Fun with constraints

[Anonymous]

Last holiday I got a cool toy which consists of a series of plastic rods
with magnets in the ends which attach to stainless steel balls. The
rods basically enforce tangent constaints on the balls, but are
otherwise free to rotate.

To test the limits of constaints in Inventor I decided to model it. I
would like to share the results with you. They are posted in the CF
under the same title. I encourage you to build your own models with the
ball and connectingRod parts. I put tangent imates on the ends of the
rods and three on the sphere to simplify assembly of new models. One
interesting consequence of the spherical cap on the ends of the rods is
that they will tangent mate to other rods just as easily as with the
spheres. You can build up the entire model with only rods!

It brought up a question that I was unable to answer. The spheres and
rods are all positionally constrained by the tangent constaints, but the
spheres have two rotational degrees of freedom and the rods have one.
Is it possible to constrain away the angle degrees of freedom, without
simply grounding the parts? I want the components to move, but there
are no "features" on the spheres that one can select!
--


---
...STeve

Steven Trainoff, Ph.D.
Director of Engineering
Wyatt Technology Corporation
30 South La Patera Lane B-7
Santa Barbara, CA 93117
Ph: (805) 681-9009 x104 Fax: (805) 681-0123

[Anonymous]

Could you add a mate constraint between the center points of the balls
and the axis of the rods?

steven.trainoff at wyatt.com wrote:

> Last holiday I got a cool toy which consists of a series of plastic
> rods with magnets in the ends which attach to stainless steel balls.
> The rods basically enforce tangent constaints on the balls, but are
> otherwise free to rotate.
>
> To test the limits of constaints in Inventor I decided to model it. I
> would like to share the results with you. They are posted in the CF
> under the same title. I encourage you to build your own models with
> the ball and connectingRod parts. I put tangent imates on the ends of
> the rods and three on the sphere to simplify assembly of new models.
> One interesting consequence of the spherical cap on the ends of the
> rods is that they will tangent mate to other rods just as easily as
> with the spheres. You can build up the entire model with only rods!
>
> It brought up a question that I was unable to answer. The spheres and
> rods are all positionally constrained by the tangent constaints, but
> the spheres have two rotational degrees of freedom and the rods have
> one. Is it possible to constrain away the angle degrees of freedom,
> without simply grounding the parts? I want the components to move,
> but there are no "features" on the spheres that one can select!

[Anonymous]

Charles Bliss wrote:
> Could you add a mate constraint between the center points of the balls
> and the axis of the rods?
>

I believe that since the sphere and spherical cap on the ends of the
rods have the same diameter, that is already implied. The balls are
positionally contrained, but they can all still rotate freely.

Another thing that I thought was interesting to do was to surpress a few
random links on the buckyball and move some the freed components. If
you then unsupress the contraints and rebuild all, it will usually snap
into another solution which is kinematically correct, but not
spherically symmetric.

This brings up another problem that I, and many others on the newsgroup,
have. It is how to get IV to choose between two, or more, possible
solutions to the contraints. In the above example, you can force IV to
"jump" to another solution by breaking constraints and then
re-establishing them. The new solution is not "connected" to the old
one since there is no smooth deformation that gets from one to the
other. However, often I find that IV will spontaneously jump to another
"equivalent" solution unintentionally.

This also happens to me in sketches when I dimension, say, the distance
between two vertical lines. In my head I assume that the first one is
the left of the second one. But the constraint is equally well
satisfied by swapping the two lines. This usually happens when I
parametrize a model and then change a parameter, thereby making a
discontinous jump, and then IV's solver hops into the "wrong" solution.
Another way of putting it, is to say that dimension constraint really
only enforces that abs(d1-d2) = dimension_value. This has two solutions.


...STeve

[Anonymous]

Oh, no! More golden ratios and *hedrons. 8~)

>> tangent constraints

I think if it were me I'd constrain spherical centers. Probably a lot less
computation involved, which may become a factor with large numbers of
constraints. (I don't ever mess with iMates. Am I missing anything good?)

>>Is it possible to constrain away the angle degrees of freedom ....

Some combination of points (not spherical centers) and planes should work for
the rotations. Why do it, though, unless you are trying to limit possible
solutions? I figure (possibly incorrectly) that the fewer things IV must
calc, the better, unlike a kinematic solver. I'd suggest axis / plane
constraints, but they are broken.

>> IV's solver hops into the "wrong" solution.

Contrary to the advertising IV doesn't think like you do, you have to think
like it does and it's a bit schizoid 8~) For assembly constraints, once all
dof's are constrained, about all you can do is add constraints that reinforce
orientations / preclude alternate solutions. IV is great about this as it
allows what would normally be considered redundant assembly constraints. If
only the sketch solver would do the same... Each sketch problem is a bit
unique, but a generic treatment would be to dimension the critical entities
from a common datum, possibly related by an equation, instead of relative to
one another. Some cases can be solved by the addition of construction
geometry that will enforce or preclude a solution. Sometimes, though, it's
hard to outsmart D-Cubed and get what you want (I fuss about it, but it's
great to have... anyone know how to define the tangent for any given point on
an ellipse?).

Have a blast (or should I say "a ball"?) with it.

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