College of Mechanical and Electronic Engineering, Nanjing Forestry University, Nanjing 210037, China.
School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210037, China.
Sensors (Basel). 2021 Jan 1;21(1):233. doi: 10.3390/s21010233.
The solution of the dynamic equations of the six-axis accelerometer is a prerequisite for sensor calibration, structural optimization, and practical application. However, the forward dynamic equations (FDEs) and inverse dynamic equations (IDEs) of this type of system have not been completely solved due to the strongly nonlinear coupling relationship between the inputs and outputs. This article presents a comprehensive study of the FDEs and IDEs of the six-axis accelerometer based on a parallel mechanism. Firstly, two sets of dynamic equations of the sensor are constructed based on the Newton-Euler method in the configuration space. Secondly, based on the analytical solution of the sensor branch chain length, the coordination equation between the output signals of the branch chain is constructed. The FDEs of the sensor are established by combining the coordination equations and two sets of dynamic equations. Furthermore, by introducing generalized momentum and Hamiltonian function and using Legendre transformation, the vibration differential equations (VDEs) of the sensor are derived. The VDEs and Newton-Euler equations constitute the IDEs of the system. Finally, the explicit recursive algorithm for solving the quaternion in the equation is given in the phase space. Then the IDEs are solved by substituting the quaternion into the dynamic equations in the configuration space. The predicted numerical results of the established FDEs and IDEs are verified by comparing with virtual and actual experimental data. The actual experiment shows that the relative errors of the FDEs and the IDEs constructed in this article are 2.21% and 7.65%, respectively. This research provides a new strategy for further improving the practicability of the six-axis accelerometer.
六轴加速度计动力学方程的求解是传感器标定、结构优化和实际应用的前提。然而，由于输入和输出之间存在强烈的非线性耦合关系，该系统的正向动力学方程（FDE）和逆向动力学方程（IDE）尚未完全解决。本文基于并联机构对六轴加速度计的 FDE 和 IDE 进行了全面研究。首先，基于牛顿-欧拉方法在配置空间中构建了传感器的两组动力学方程。其次，基于传感器分支链长度的解析解，构建了分支链输出信号之间的协调方程。通过结合协调方程和两组动力学方程，建立了传感器的 FDE。此外，通过引入广义动量和哈密顿函数并使用勒让德变换，推导出了传感器的振动微分方程（VDE）。VDE 和牛顿-欧拉方程构成了系统的 IDE。最后，在相空间中给出了方程中四元数的显式递归算法。然后通过将四元数代入配置空间中的动力学方程来求解 IDE。通过与虚拟和实际实验数据进行比较，验证了所建立的 FDE 和 IDE 的预测数值结果。实际实验表明，本文所构建的 FDE 和 IDE 的相对误差分别为 2.21%和 7.65%。该研究为进一步提高六轴加速度计的实用性提供了新的策略。
