Analysis of Passive Walking Gait and Non-Synchronization of Combined Flexible Legged Rimless Wheels
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摘要:
提出了具有可变相位差的柔性腿组合无缘轮模型，通过调节系统初值，对模型被动行走步态进行了分析. 通过观察模型在不同相位差时的运动步态，分析了改变相位差对模型行走步态的影响. 首先，采用第二类Lagrange方法建立了具有可变相位差的柔性腿组合无缘轮动力学模型，通过调整初值，使模型运动步态能够在不同相位差条件下逐渐形成收敛的闭环极限环；其次，通过仿真实验对模型的典型步态进行了对比分析，注意到模型行走步态与初始相位差间存在着密切联系；最后，通过改变相位差，借助数值模拟和仿真实验验证了行走步态与初始相位差间的关系. 结果表明：通过改变初始时刻前、后无缘轮支撑腿间的相位差，可以改变模型在斜坡上的周期运动步态，当相位差接近半髋角时，模型沿斜面运动的平均速率降低，但在垂直斜面方向上的颠簸程度较小，受到斜面法线方向的最大反向支撑力也较小.
Abstract:A combined flexible-legged rimless wheels model with variable phase difference was introduced for the analysis of passive walking gait by adjusting the initial value of the system. The model's motions under various phase differences were simulated, and the effects of phase differences on the walking gait were investigated. Firstly, the 2nd-type Lagrangian method was used to establish a dynamic model for combined flexible legged rimless wheels with variable phase differences, and the initial value was adjusted to gradually form the convergent closed-loop limit cycle for the model motion gait under various phase differences. Secondly, the typical model gaits were simulated and comparatively analyzed to expose the close relationship between the model walking gait and the initial phase difference, which were verified through numerical experiments. The results show that, the variation of the phase differences between the rimless wheel support legs before and after the initial moments change the model periodical motion gait on the inclined plane. With a phase difference close to the half hip angle, the model average moving speed along the inclined plane will decrease, while the bump motion perpendicular to the inclined plane will be relatively small, and the maximum reverse support force in the normal direction of the inclined plane will also be relatively small.
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图 1 具有可变相位差的柔性腿组合无缘轮的简化模型
Figure 1. The simplified model for combined flexible legged rimless wheels with variable phase differences
图 2 前、后轮均为单支撑状态时的简化模型
Figure 2. The simplified model with both front and rear wheels in the single support state
图 3 前轮为单支撑、后轮为双支撑状态时的简化模型
Figure 3. The simplified model with the front wheel of a single support and the rear wheel of double supports
图 4 前、后轮均为单支撑状态时的简化模型
Figure 4. The simplified model with both front and rear wheels in the double support state
图 5 前轮为双支撑、后轮为单支撑状态时的简化模型
Figure 5. The simplified model with the front wheel of double supports and the rear wheel of a single support
图 6 相位差为零状态下的模型运动步态
注 为了解释图中的颜色，读者可以参考本文的电子网页版本，后同.
Figure 6. The motion gait of the model with 0 phase difference
图 7 相位差γ=22.5°状态下的模型运动步态
Figure 7. The motion gait of the model with the γ=22.5° phase differenc
图 10 模型沿斜面法线方向上的反向支撑力曲线
Figure 10. The reverse support curves of the model along the normal of the inclined plane
图 11 不同相位差下连杆质心沿斜面的位移大小及平均步行速率
Figure 11. The con rod barycenter displacement along the inclined plane and the average walking speed under different phase differences
图 12 不同相位差下连杆质心垂直斜面的最大颠簸程度及平均颠簸速率
Figure 12. The con rod barycenter maximum bump displacement and speed perpendicular to the inclined plane under different phase differences
图 13 不同相位差下平均反向支撑力和最大反向支撑力
Figure 13. Average and maximum reverse support forces under different phase differences
表 1 仿真模型的物理参数
Table 1. The physical parameters of the simulation model
parameter m1=m2/kg m3/kg l0=l3/m ϕ/rad I/(kg·m2) k0/(N/m) value 8 10 1.0 0.2 0.25 900 
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