A Screw Theory Approach to Computing the Instantaneous Rotation Centers of Indeterminate Planar Linkages
This paper presents a screw theory approach for the computation of the instantaneous rotation centers of indeterminate planar linkages. Since the end of the 19th century, the determination of the instantaneous rotation, or velocity centers of planar mechanisms has been an important topic in kinemati...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2021-12-01
|
| Series: | Robotics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2218-6581/11/1/6 |
| _version_ | 1797476775084687360 |
|---|---|
| author | Juan Ignacio Valderrama-Rodríguez José M. Rico J. Jesús Cervantes-Sánchez Ricardo García-García |
| author_facet | Juan Ignacio Valderrama-Rodríguez José M. Rico J. Jesús Cervantes-Sánchez Ricardo García-García |
| author_sort | Juan Ignacio Valderrama-Rodríguez |
| collection | DOAJ |
| description | This paper presents a screw theory approach for the computation of the instantaneous rotation centers of indeterminate planar linkages. Since the end of the 19th century, the determination of the instantaneous rotation, or velocity centers of planar mechanisms has been an important topic in kinematics that has led to the well-known Aronhold–Kennedy theorem. At the beginning of the 20th century, it was found that there were planar mechanisms for which the application of the Aronhold–Kennedy theorem was unable to find all the instantaneous rotation centers (IRCs). These mechanisms were denominated complex or indeterminate. The beginning of this century saw a renewed interest in complex or indeterminate planar mechanisms. In this contribution, a new and simpler screw theory approach for the determination of indeterminate rotation centers of planar linkages is presented. The new approach provides a simpler method for setting up the equations. Furthermore, the algebraic equations to be solved are simpler than the ones published to date. The method is based on the systematic application of screw theory, isomorphic to the Lie algebra, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>s</mi><mi>e</mi><mo>(</mo><mn>3</mn><mo>)</mo></mrow></semantics></math></inline-formula>, of the Euclidean group, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mi>E</mi><mo>(</mo><mn>3</mn><mo>)</mo></mrow></semantics></math></inline-formula>, and the invariant symmetric bilinear forms defined on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>s</mi><mi>e</mi><mo>(</mo><mn>3</mn><mo>)</mo></mrow></semantics></math></inline-formula>. |
| first_indexed | 2024-03-09T21:07:25Z |
| format | Article |
| id | doaj.art-bcadd076a8b74f4d990bf2341ae23dce |
| institution | Directory Open Access Journal |
| issn | 2218-6581 |
| language | English |
| last_indexed | 2024-03-09T21:07:25Z |
| publishDate | 2021-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Robotics |
| spelling | doaj.art-bcadd076a8b74f4d990bf2341ae23dce2023-11-23T21:57:00ZengMDPI AGRobotics2218-65812021-12-01111610.3390/robotics11010006A Screw Theory Approach to Computing the Instantaneous Rotation Centers of Indeterminate Planar LinkagesJuan Ignacio Valderrama-Rodríguez0José M. Rico1J. Jesús Cervantes-Sánchez2Ricardo García-García3Independent Researcher, Ciudad de Duitama 150461, ColombiaMechanical Engineering Department, División de Ingenierías, Campus Irapuato-Salamanca, Universidad de Guanajuato, Guanajuato 36885, MexicoMechanical Engineering Department, División de Ingenierías, Campus Irapuato-Salamanca, Universidad de Guanajuato, Guanajuato 36885, MexicoMechanical Engineering Department, División de Ingenierías, Campus Irapuato-Salamanca, Universidad de Guanajuato, Guanajuato 36885, MexicoThis paper presents a screw theory approach for the computation of the instantaneous rotation centers of indeterminate planar linkages. Since the end of the 19th century, the determination of the instantaneous rotation, or velocity centers of planar mechanisms has been an important topic in kinematics that has led to the well-known Aronhold–Kennedy theorem. At the beginning of the 20th century, it was found that there were planar mechanisms for which the application of the Aronhold–Kennedy theorem was unable to find all the instantaneous rotation centers (IRCs). These mechanisms were denominated complex or indeterminate. The beginning of this century saw a renewed interest in complex or indeterminate planar mechanisms. In this contribution, a new and simpler screw theory approach for the determination of indeterminate rotation centers of planar linkages is presented. The new approach provides a simpler method for setting up the equations. Furthermore, the algebraic equations to be solved are simpler than the ones published to date. The method is based on the systematic application of screw theory, isomorphic to the Lie algebra, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>s</mi><mi>e</mi><mo>(</mo><mn>3</mn><mo>)</mo></mrow></semantics></math></inline-formula>, of the Euclidean group, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mi>E</mi><mo>(</mo><mn>3</mn><mo>)</mo></mrow></semantics></math></inline-formula>, and the invariant symmetric bilinear forms defined on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>s</mi><mi>e</mi><mo>(</mo><mn>3</mn><mo>)</mo></mrow></semantics></math></inline-formula>.https://www.mdpi.com/2218-6581/11/1/6planar linkagesindeterminate linkagesscrew theory |
| spellingShingle | Juan Ignacio Valderrama-Rodríguez José M. Rico J. Jesús Cervantes-Sánchez Ricardo García-García A Screw Theory Approach to Computing the Instantaneous Rotation Centers of Indeterminate Planar Linkages Robotics planar linkages indeterminate linkages screw theory |
| title | A Screw Theory Approach to Computing the Instantaneous Rotation Centers of Indeterminate Planar Linkages |
| title_full | A Screw Theory Approach to Computing the Instantaneous Rotation Centers of Indeterminate Planar Linkages |
| title_fullStr | A Screw Theory Approach to Computing the Instantaneous Rotation Centers of Indeterminate Planar Linkages |
| title_full_unstemmed | A Screw Theory Approach to Computing the Instantaneous Rotation Centers of Indeterminate Planar Linkages |
| title_short | A Screw Theory Approach to Computing the Instantaneous Rotation Centers of Indeterminate Planar Linkages |
| title_sort | screw theory approach to computing the instantaneous rotation centers of indeterminate planar linkages |
| topic | planar linkages indeterminate linkages screw theory |
| url | https://www.mdpi.com/2218-6581/11/1/6 |
| work_keys_str_mv | AT juanignaciovalderramarodriguez ascrewtheoryapproachtocomputingtheinstantaneousrotationcentersofindeterminateplanarlinkages AT josemrico ascrewtheoryapproachtocomputingtheinstantaneousrotationcentersofindeterminateplanarlinkages AT jjesuscervantessanchez ascrewtheoryapproachtocomputingtheinstantaneousrotationcentersofindeterminateplanarlinkages AT ricardogarciagarcia ascrewtheoryapproachtocomputingtheinstantaneousrotationcentersofindeterminateplanarlinkages AT juanignaciovalderramarodriguez screwtheoryapproachtocomputingtheinstantaneousrotationcentersofindeterminateplanarlinkages AT josemrico screwtheoryapproachtocomputingtheinstantaneousrotationcentersofindeterminateplanarlinkages AT jjesuscervantessanchez screwtheoryapproachtocomputingtheinstantaneousrotationcentersofindeterminateplanarlinkages AT ricardogarciagarcia screwtheoryapproachtocomputingtheinstantaneousrotationcentersofindeterminateplanarlinkages |