The Index of Curvature and the Theoretical Framework for Bipedal Modules

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.