Dynamics of a novel robotic leg based on the Peaucellier–Lipkin mechanism on linear paths during the transfer phase

Abstract

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.