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.

Chlorella vulgaris is a microalgae belonging to the order of the Chlorococcales, of the Oocytaceae family, of the genus Chlorella, which has a green colour due to the chloroplasts it contains. Its shape is spherical with a size that varies from 1 to 10 microns. These microalgae contain, in addition to chlorophyll, a significant amount of intracellular proteins, carbohydrates, lipids, vitamin C, β-carotenes and B vitamins (B1, B2, B6 and B12), which is why it is commonly used for the preparation of food supplements, as well as for the production of cosmetics, clinical treatments and even for the detoxification of heavy metals in wastewater. For this reason, the following review speaks from the morphology of the microalgae C. vulgaris to recent investigations regarding the primary and secondary metabolites. This research also provides an overview of the areas of opportunity for the development of new products and process improvements in order to increase the existing yields so far to optimize responses based on the desired products, the formulation of various growth media or the design of new photobioreactors which allow greater control of growth conditions and easy scaling for high productions at the industrial level that cover the current global needs.

We study the nonlinear damped wave equation with a linear pumping and a convective nonlinearity. We consider the solutions, which satisfy the periodic boundary conditions. Our aim is to prove global existence of solutions to the periodic problem for the nonlinear damped wave equation by applying the energy‐type estimates and estimates for the Green operator. Moreover, we study the asymptotic profile of global solutions.

This article describes the way in which six nontraditional legs collaborate to provide locomotion to a walking machine when it moves along a path. Such legs are based on the one-degree-of-freedom Peaucellier-Lipkin mechanism, which was modified by the addition of four degrees of freedom. Such five-degree-of-freedom legs have the ability to adapt their postures according to the center of rotation around of which the machine walks. The attributes and abilities of the hexapod are expressed by means of a mathematical framework, which grants the spatial description and required joint variables, according to a specific task, resulting in the configuration of its legs for a particular path planning. Additionally, the article presents an illustrative example describing a detailed procedure concerning the configurations and collaboration of their legs according to an imposed center of rotation around of which the six-legged robot walks.

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Abstract. We consider the question of global existence and asymptotics of small, smooth, and localized solutions of a certain pseudoparabolic equation in one dimension, posed on half-linewhereThis model is motivated by the a wave equation for media with a strong spatial dispersion, which appear in the nonlinear theory of the quasy-stationary processes in the electric media. We show that the problem (0.1) admits global solutions whose long-time behavior depend on boundary data. More precisely, we prove global existence and modified by boundary scattering of solutions.

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