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).
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机译：描述了相对于生物参考系具有四个自由度的生物的螺旋运动学。它可以绕三个正交轴中的任何一个旋转，但只能沿一个轴的方向平移。特别是，开发了方程，用于根据微生物的平移和旋转速度计算螺旋路径的螺距，半径和角频率，从而校正和扩展Gray J.（1955. J. Exp。Biol。32 ：775-801）。
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