Rolling Curves: An Old Proof of the Roulette Lemma

Abel, Ulrich; Beukemann, Linda; Kushnirevych, Vitaliy

doi:10.4169/amer.math.monthly.124.8.723

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Cited by 5 publications

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“…The spirograph seems to be a toy but in fact it is a mathematical instrument that generates curve known as spirographs and are subset of the Roulette family of curve [5,6]. These curves are very important in engineering and scientific research as such curves have been found as the locus trace of many physical events.…”

Section: Introductionmentioning

confidence: 99%

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2024

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Section: Introductionmentioning

confidence: 99%

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2024

INDJCSE

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Music recommendation algorithm based on user portrait

2021

2021 IEEE International Conference on Computer Science, Electronic Information Engineering and Intelligent Control Technology (

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Coronal Plane Spine Twisting Composes Shape To Adjust the Energy Landscape for Grounded Reorientation

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et al. 2020

2020 IEEE International Conference on Robotics and Automation (ICRA)

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Despite substantial evidence for the crucial role played by an active backbone or spine in animal locomotion, its adoption in legged robots remains limited because the added mechanical complexity and resulting dynamical challenges pose daunting obstacles to characterizing even a partial range of potential performance benefits. This paper takes a next step toward such a characterization by exploring the quasistatic terrestrial self-righting mechanics of a model system with coronal plane spine twisting (CPST). Reduction from a full 3D kinematic model of CPST to a two parameter, two degree of freedom coronal plane representation of body shape affordance predicts a substantial benefit to ground righting by lowering the barrier between stable potential energy basins. The reduced model predicts the most advantageous twist angle for several cross-sectional geometries, reducing the required righting torque by up to an order of magnitude depending on constituent shapes. Experiments with a three actuated degree of freedom physical mechanism corroborate the kinematic model predictions using two different quasistatic reorientation maneuvers for both elliptical and rectangular shaped bodies with a range of eccentricities or aspect ratios. More speculative experiments make intuitive use of the kinematic model in a highly dynamic maneuver to suggest still greater benefits of CPST achievable by coordinating kinetic as well as potential energy, for example as in a future multi-appendage system interacting with a contact-rich 3D environment.

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Rolling Curves: An Old Proof of the Roulette Lemma

Cited by 5 publications

References 3 publications

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Music recommendation algorithm based on user portrait

Coronal Plane Spine Twisting Composes Shape To Adjust the Energy Landscape for Grounded Reorientation

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