On the Ball
A colleague showed me a small plastic toy soccer ball,
complete with markings, and wondered how to replicate the ball in Pro/E. Since it took
quite a lot of thinking about, but turned out to be relatively simple, I thought it was a
good candidate for a training example.
Hows it done?
When you first study the pattern, you realize its a collection of pentagons and hexagons. You may immediately think about complex relations of line segments and equators, and projected datum curves, but the solution turns out to be much simpler. In fact, I used a total of five dimensions.
Instead of starting from a spherical shape and then wondering how to divide it into segments, think the other way around, and as in most modeling techniques in Pro/E, try to model the same way as the manufacturing process would be. In this case, by sewing together the individual patches of leather, we end up with a full spherical globe. So lets model it in Pro/E the same way.
The first step is to start a new part for the pentagon. Sketch a Datum Curve to form a pentagon shape, making sure you have one of the default datum planes through the center as shown - well be using that later.
Then start a new part for the hexagon, and sketch a datum curve to form the hexagon shape. Notice only one dimension was used in each sketch - Sketcher was forced to assume equal line lengths.
Start a new assembly, and add the pentagon part as the first component. Now, if you were to draw a couple of hexagons attached to this pentagon (in 2D) you'd get the following: there would be a gap between the outer vertices of the hexagons. It's when you pull these two vertices together that the sphere will begin to form.
So, add the first hexagon part by aligning two vertices at the attachment line, and add a third constraint for point on surface, picking the central YZ plane.
This "folds back" the hexagon part correctly. Add a second hexagon part by aligning three vertices, and then carry on adding hexagons and pentagons in the correct pattern until a spherical shape is formed. This concept was developed by Buckminster Fuller, for geodesic dome building construction.
To find the center, create a datum curve from one curve vertex to the exact opposite curve vertex, and then create a datum point along the curve with a length ratio of .5.
Making the solid
Working in the pentagon part window, create a blended protrusion from the part's curve's sketching plane to a sharp point. Before you do this, do an INFO > MEASURE in the assembly to determine what the blind length should be.
Then do the same for the hexagon part (different blind depth).
You should now have an assembly of solid parts. Because we used a line length of 4", the resulting solid is much larger than an actual soccer ball. To create the spherical shape, create an assembly revolved cut of 6" radius, (or whatever the radius should be for a soccer ball). You may have to manually pick some of the components to be intersected.
It can be seen now that the datum curves were used to construct the framework of the ball (they are construction features after all). If we now layer off all construction features, and apply colors to the parts, we get the completed soccer ball.
Note: We could set up relations to ensure the blended protrusions always reached the center if we were to modify the two 4" dimensions.
Kick it around and see if you can do it differently!