中文摘要：

为了实现移动平台具有轮式行进和跨步行走的双重功能，柔性轴的姿态算法根据移动平台的运动特点，建立了控制机构和轴姿态之间的关系。文中概述了柔性轴工作原理。建立了坐标变换矩阵，并计算出直线电机伸长量与柔性轴姿态之间的关系。与此同时，还对两者关系的一一对应性进行了证明，为下一步进行控制系统设计做出了数学铺垫。

英文摘要：

In order to realize the dual functions of wheeled mobile and walking step of the mobile platform, the relationship between axis attitude and the control system was proposed according to that the flexible-axis attitude algorithm is based on the movement characteristics of mobile platforms. The operational principle of the flexible shaft was summarized, the coordinate transformation matrix was established, and the relationship between the linear motor shaft elongation and the posture of flexible shaft was calculated, at the same time, the correlative relationship between them was proved. All the above established a mathematic foundation for further control system design.