Purpose

Spinal cord injury (SCI) subjects use passive orthosis to assist them with the postural balance in daily life. Vertical vibrations are used to improve the postural balance of theses patients, mainly in terms of whole-body-vibrations, as in therapies. It is noteworthy to understand in what situation these patients are able to tolerate vertical vibrations while wearing orthosis. The main focus of this paper is to model vertical vibrations in the postural balance of arm free standing of the paraplegic subjects who use passive orthosis, and, mathematically understand the stability limits for these vibrations.

Methods

To find the stable amplitudes and frequencies, equations of motions of the system are translated into non-homogeneous Mathieu equations, which are then analytically solved and the results are numerically plotted. In addition, the effect of shoe stiffness on the amplitude and frequency of the vibrations which violate stability are studied.

Results

The results show to be sure of the stability of the paraplegics in vertical vibrations, the shoe sole of the orthosis should have high values of stiffness, and this will guarauntee bigger ranges of stable vibrations and safer stance for the patients.

Conclusion

Using the results, one can interpret how a paraplegic subject with passive orthosis may react to vertical perturbations, meaning, what ranges of frequencies and amplitudes of perturbations is tolerable without losing stability. This study is one of the necessities in designing new passive orthosis with more stability when exposed to perturbations.

中文翻译：

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截瘫患者使用被动矫形器时垂直振动的稳定性极限

目的

脊髓损伤（SCI）受试者使用被动矫形器来帮助他们在日常生活中保持姿势平衡。垂直振动被用来改善这些患者的姿势平衡，主要是在全身振动方面，如在治疗中。值得注意的是，要了解这些患者在佩戴矫形器的情况下能够承受垂直振动的情况。本文的主要重点是对使用被动矫形器的截瘫患者的手臂自由站立姿势平衡中的垂直振动进行建模，并从数学上理解这些振动的稳定性极限。

方法

为了找到稳定的振幅和频率，将系统的运动方程式转化为非均质的Mathieu方程式，然后对其进行解析求解并以数值方式绘制结果。此外，研究了鞋的刚度对破坏稳定性的振动幅度和频率的影响。

结果

结果表明，可以肯定截瘫患者在垂直振动中的稳定性，矫形器的鞋底应具有较高的刚度值，这将确保更大范围的稳定振动和对患者更安全的姿势。

结论

使用这些结果，可以解释患有被动矫形器的截瘫患者如何对垂直扰动做出反应，这意味着在不损失稳定性的情况下，可以容许的扰动频率和幅度范围是多少。这项研究是设计新的被动矫形器的必要条件之一，当它受到扰动时具有更高的稳定性。