Forward and Inverse Dynamics of a Six-Axis Accelerometer Based on a Parallel Mechanism
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...
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MDPI AG
2021-01-01
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| Series: | Sensors |
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| Online Access: | https://www.mdpi.com/1424-8220/21/1/233 |
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| author | Linkang Wang Jingjing You Xiaolong Yang Huaxin Chen Chenggang Li Hongtao Wu |
| author_facet | Linkang Wang Jingjing You Xiaolong Yang Huaxin Chen Chenggang Li Hongtao Wu |
| author_sort | Linkang Wang |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T13:33:46Z |
| format | Article |
| id | doaj.art-4d095f6f32d24d25947f2628e5e44d32 |
| institution | Directory Open Access Journal |
| issn | 1424-8220 |
| language | English |
| last_indexed | 2024-03-10T13:33:46Z |
| publishDate | 2021-01-01 |
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| series | Sensors |
| spelling | doaj.art-4d095f6f32d24d25947f2628e5e44d322023-11-21T07:41:24ZengMDPI AGSensors1424-82202021-01-0121123310.3390/s21010233Forward and Inverse Dynamics of a Six-Axis Accelerometer Based on a Parallel MechanismLinkang Wang0Jingjing You1Xiaolong Yang2Huaxin Chen3Chenggang Li4Hongtao Wu5College of Mechanical and Electronic Engineering, Nanjing Forestry University, Nanjing 210037, ChinaCollege of Mechanical and Electronic Engineering, Nanjing Forestry University, Nanjing 210037, ChinaSchool of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210037, ChinaCollege of Mechanical and Electronic Engineering, Nanjing Forestry University, Nanjing 210037, ChinaSchool of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, ChinaSchool of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, ChinaThe 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.https://www.mdpi.com/1424-8220/21/1/233six-axis accelerometerparallel mechanismforward dynamicsinverse dynamicsdecoupling |
| spellingShingle | Linkang Wang Jingjing You Xiaolong Yang Huaxin Chen Chenggang Li Hongtao Wu Forward and Inverse Dynamics of a Six-Axis Accelerometer Based on a Parallel Mechanism Sensors six-axis accelerometer parallel mechanism forward dynamics inverse dynamics decoupling |
| title | Forward and Inverse Dynamics of a Six-Axis Accelerometer Based on a Parallel Mechanism |
| title_full | Forward and Inverse Dynamics of a Six-Axis Accelerometer Based on a Parallel Mechanism |
| title_fullStr | Forward and Inverse Dynamics of a Six-Axis Accelerometer Based on a Parallel Mechanism |
| title_full_unstemmed | Forward and Inverse Dynamics of a Six-Axis Accelerometer Based on a Parallel Mechanism |
| title_short | Forward and Inverse Dynamics of a Six-Axis Accelerometer Based on a Parallel Mechanism |
| title_sort | forward and inverse dynamics of a six axis accelerometer based on a parallel mechanism |
| topic | six-axis accelerometer parallel mechanism forward dynamics inverse dynamics decoupling |
| url | https://www.mdpi.com/1424-8220/21/1/233 |
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