Elasto-Kinematics and Instantaneous Invariants of Compliant Mechanisms Based on Flexure Hinges
The kinematic synthesis of compliant mechanisms based on flexure hinges is not an easy task. A commonly used method is the equivalent rigid model, which involves replacing the flexure hinges with rigid bars connected with lumped hinges using the already known methods of synthesis. This way, albeit s...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-03-01
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| Series: | Micromachines |
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| Online Access: | https://www.mdpi.com/2072-666X/14/4/783 |
| _version_ | 1797604312989302784 |
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| author | Christian Iandiorio Pietro Salvini |
| author_facet | Christian Iandiorio Pietro Salvini |
| author_sort | Christian Iandiorio |
| collection | DOAJ |
| description | The kinematic synthesis of compliant mechanisms based on flexure hinges is not an easy task. A commonly used method is the equivalent rigid model, which involves replacing the flexure hinges with rigid bars connected with lumped hinges using the already known methods of synthesis. This way, albeit simpler, hides some interesting issues. This paper addresses the elasto-kinematics and instantaneous invariants of flexure hinges with a direct approach, making use of a nonlinear model to predict their behaviour. The differential equations that govern the nonlinear geometric response are given in a comprehensive form and are solved for flexure hinges with constant sections. The solution to the nonlinear model is then used to obtain an analytical description of two instantaneous invariants: the centre of instantaneous rotation (c.i.r.) and the inflection circle. The main result is that the c.i.r. evolution, namely the fixed polode, is not conservative but is loading-path dependent. Consequently, all other instantaneous invariants are loading-path dependent, and the property of instantaneous geometric invariants (independent of the motion time law) can no longer be used. This result is analytically and numerically evidenced. In other words, it is shown that a careful kinematic synthesis of compliant mechanisms cannot be addressed by only considering the kinematics as rigid mechanisms, and it is essential to take into consideration the applied loads and their histories. |
| first_indexed | 2024-03-11T04:44:39Z |
| format | Article |
| id | doaj.art-6fa7cadc248647d7b993201cc82a338a |
| institution | Directory Open Access Journal |
| issn | 2072-666X |
| language | English |
| last_indexed | 2024-03-11T04:44:39Z |
| publishDate | 2023-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Micromachines |
| spelling | doaj.art-6fa7cadc248647d7b993201cc82a338a2023-11-17T20:29:17ZengMDPI AGMicromachines2072-666X2023-03-0114478310.3390/mi14040783Elasto-Kinematics and Instantaneous Invariants of Compliant Mechanisms Based on Flexure HingesChristian Iandiorio0Pietro Salvini1Department of Enterprise Engineering, University of Rome “Tor Vergata”, Via del Politecnico 1, 00133 Rome, ItalyDepartment of Enterprise Engineering, University of Rome “Tor Vergata”, Via del Politecnico 1, 00133 Rome, ItalyThe kinematic synthesis of compliant mechanisms based on flexure hinges is not an easy task. A commonly used method is the equivalent rigid model, which involves replacing the flexure hinges with rigid bars connected with lumped hinges using the already known methods of synthesis. This way, albeit simpler, hides some interesting issues. This paper addresses the elasto-kinematics and instantaneous invariants of flexure hinges with a direct approach, making use of a nonlinear model to predict their behaviour. The differential equations that govern the nonlinear geometric response are given in a comprehensive form and are solved for flexure hinges with constant sections. The solution to the nonlinear model is then used to obtain an analytical description of two instantaneous invariants: the centre of instantaneous rotation (c.i.r.) and the inflection circle. The main result is that the c.i.r. evolution, namely the fixed polode, is not conservative but is loading-path dependent. Consequently, all other instantaneous invariants are loading-path dependent, and the property of instantaneous geometric invariants (independent of the motion time law) can no longer be used. This result is analytically and numerically evidenced. In other words, it is shown that a careful kinematic synthesis of compliant mechanisms cannot be addressed by only considering the kinematics as rigid mechanisms, and it is essential to take into consideration the applied loads and their histories.https://www.mdpi.com/2072-666X/14/4/783compliant mechanismsinstantaneous invariantsMEMSlarge displacementsnonlinear analysis |
| spellingShingle | Christian Iandiorio Pietro Salvini Elasto-Kinematics and Instantaneous Invariants of Compliant Mechanisms Based on Flexure Hinges Micromachines compliant mechanisms instantaneous invariants MEMS large displacements nonlinear analysis |
| title | Elasto-Kinematics and Instantaneous Invariants of Compliant Mechanisms Based on Flexure Hinges |
| title_full | Elasto-Kinematics and Instantaneous Invariants of Compliant Mechanisms Based on Flexure Hinges |
| title_fullStr | Elasto-Kinematics and Instantaneous Invariants of Compliant Mechanisms Based on Flexure Hinges |
| title_full_unstemmed | Elasto-Kinematics and Instantaneous Invariants of Compliant Mechanisms Based on Flexure Hinges |
| title_short | Elasto-Kinematics and Instantaneous Invariants of Compliant Mechanisms Based on Flexure Hinges |
| title_sort | elasto kinematics and instantaneous invariants of compliant mechanisms based on flexure hinges |
| topic | compliant mechanisms instantaneous invariants MEMS large displacements nonlinear analysis |
| url | https://www.mdpi.com/2072-666X/14/4/783 |
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