilvenassociates at googlemail.com>
• Date: Wed, 1 Sep 2010 06:27:36 -0400 (EDT)

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

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