Abstract The random positioning machine (RPM), which continuously changes the gravity direction acting on a subject, can provide the simulated microgravity and planet hypogravity environments to the bioreactor on Earth. In this study, a theoretical analysis of the microgravity and planet hypogravity fields generated by the RPM motion was attempted. The simulated microgravity fields around the subject were quantitatively analyzed by the newly defined degree of gravity dispersion (DGD) parameter, and the simulated planet hypogravity fields were analyzed by the gravity ratio between the RPM simulation and a real planet, corresponding to the normalized DGD. The motion of the gravity vector tip (GVT) on an imaginary sphere attached to a rotational subject was traced and the cause of the GVT trajectory repetitions, which occur in certain combinations of constant (C) angular velocities of the inner and outer frames in the RPM, was identified. A countermeasure for the trajectory repetition was also developed. The linear sawtooth (LS) and parabolic sawtooth (PS) time-varying angular velocity profiles for the outer rotational frame were suggested to prevent concentration of the GVT trajectory, and their effectiveness was numerically verified using an in-house program. Furthermore, appropriate RPM operating conditions for simulating the hypogravity fields were proposed for the Moon and Mars. The mathematical theory presented for the first time in this study can be extended as an important theoretical background in research on the bioreactor, which can be applied to enhanced three-dimensional cell culturing conditions using the RPM.

中文翻译：

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随机定位机模拟的微重力和低重力理论研究

摘要 随机定位机（RPM）不断改变作用在物体上的重力方向，可以为地球上的生物反应器提供模拟的微重力和行星低重力环境。在这项研究中，尝试对 RPM 运动产生的微重力和行星低重力场进行理论分析。通过新定义的重力分散度 (DGD) 参数对对象周围的模拟微重力场进行定量分析，并通过 RPM 模拟与真实行星之间的重力比分析模拟的行星低重力场，对应于归一化的 DGD。追踪重力矢量尖端 (GVT) 在连接到旋转对象的假想球体上的运动，以及 GVT 轨迹重复的原因，确定了 RPM 中内部和外部框架的恒定 (C) 角速度的某些组合。还制定了轨迹重复的对策。建议使用外旋转框架的线性锯齿 (LS) 和抛物线锯齿 (PS) 时变角速度剖面来防止 GVT 轨迹的集中，并使用内部程序对它们的有效性进行了数值验证。此外，还为月球和火星提出了用于模拟低重力场的适当 RPM 操作条件。本研究中首次提出的数学理论可以作为生物反应器研究的重要理论背景进行扩展，可以应用于使用 RPM 的增强型三维细胞培养条件。