This article shows the characteristics of a sprawling robotic leg inspired by the limb postures of certain reptilian animals known as sprawling-legged creatures. The main part of the robotic limb is based on the eight-bar Peaucellier–Lipkin linkage, and its main attribute is the ability to trace a true straight line, due to the rotational motion of the input link. However, when the eight-bar linkage is modified, it is capable of tracing true circular concave or convex arcs, when two of its constitutive links have distinct and precise lengths. This gives rise to the concepts of concavity and convexity, related to a robotic leg based on the Peaucellier–Lipkin mechanism, such as the one described herein. Our bioinspired robotic leg can trace concave or convex curves, as well as straight lines, making it a reptile-like robotic limb that is very similar to the natural one. We also introduce the concept of rotation center tuning, which refers to the ability of the leg to adapt its posture to the center of rotation of the entire walking machine, resulting in an easy and suitable gait process. The theoretical information is illustrated through the simulation of an example that provides a path-planning procedure, focusing on the rotation center tuning process and a walking gait. The example also includes the design of an elliptical path projected onto the cylindrical workspace and followed by the reptilian foot.

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This article deals with the kinematics and dynamics of a novel leg based on the Peaucellier-Lipkin mechanism, which is better known as the straight path tracer. The basic Peaucellier-Lipkin linkage with 1 degree of freedom was transformed into a more skillful mechanism, through the addition of 4 more degrees of freedom. The resulting 5-degree-of-freedom leg enables the walking machine to move along paths that are straight lines and/or concave or convex curves. Three degrees of freedom transform the leg in relation to a reachable center of rotation that the machine walks around. Once the leg is transformed, the remaining 2 degrees of freedom position the foot at a desirable Cartesian point during the transfer or support phase. We analyzed the direct and inverse kinematics developed for the leg when the foot describes a straight line and found some interesting relationships among the motion parameters. The dynamic model equations of motion for the leg were derived from the Lagrangian dynamic formulation to calculate the required torques during a particular transfer phase.

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