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...

Full description

Saved in:
Bibliographic Details
Main Authors: Lovasz Erwin-Christian, Ciupe Valentin, Demjen Tivadar, Oarcea Alexandru, Tulcan Elida-Gabriela, Sandu Melania-Olivia
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