@TedShifrin Crookedness in v direction = number of local maxima of v * r(t). Crookedness = min crookedness in v direction (letting v vary).
Crookedness = 1 means that you can rotate space so that the curve's height has exactly one local maximum.
So pick a knot diagram so that height has exactly one local maximum, and crossings all have different height.
Exactly one local maximum => portion above the top crossing lies inside the knot, and forms a simple closed polygon in the plane
(left side of crossing goes up to that local max, as does right side of crossing)