8.1.4.1 Torsion of space curves

As we discussed in Sect. 2.3 torsion describes the deviation of a space curve away from its osculating plane spanned by the curve's tangent and normal vectors. For planar curves, the torsion is always zero. For an arbitrary speed parametric space curve , the torsion at points with nonzero curvature is given by (2.48).

From (2.48), a condition for zero torsion at a nonzero curvature point is

Figure 8.8 shows a point of zero torsion, marked by at the midpoint of the curve. The sign of torsion has geometric significance [206]. If changes its sign from ( ) to ( ) when passing a point its features change from a right-handed (left-handed) curve to a left-handed (right-handed) one, respectively.