Suppose one has a knot $K$ embedded in $\mathbb{R}^3$;
but view $\mathbb{R}^3$ as a 3-flat in $\mathbb{R}^4$.
Of course $K$ is not a knot in $\mathbb{R}^4$.
I am wondering if there has been any study of how many "moves"
are needed to unravel $K$ using the 4th dimension?

One might make this a sharper question in several ways.
Here is one attempt.  Say $K$ is represented as a 3D polygon
of $n$ vertices in $\mathbb{R}^3$.
A *move* consists of rotating a subchain of $C \subset K$
with endpoints $(a,b)$ into 4D
and then back again at some new orientation into the 3-flat containing $K$.
The endpoints $a$ and $b$ remain fixed, 
while $C$ is replaced by $C'$.
Call the result knot $K'$.

> <b>Q1</b>.
Can every knot $K \subset \mathbb{R}^3$ be unraveled by these moves?
If so...

> <b>Q2</b>.
How many such moves are needed to untangle $K$, as a function of
some measure of $K$'s complexity, say, its crossing number?

These are entirely naïve questions, and I am not sure I have formulated
them coherently. If not, apologies for the distraction!