Kinematics of helical motion of microorganisms capable of motion with four degrees of freedom.

The kinematics of helical motion are described for an organism with four degrees of freedom, relative to the organism's frame of reference. It can rotate about any of three orthogonal axes, but can translate only in the direction of one axis. In particular, equations are developed for calculating the pitch, radius, and angular frequency of the helical path from the translational and rotational velocities of the microorganism, correcting, and expanding the analysis of Gray J. (1955. J. Exp. Biol. 32:775-801).