2 dimensional engineering problem
Dave Francis
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
Joseph Gwinn
Dave Francis <suilvena...@googlemail.com> wrote:
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
Dave Francis
> In article <i5l9qg$7g...@smc.vnet.net>,
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?
Thanks for your interest,
Dave
Chris Pemberton
then code the positions, velocities, accelerations, and the forces of
4-bar linkages, cams, etc. It was mostly trig; with a few tricks thrown
in to take care of special cases. The entire class used C or C++ to do
the coding, then imported their data into excel to plot the coupler
curves, velocities, etc. I was the only student who chose Mathematica
(this was back in 1997).
Mathematica gave me a few advantages over C or C++ coupled with Excel:
1. I could easily "animate" my homework; you could see the linkages
moving, rotating. If there was an error in my derivation of the coupler
equations, my linkages would literally fly apart on the screen. It was
quite comical to see a linkage come apart, fly upwards like a baton, and
land right back in place the next go around.
2. If a picture is worth a thousand words, an animation is worth a
million. My classmates had to hope their static graphs were correct,
but the graphical capabilities of Mathematica allowed me to prove I was
correct.
In my opinion, you'll need to solve whatever problem you've described
using 3-dimensional trig techniques "by hand". Then, code it in
Mathematica, using the graphic abilities of the software to see if your
solution is correct. I have no idea if there exist software that will
do what you've described; probably so.
I know I've got my old homework sitting around here somewhere; and I'd
be happy to send it to you. I can send a scan of all the hand-written
derivations and the Mathematica notebooks as well. It ran in
Mathematica 3.0; so it may need a tweak or two to get going in anything
more up-to-date. Just let me know.
Chris
Dave Francis
> In article <i5l9qg$7g...@smc.vnet.net>,
Joe,
My earlier posting has not appeared, so sorry is if you see double.
Thanks for taking an interest. Could you point us at an information
source that might help us decide if either of us wants to get into the
mathematics of cams? My friends used SolidWorks CAD and has not found
any add-ins that will help with this.
Thanks again,
Dave
Fred Klingener
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
What you describe is a desmodromic (Greek: desmo = bound, dromos path) valve train, and Mathematica is well suited to design and
analysis. The arrangement is famous for its appearance in high
performance internal combustion engines by Ducati (current
motorcycles) and Mercedes Benz (mid-fifties Grand Prix racing cars.)
Take a look at the Demonstration http://demonstrations.wolfram.com/DesmodromicValveTrain/
for a start. That's a rendering of an existing design; the approach to
synthesis would be different but would share some ideas.
After you knock off your new animated, interactive design with a few
dense lines of Mathematica code, contemplate the evolution of the
process, in a single generation of engineers, from push pins and
tracing paper and pencils and lots and lots of erasers.
Hth,
Fred Klingener
Joseph Gwinn
Dave Francis <suilvena...@googlemail.com> wrote:
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
richard i pelletier
i hope someone can answer two questions about LinearModelFit (hence,
version 7)...
1. exactly how is the variance partition in EigenstructureTable computed?
i can see that the eigenvalues are those of the parameter correlation
matrix, but i have no idea how to get the variance partition.
2. what is the difference between MeanPredictionBands and
SinglePredictionBands?
i can see that they create different interval estimates of predicted
response, but how do they differ conceptually?
thanks in advance.
rip
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