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