Abstract Pneumatic Artificial Muscles (PAMs) mimic the behavior of skeletal muscles by generating contractile force when they are pressurized. Stiffness of these actuators depends on the applied pressure because the inner elastomeric tube exhibits non-linear mechanical behavior which also makes control of the actuator difficult. Therefore, it is crucial to obtain a precise mechanical model for these actuators. In this work, based on the theory of limiting chain extensibility, a new continuum mechanics-based model is developed for elastomeric McKibben PAMs to predict stiffness and output parameters such as free contraction, blocked force, and dead-band pressure during the actuation course. The developed model is consistent with network alternation theories, which allow predicting the softening observed in first cycles of inflation-deflation (Mullins effect). The established relations can predict variations of the actuation force due to the alternation of the material network parameters as a result of Mullins softening. In order to determine the material parameters of the bladder, uniaxial tensile tests have been conducted on a virgin silicon rubber. Cyclic tests have also been conducted on the fabricated PAMs in virgin and completely softened states to obtain their characteristic curves. It is concluded that, fractional evolution laws can be well combined with the developed model to predict the behavior of PAMs during cyclic deformations. It is observed that, even for contractions less than 25%, the maximum principal stretch in a PAM can exceed three which implies that, simple strain energy functions such as NeoHookean and Mooney-Rivlin should not be employed for PAMs. It is also concluded that, the Mullins softening increases the free contraction while makes no remarkable effect on the blocked force.

中文翻译：

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基于有限链可扩展性和网络改变理论的 3D 应用的 McKibben 气动人工肌肉力学模型

摘要 气动人工肌肉 (PAM) 通过在加压时产生收缩力来模拟骨骼肌的行为。这些致动器的刚度取决于施加的压力，因为内部弹性管表现出非线性机械行为，这也使得致动器的控制变得困难。因此，获得这些执行器的精确机械模型至关重要。在这项工作中，基于限制链延展性理论，为弹性 McKibben PAM 开发了一种新的基于连续介质力学的模型，以预测驱动过程中的刚度和输出参数，例如自由收缩、阻塞力和死区压力。开发的模型与网络交替理论一致，这允许预测在第一个通货膨胀-通货紧缩周期中观察到的软化（穆林斯效应）。建立的关系可以预测由于 Mullins 软化导致材料网络参数的变化而引起的致动力的变化。为了确定球胆的材料参数，对原始硅橡胶进行了单轴拉伸试验。还对原始和完全软化状态下制造的 PAM 进行了循环测试，以获得它们的特性曲线。结论是，分数演化规律可以与开发的模型很好地结合，以预测循环变形过程中 PAM 的行为。据观察，即使收缩小于 25%，PAM 中的最大主要拉伸也可以超过 3，这意味着，PAM 不应使用简单的应变能函数，例如 NeoHookean 和 Mooney-Rivlin。还得出结论，Mullins 软化增加了自由收缩，而对受阻力没有显着影响。