The right way to ride the wrong bike: An exploration of Klein's 'unridable' bicycle.
Professor Richard Klein and his students built a bicycle with a rather interesting feature: no one was able to ride it. A prize was offered. Hundreds of students and cycling enthusiasts attempted it. Years passed, and the prize money grew. Klein's rear-steered bicycle became a canonical example...
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| Language: | English |
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Public Library of Science (PLoS)
2025-01-01
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| Series: | PLoS ONE |
| Online Access: | https://doi.org/10.1371/journal.pone.0315769 |
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| author | B D Coller |
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| description | Professor Richard Klein and his students built a bicycle with a rather interesting feature: no one was able to ride it. A prize was offered. Hundreds of students and cycling enthusiasts attempted it. Years passed, and the prize money grew. Klein's rear-steered bicycle became a canonical example of how non-minimum phase systems can be difficult and sometimes nearly impossible to control. It has been lauded as a particularly effective educational example in which students can experience the loss of controllability in a seemingly simple, albeit unorthodox bicycle. The primary result of the work reported here is a demonstration that it is possible for a human of modest athletic ability to ride Klein's unridable bicycle, to keep it balanced, and to control its direction of travel. There is a secret to riding Klein's rear-steer bicycle. The secret is revealed through an exploration of the dynamics and control of the bike that contains three elements: (1) modeling the physics of the actively steered bicycle as an inverted pendulum riding atop a carriage; (2) recognizing that the steer kinematics leads to competing physical mechanisms which an aspiring rider might exploit; and (3) examining limitations of controllability and stabilizability of the system from a state space perspective. From this vantage point, one can devise a novel strategy, based on a component of lateral acceleration that dominates at low speed, for riding the so-called "unridable" bike and solving Klein's puzzle. The work adds a new chapter on the dynamics and control of the rear-steered bicycle, a problem of academic interest. |
| format | Article |
| id | doaj-art-9f099e9bd8f34e8389b9778c9a96bd42 |
| institution | Kabale University |
| issn | 1932-6203 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Public Library of Science (PLoS) |
| record_format | Article |
| series | PLoS ONE |
| spelling | doaj-art-9f099e9bd8f34e8389b9778c9a96bd422025-01-08T05:31:57ZengPublic Library of Science (PLoS)PLoS ONE1932-62032025-01-01201e031576910.1371/journal.pone.0315769The right way to ride the wrong bike: An exploration of Klein's 'unridable' bicycle.B D CollerProfessor Richard Klein and his students built a bicycle with a rather interesting feature: no one was able to ride it. A prize was offered. Hundreds of students and cycling enthusiasts attempted it. Years passed, and the prize money grew. Klein's rear-steered bicycle became a canonical example of how non-minimum phase systems can be difficult and sometimes nearly impossible to control. It has been lauded as a particularly effective educational example in which students can experience the loss of controllability in a seemingly simple, albeit unorthodox bicycle. The primary result of the work reported here is a demonstration that it is possible for a human of modest athletic ability to ride Klein's unridable bicycle, to keep it balanced, and to control its direction of travel. There is a secret to riding Klein's rear-steer bicycle. The secret is revealed through an exploration of the dynamics and control of the bike that contains three elements: (1) modeling the physics of the actively steered bicycle as an inverted pendulum riding atop a carriage; (2) recognizing that the steer kinematics leads to competing physical mechanisms which an aspiring rider might exploit; and (3) examining limitations of controllability and stabilizability of the system from a state space perspective. From this vantage point, one can devise a novel strategy, based on a component of lateral acceleration that dominates at low speed, for riding the so-called "unridable" bike and solving Klein's puzzle. The work adds a new chapter on the dynamics and control of the rear-steered bicycle, a problem of academic interest.https://doi.org/10.1371/journal.pone.0315769 |
| spellingShingle | B D Coller The right way to ride the wrong bike: An exploration of Klein's 'unridable' bicycle. PLoS ONE |
| title | The right way to ride the wrong bike: An exploration of Klein's 'unridable' bicycle. |
| title_full | The right way to ride the wrong bike: An exploration of Klein's 'unridable' bicycle. |
| title_fullStr | The right way to ride the wrong bike: An exploration of Klein's 'unridable' bicycle. |
| title_full_unstemmed | The right way to ride the wrong bike: An exploration of Klein's 'unridable' bicycle. |
| title_short | The right way to ride the wrong bike: An exploration of Klein's 'unridable' bicycle. |
| title_sort | right way to ride the wrong bike an exploration of klein s unridable bicycle |
| url | https://doi.org/10.1371/journal.pone.0315769 |
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