Quasi-Coordinates-Based Closed-Form Dynamic Modeling and Analysis for a 2R1T PKM with a Rigid–Flexible Structure
This work derives a closed-form dynamic model for a two rotational and one translational degrees-of-freedom (2R1T) parallel kinematic mechanism (PKM) with a hybrid rigid–flexible structure for force-control applications. Based on the three-prismatic-prismatic-spherical (3PPS) kinematic configuration...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-02-01
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| Series: | Machines |
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| Online Access: | https://www.mdpi.com/2075-1702/11/2/260 |
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| author | Renfeng Zhu Guilin Yang Zaojun Fang Chin-Yin Chen Huamin Li Chi Zhang |
| author_facet | Renfeng Zhu Guilin Yang Zaojun Fang Chin-Yin Chen Huamin Li Chi Zhang |
| author_sort | Renfeng Zhu |
| collection | DOAJ |
| description | This work derives a closed-form dynamic model for a two rotational and one translational degrees-of-freedom (2R1T) parallel kinematic mechanism (PKM) with a hybrid rigid–flexible structure for force-control applications. Based on the three-prismatic-prismatic-spherical (3PPS) kinematic configuration of the 2R1T PKM and its zero-torsion motion characteristics, a symbolic formulation approach is proposed to establish closed-form kinematic models for both forward and inverse kinematics analysis. As the moving platform pose of the 2R1T 3PPS PKM can be readily determined by the three active prismatic joint variables and the three passive prismatic joint variables, these six joint variables are selected as the quasi-coordinates so as to systematically develop the closed-form dynamic model with a Lagrangian formulation, in which the stiffness and deformation of the three flexure-based passive prismatic joints are uniformly taken into consideration. Through eliminating the three passive prismatic joint variables based on the principle of virtual work and the relationships between the active and passive prismatic joint variables, a closed-form dynamic model for the 2R1T 3PPS PKM with a rigid–flexible structure is finally obtained. The correctness of the closed-form dynamic model was validated with the commercial dynamic simulation software. Utilizing the closed-form dynamic model, the effects of different flexure stiffness in driving directions on the required active joint force were investigated, which indicated that little flexure stiffness in driving directions is desired. |
| first_indexed | 2024-03-11T08:32:01Z |
| format | Article |
| id | doaj.art-f230ccc7008e4294a5206ddd9995ef33 |
| institution | Directory Open Access Journal |
| issn | 2075-1702 |
| language | English |
| last_indexed | 2024-03-11T08:32:01Z |
| publishDate | 2023-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Machines |
| spelling | doaj.art-f230ccc7008e4294a5206ddd9995ef332023-11-16T21:46:06ZengMDPI AGMachines2075-17022023-02-0111226010.3390/machines11020260Quasi-Coordinates-Based Closed-Form Dynamic Modeling and Analysis for a 2R1T PKM with a Rigid–Flexible StructureRenfeng Zhu0Guilin Yang1Zaojun Fang2Chin-Yin Chen3Huamin Li4Chi Zhang5Ningbo Institute of Materials Technology and Engineering, Chinese Academy of Sciences, Ningbo 315201, ChinaNingbo Institute of Materials Technology and Engineering, Chinese Academy of Sciences, Ningbo 315201, ChinaNingbo Institute of Materials Technology and Engineering, Chinese Academy of Sciences, Ningbo 315201, ChinaNingbo Institute of Materials Technology and Engineering, Chinese Academy of Sciences, Ningbo 315201, ChinaNingbo Institute of Materials Technology and Engineering, Chinese Academy of Sciences, Ningbo 315201, ChinaNingbo Institute of Materials Technology and Engineering, Chinese Academy of Sciences, Ningbo 315201, ChinaThis work derives a closed-form dynamic model for a two rotational and one translational degrees-of-freedom (2R1T) parallel kinematic mechanism (PKM) with a hybrid rigid–flexible structure for force-control applications. Based on the three-prismatic-prismatic-spherical (3PPS) kinematic configuration of the 2R1T PKM and its zero-torsion motion characteristics, a symbolic formulation approach is proposed to establish closed-form kinematic models for both forward and inverse kinematics analysis. As the moving platform pose of the 2R1T 3PPS PKM can be readily determined by the three active prismatic joint variables and the three passive prismatic joint variables, these six joint variables are selected as the quasi-coordinates so as to systematically develop the closed-form dynamic model with a Lagrangian formulation, in which the stiffness and deformation of the three flexure-based passive prismatic joints are uniformly taken into consideration. Through eliminating the three passive prismatic joint variables based on the principle of virtual work and the relationships between the active and passive prismatic joint variables, a closed-form dynamic model for the 2R1T 3PPS PKM with a rigid–flexible structure is finally obtained. The correctness of the closed-form dynamic model was validated with the commercial dynamic simulation software. Utilizing the closed-form dynamic model, the effects of different flexure stiffness in driving directions on the required active joint force were investigated, which indicated that little flexure stiffness in driving directions is desired.https://www.mdpi.com/2075-1702/11/2/2602R1T parallel kinematic mechanismrigid–flexible structureclosed-form dynamic modelquasi-coordinatesLagrangian formulationprinciple of virtual work |
| spellingShingle | Renfeng Zhu Guilin Yang Zaojun Fang Chin-Yin Chen Huamin Li Chi Zhang Quasi-Coordinates-Based Closed-Form Dynamic Modeling and Analysis for a 2R1T PKM with a Rigid–Flexible Structure Machines 2R1T parallel kinematic mechanism rigid–flexible structure closed-form dynamic model quasi-coordinates Lagrangian formulation principle of virtual work |
| title | Quasi-Coordinates-Based Closed-Form Dynamic Modeling and Analysis for a 2R1T PKM with a Rigid–Flexible Structure |
| title_full | Quasi-Coordinates-Based Closed-Form Dynamic Modeling and Analysis for a 2R1T PKM with a Rigid–Flexible Structure |
| title_fullStr | Quasi-Coordinates-Based Closed-Form Dynamic Modeling and Analysis for a 2R1T PKM with a Rigid–Flexible Structure |
| title_full_unstemmed | Quasi-Coordinates-Based Closed-Form Dynamic Modeling and Analysis for a 2R1T PKM with a Rigid–Flexible Structure |
| title_short | Quasi-Coordinates-Based Closed-Form Dynamic Modeling and Analysis for a 2R1T PKM with a Rigid–Flexible Structure |
| title_sort | quasi coordinates based closed form dynamic modeling and analysis for a 2r1t pkm with a rigid flexible structure |
| topic | 2R1T parallel kinematic mechanism rigid–flexible structure closed-form dynamic model quasi-coordinates Lagrangian formulation principle of virtual work |
| url | https://www.mdpi.com/2075-1702/11/2/260 |
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