Change the shape of a path without changing the length of the path.

You may also try to mimic it with brushes.

Take a look at this sample file (just move some anchor points or segments around or scale the entire objects to see the effect).

https://drive.google.com/open?id=1f12cYtbWoI0kOOWB-guT4lyHHmsRsyB2

Robert,

Your concept of shape is actually a double concept, namely (pure) shape and size, which is quite meaningful in the real world, as well as in final artwork that contains other paths/objects.

In the real world you are unable to change a string into any shape and size of a string any way you like, exactly because it has an unchangeable length; you can only do it (more or less) with a rubber band.

If you need to reshape from one end in the same way as with a(n unstretchable) string, Doug has already given you the equivalent of the string.

Otherwise, you can do it quite easily by using a two step way where you first forget about the length requirement while you change your (pure) path into any shape you wish, and then you resize it to meet the length requirement, using the Info panel and scaling, which is quite easy.

I believe that most likely, whichever way you do it, even with a (possible) plugin as mentioned by Lutz, you will need to try and fail, then redo until you are saisfied.

You can sort of -- using a dashed stroke with a long dash and an even longer gap.

The maximum you can have is 1000 px/pt, however, so your path needs to be shorter than 2000 pt to prevent the next dash appearing.

You can then expand the path (if that's what you want) by applying an art brush consisting of a basic stroke to it, then using Object > Expand Appearance

Not without plug-ins, most likely, though off hand I'm not even sure if there is anything of that sort. Constraining the length of Bèziers or for that matter any n-th power spline is complicated math, as you usually reverse-calculate the underlying formula. AI is not a simulation tool, just a drawing program, you know. That being the case, your chances are far better if you simply try to fake it by limiting strokes to specific segments of paths and the like. Otherwise you may have to move on to more technically-based tools like actual CAD/ 2D drafting programs where such unwrap functions are more common.

Mylenium