Optimal Synthesis of Five-Bar Linkage Based on Singularity-Free Workspaces with Predefined Shapes
The five-bar linkage, used in the form of a planar manipulator, benefits from easy controllability and relatively simple kinematic structures, which mean that it can be used in several applications in robotics, rehabilitation, and haptic devices, etc. This paper proposes an optimal synthesis method...
Saved in:
| Main Authors: | , , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2024-12-01
|
| Series: | Robotics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2218-6581/13/12/173 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850035881155493888 |
|---|---|
| author | Lovasz Erwin-Christian Ciupe Valentin Demjen Tivadar Oarcea Alexandru Tulcan Elida-Gabriela Sandu Melania-Olivia |
| author_facet | Lovasz Erwin-Christian Ciupe Valentin Demjen Tivadar Oarcea Alexandru Tulcan Elida-Gabriela Sandu Melania-Olivia |
| author_sort | Lovasz Erwin-Christian |
| collection | DOAJ |
| description | The five-bar linkage, used in the form of a planar manipulator, benefits from easy controllability and relatively simple kinematic structures, which mean that it can be used in several applications in robotics, rehabilitation, and haptic devices, etc. This paper proposes an optimal synthesis method for a symmetrical five-bar linkage of type 5-RRRRR, with a singularity-free dexterous workspace, based on workspaces with predefined shapes, like squares, rectangles, triangles, circles, and ellipses. The synthesis conditions, to avoid singularities, are given as inequations, which can be further substituted with a system of equations, by introducing the supraunitary coefficient, k. The analytical solutions of the resulting system of equations enable the computation of the link lengths of the five-bar linkage. The optimization method provides the optimal value of the supraunitary coefficient, in order to obtain a maximum value for the minimum input transmission angle and a minimum value for the manipulator size. In this paper, the authors present an analytical approach to the optimal synthesis of a symmetrical five-bar linkage for different shapes of workspace, with the same surface and coordinates in terms of the mass center, as well as the resulting link lengths. In regard to the numerical examples, the authors considered and compared performance indices, such as manipulability, the condition number, and stiffness. The considered examples showed that an equilateral triangle-shaped workspace achieved higher global manipulability, a square-shaped workspace achieved higher global dexterity and the minimum input transmission angle, and circular workspaces achieved the highest mean stiffness and total surface size. It was observed that the synthesis method generates structures that are well-suited to singularity-free dexterous workspaces, with nonzero stiffness values. |
| format | Article |
| id | doaj-art-187d1d0f96dc4f839085b3583383bf77 |
| institution | DOAJ |
| issn | 2218-6581 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Robotics |
| spelling | doaj-art-187d1d0f96dc4f839085b3583383bf772025-08-20T02:57:21ZengMDPI AGRobotics2218-65812024-12-01131217310.3390/robotics13120173Optimal Synthesis of Five-Bar Linkage Based on Singularity-Free Workspaces with Predefined ShapesLovasz Erwin-Christian0Ciupe Valentin1Demjen Tivadar2Oarcea Alexandru3Tulcan Elida-Gabriela4Sandu Melania-Olivia5Department of Mechatronics, University Politehnica Timişoara, 300006 Timisoara, RomaniaDepartment of Mechatronics, University Politehnica Timişoara, 300006 Timisoara, RomaniaDepartment of Mechatronics, University Politehnica Timişoara, 300006 Timisoara, RomaniaDepartment of Mechatronics, University Politehnica Timişoara, 300006 Timisoara, RomaniaDepartment of Mechatronics, University Politehnica Timişoara, 300006 Timisoara, RomaniaDepartment of Mechatronics, University Politehnica Timişoara, 300006 Timisoara, RomaniaThe five-bar linkage, used in the form of a planar manipulator, benefits from easy controllability and relatively simple kinematic structures, which mean that it can be used in several applications in robotics, rehabilitation, and haptic devices, etc. This paper proposes an optimal synthesis method for a symmetrical five-bar linkage of type 5-RRRRR, with a singularity-free dexterous workspace, based on workspaces with predefined shapes, like squares, rectangles, triangles, circles, and ellipses. The synthesis conditions, to avoid singularities, are given as inequations, which can be further substituted with a system of equations, by introducing the supraunitary coefficient, k. The analytical solutions of the resulting system of equations enable the computation of the link lengths of the five-bar linkage. The optimization method provides the optimal value of the supraunitary coefficient, in order to obtain a maximum value for the minimum input transmission angle and a minimum value for the manipulator size. In this paper, the authors present an analytical approach to the optimal synthesis of a symmetrical five-bar linkage for different shapes of workspace, with the same surface and coordinates in terms of the mass center, as well as the resulting link lengths. In regard to the numerical examples, the authors considered and compared performance indices, such as manipulability, the condition number, and stiffness. The considered examples showed that an equilateral triangle-shaped workspace achieved higher global manipulability, a square-shaped workspace achieved higher global dexterity and the minimum input transmission angle, and circular workspaces achieved the highest mean stiffness and total surface size. It was observed that the synthesis method generates structures that are well-suited to singularity-free dexterous workspaces, with nonzero stiffness values.https://www.mdpi.com/2218-6581/13/12/173five-bar linkageplanar manipulatoroptimal synthesissingularity-free workspaceperformance indices |
| spellingShingle | Lovasz Erwin-Christian Ciupe Valentin Demjen Tivadar Oarcea Alexandru Tulcan Elida-Gabriela Sandu Melania-Olivia Optimal Synthesis of Five-Bar Linkage Based on Singularity-Free Workspaces with Predefined Shapes Robotics five-bar linkage planar manipulator optimal synthesis singularity-free workspace performance indices |
| title | Optimal Synthesis of Five-Bar Linkage Based on Singularity-Free Workspaces with Predefined Shapes |
| title_full | Optimal Synthesis of Five-Bar Linkage Based on Singularity-Free Workspaces with Predefined Shapes |
| title_fullStr | Optimal Synthesis of Five-Bar Linkage Based on Singularity-Free Workspaces with Predefined Shapes |
| title_full_unstemmed | Optimal Synthesis of Five-Bar Linkage Based on Singularity-Free Workspaces with Predefined Shapes |
| title_short | Optimal Synthesis of Five-Bar Linkage Based on Singularity-Free Workspaces with Predefined Shapes |
| title_sort | optimal synthesis of five bar linkage based on singularity free workspaces with predefined shapes |
| topic | five-bar linkage planar manipulator optimal synthesis singularity-free workspace performance indices |
| url | https://www.mdpi.com/2218-6581/13/12/173 |
| work_keys_str_mv | AT lovaszerwinchristian optimalsynthesisoffivebarlinkagebasedonsingularityfreeworkspaceswithpredefinedshapes AT ciupevalentin optimalsynthesisoffivebarlinkagebasedonsingularityfreeworkspaceswithpredefinedshapes AT demjentivadar optimalsynthesisoffivebarlinkagebasedonsingularityfreeworkspaceswithpredefinedshapes AT oarceaalexandru optimalsynthesisoffivebarlinkagebasedonsingularityfreeworkspaceswithpredefinedshapes AT tulcanelidagabriela optimalsynthesisoffivebarlinkagebasedonsingularityfreeworkspaceswithpredefinedshapes AT sandumelaniaolivia optimalsynthesisoffivebarlinkagebasedonsingularityfreeworkspaceswithpredefinedshapes |