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The Index of Curvature and the Theoretical Framework for Bipedal Modules.

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Title: The Index of Curvature and the Theoretical Framework for Bipedal Modules.
Authors: Juárez-Campos, Martha Eunice1 (AUTHOR), Juárez-Campos, Ignacio1,2 (AUTHOR) ignacio.jc@morelia.tecnm.mx, Cahue-Díaz, Daniel1 (AUTHOR), González-Hernández, Juan Carlos1 (AUTHOR), Herrera-Sandoval, Nicolás David1 (AUTHOR), Yi, Hao (AUTHOR) haoyi@cqu.edu.cn
Source: Journal of Engineering (2314-4912). 2/23/2026, Vol. 2026, p1-28. 28p.
Subjects: Curvature measurements, Bipedalism, Curvilinear motion, Kinematics
Abstract: The Index of Curvature was invented to describe the kinematic properties of a three‐degree‐of‐freedom mechanism based on the Peaucellier–Lipkin linkage when it traces circular curves. This mechanism serves as the basis of a particular class of sprawling legs. When a machine, equipped with them, walks along a circular path, some legs become configured to develop convex‐type trajectories, while some others are arranged to perform concave curves. It was discovered that the Index of Curvature can mutually relate legs developing concave and convex trajectories so that one mechanism's kinematic qualities can predict the other's qualities. This article presents a solid mathematical framework describing the kinematic qualities of a robotic leg and the interdependence between legs developing concave and convex trajectories in terms of the Index of Curvature, which is the leading contribution. This article offers the use of this mathematical framework in conceiving, modeling, and simulating a theoretical bipedal module to create multipedal walking machines, which, although using sprawling legs, acquire narrower profiles as those presented in mammalian type walking robots. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Engineering (2314-4912) is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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Header DbId: egs
DbLabel: Engineering Source
An: 191835723
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
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  Data: The Index of Curvature and the Theoretical Framework for Bipedal Modules.
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  Data: <searchLink fieldCode="AR" term="%22Juárez-Campos%2C+Martha+Eunice%22">Juárez-Campos, Martha Eunice</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Juárez-Campos%2C+Ignacio%22">Juárez-Campos, Ignacio</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> ignacio.jc@morelia.tecnm.mx</i><br /><searchLink fieldCode="AR" term="%22Cahue-Díaz%2C+Daniel%22">Cahue-Díaz, Daniel</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22González-Hernández%2C+Juan+Carlos%22">González-Hernández, Juan Carlos</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Herrera-Sandoval%2C+Nicolás+David%22">Herrera-Sandoval, Nicolás David</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Yi%2C+Hao%22">Yi, Hao</searchLink> (AUTHOR)<i> haoyi@cqu.edu.cn</i>
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Engineering+%282314-4912%29%22">Journal of Engineering (2314-4912)</searchLink>. 2/23/2026, Vol. 2026, p1-28. 28p.
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  Data: <searchLink fieldCode="DE" term="%22Curvature+measurements%22">Curvature measurements</searchLink><br /><searchLink fieldCode="DE" term="%22Bipedalism%22">Bipedalism</searchLink><br /><searchLink fieldCode="DE" term="%22Curvilinear+motion%22">Curvilinear motion</searchLink><br /><searchLink fieldCode="DE" term="%22Kinematics%22">Kinematics</searchLink>
– Name: Abstract
  Label: Abstract
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  Data: The Index of Curvature was invented to describe the kinematic properties of a three‐degree‐of‐freedom mechanism based on the Peaucellier–Lipkin linkage when it traces circular curves. This mechanism serves as the basis of a particular class of sprawling legs. When a machine, equipped with them, walks along a circular path, some legs become configured to develop convex‐type trajectories, while some others are arranged to perform concave curves. It was discovered that the Index of Curvature can mutually relate legs developing concave and convex trajectories so that one mechanism's kinematic qualities can predict the other's qualities. This article presents a solid mathematical framework describing the kinematic qualities of a robotic leg and the interdependence between legs developing concave and convex trajectories in terms of the Index of Curvature, which is the leading contribution. This article offers the use of this mathematical framework in conceiving, modeling, and simulating a theoretical bipedal module to create multipedal walking machines, which, although using sprawling legs, acquire narrower profiles as those presented in mammalian type walking robots. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Engineering (2314-4912) is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1155/je/9696524
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      – Code: eng
        Text: English
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      Pagination:
        PageCount: 28
        StartPage: 1
    Subjects:
      – SubjectFull: Curvature measurements
        Type: general
      – SubjectFull: Bipedalism
        Type: general
      – SubjectFull: Curvilinear motion
        Type: general
      – SubjectFull: Kinematics
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            NameFull: Juárez-Campos, Martha Eunice
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            NameFull: Juárez-Campos, Ignacio
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            NameFull: Cahue-Díaz, Daniel
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            NameFull: González-Hernández, Juan Carlos
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            NameFull: Herrera-Sandoval, Nicolás David
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            – D: 23
              M: 02
              Text: 2/23/2026
              Type: published
              Y: 2026
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