How to create a chubby mobius strip

Using the trajpar parameter in PTC Creo

1.

Create a sketch and draw a circle with a diameter of 50mm.

2.

Start a sweep feature.

Select half of the circle as the trajectory, allow the section to change along the sweep, and select Create or edit sweep section.

3.

Draw a square center rectangle, with the center coincident with the trajectory start point. Make the sides 20mm.

4.

Select the entire sketch, cut it (ctrl+x) and paste it back in (ctrl+v).

Re-center it and rotate it a couple of degrees before accepting the new position.

5.

Dimension the angle between the top of the square and the horizontal center line. The amount is not important, as this angle is going to vary along the trajectory. If we didn't do the cut+paste operation, we would not have been able to define this angle.

6.

Now for the interesting stuff. The trajpar parameter: The trajpar parameter is simply a value that varies from 0 to 1 along a trajectory. When used together with a relation equation and a variable sweep, it’s possible to create some interesting shapes fast.

In this particular case, we want the square to rotate 90 degrees along the half circle trajectory.

While still in sketch mode go to tools and select relations. An editor will appear and here we’ll write the following equation:
sd6=trajpar*90

Sd6 is the dimension we want to vary (Yours might be different. Look what it says at the angled dimension).

In the start of the trajectory the trajpar is equal to zero, making the angle 0*90=0 degrees. In the end of the trajectory the trajpar is equal to one, making the angle 1*90=90 degrees. At the middle of the trajectory the trajpar will be 0.5 making the angle 0.5*90=45 degrees. Get the point? Else read a bit more here: http://en.wikipedia.org/wiki/Trajpar

7.

Press OK to exit the relation editor and then exit the sketch. Here is what it should look like if everything is done correctly:

8.

Now, do the exact same for the other half of the circle.

9.

You probably still have the square stored in your computer memory. Just press ctrl+v to bring it back in. If not, you have to draw it, before cutting and pasting it.

10.

Use the exact same equation as before. The important step here is to pick the right angle to vary along the path. In order to create the mobius strip we need the square to keep spinning in the same direction as in the first sweep.

11.

Now you should have a chubby looking mobius strip.

Ultimately, the entire mobius strip should be created with one sweep only, using the entire circle as trajectory… I just haven’t succeeded in doing that yet. It just won’t work. If your are better than me, and are able to doing so, please tell me how to do it!

12.

Apply some edge chamfer and roundings to finish it. You’ll probably be surprised (I did at least) by the fact that you only need to select two edges to chamfer them all… ‘cause there are no more than two edges in this shape.

13.

As always, bring the model to your favorite rendering software and make it sexy. Here I used KeyShot. Before importing it into KeyShot, I assigned a different color to one of the surfaces, making me able to apply different textures to the different surfaces in KeyShot. If you don’t know how to do this, take a look here: https://medium.com/p/fdb96a4c8d0a

I gave one surface a black shiny paint material and the other an area light diffuse material. I added in a ground plane, gave it a soft touch black texture and softened the edges of it with an opacity map.

That’s it. If you have any questions please ask, I’ll be happy to elaborate.