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.

Hexapod with legs based on Peaucellier–Lipkin mechanisms

“…Considering that the strategy of a legged robot in the walking process depends mostly on the characteristics and attributes of their legs and is affected by the number of them, 15 the third part offers a comprehensive study on the attributes of the robotic PL-based leg. Although it has been previously presented by Nuñ ez-Altamirano et al 2,3 and by Juárez-Campos et al, 4 in this part, we show the concepts of concavity and convexity, which are related to the variation of the lengths of two constitutive adjustable links. Concavity and convexity are the strongest supports on which the PL linkage gets the attention to be used as a robotic leg.…”

“…The first one, presented by Nuñez-Altamirano et al, 2 explains the skills by means of which the PL-based leg reconfigures itself according to the spatial descriptions of three points found on the route where the robotic machine walks. The second one, written by Núñez-Altamirano et al, 3 formulates the dynamics of a single PL-based leg when it executes the swing phase along a straight path. The third one, reported by Juárez-Campos et al, 4 explains the origins of conception of the PL-based leg.…”

“…According to equations (1) and (2), d AB and d BC can be expressed as function of r c and k AC , see equations (3) and (4)…”

“…The contribution of this research concerns the bioinspired design of long legs relative to its body, created in the likeness of the arthropod known as harvestman. 20 The five-DoF robotic leg presented in this article and in other works [2][3][4]7 was conceived from the one-DoF PL mechanism, which is commonly referred to as Straight Line Mechanism because it uses a rotation of the input link to create a straight line motion of the output point. 21 It was invented by Peaucellier (1864), an officer of the French army, and by Lipkin (1871), a Russian mathematician.…”

“…Once reachable footholds have been chosen, inverse kinematics and joint motors position feet on the footholds. 1 Although specialized literature shows a rich knowledge, dealing with walking machines using a huge diversity of legs, this investigation has found a lack of information concerning apparatuses equipped with legs based on the Peaucellier-Lipkin (PL) mechanism, except those mechanical systems described by Nú ñ ez-Altamirano et al 2,3 Juárez-Campos et al 4 and Godoy et al, 5 which deal with the same robotic leg presented in this article and the leg of a biped nonanthropomorphic exoskeleton.…”