I would like to build knots in $\mathbb{R}^3$ from arcs
of unit-radius (planar) circles, joined together at points where
the tangents match. Thus the knot will have
curvature $1$ at all but the joints.
Here is an example of how two arcs might join:

Define the *circle-arc number* $C(K)$ of a knot $K$ as the fewest
number of such arcs from which one can build a nonselfinterecting
curve in space representing $K$.
This number is analogous to the
stick number of a knot,
except that the pieces are arcs,
and there is a tangent-joining condition.

I would be interested to learn of bounds on $C(K)$ in terms of other knot quantities, for example, the stick number, or the crossing number cr$(K)$.

Here is an example of what I have in mind.
It appears that one might be able to build a trefoil from six
arcs, something like this:

However, the above picture is actually planar, and I have not
verified carefully that this is achievable in $\mathbb{R}^3$!

Has this concept been studied before? If so, pointers would be welcomed. Thanks!

**Addendum**. The trefoil can be realized with six arcs:

(The black triangle vertices indicate the circle centers on the plane before their arcs are twisted into 3D.)