Hi Fredrik, that twisting is provided by a mechanism called "Parallel transport":
http://en.wikipedia.org/wiki/Parallel_transport

It is also sometimes called a "Bishop" frame:
Bishop, R. L. "There is more than one way to frame a curve.", American Mathematical Monthly (1975) pp. 245-251

It is a bit difficult to describe shortly, but it basically has a kind of continuously minimally changing twist instead of there being any sudden changes.

Sometimes it is also called a "relatively parallel" frame if I remember right.

The whole problem of how to assign a perpendicular direction to a curve tangent in a coherent way as it travels along the curve is often referred to as "curve framing".

- Michael