Fig. 5.

The effect of nonzero torsion on body postures and no-slip trails. (A) Curves defined by the harmonic curvature (normalized amplitude $A/q=1$) and constant torsion (normalized magnitude ${\tau }_0/q$ as labeled). The green, blue, and red arrows are the unit tangent, normal, and binormal vectors, respectively. A, Left shows projection of nematode trajectories on the $z$–$y$ plane, where the direction of travel is along the $z$ axis. A, Right shows $x$–$y$ projections of the respective trajectories. The green and red circles represent the initial and final points of the trajectories. (B) The torsional roll-rotation rate per undulation period ${\omega }^{\text{roll}}$ (in degrees) vs. normalized body torsion ${\tau }_0/q$ for one-mode torsional roll with harmonic-curvature amplitude $A/q$ as labeled. (C) A crawling nematode undergoing a nonplanar body deformation. The lifted body segment is indicated by the arrow. Reprinted with permission from ref. 47; www.sciencedirect.com/science/journal/09252312. The thick line segment shown for ${\tau }_0/q=0.075$ in A represents a nematode shape approximately matching the image depicted in C.