A New Foot Trajectory Planning Method for Legged Robots and Its Application in Hexapod Robots

Compared with wheeled and tracked robots, legged robots have better movement ability and are more suitable for the exploration of unknown environments. In order to further improve the adaptability of legged robots to complex terrains such as slopes, obstacle environments, and so on, this paper makes a new design of the legged robot’s foot sensing structure that can successfully provide accurate feedback of the landing information. Based on this information, a new foot trajectory planning method named three-element trajectory determination method is proposed. For each leg in one movement period, the three elements are the start point in the support phase, the end point in the support phase, and the joint angle changes in the transfer phase where the first two elements are used to control the height, distance, and direction of the movement, and the third element is used make decisions during the lifting process of the leg. For the support phase, the trajectory is described in Cartesian space, and a spline of linear function with parabolic blends is used. For the transfer phase, the trajectory is described in joint-space, and the joint angle function is designed as the superposition of the joint angle reverse-chronological function and the interpolation function which is obtained based on joint angle changes. As an important legged robot, a hexapod robot that we designed by ourselves with triangle gait is chosen to test the proposed foot trajectory planning method. Experiments show that, while the foot’s landing information can be read and based on the three-element trajectory planning method, the hexapod robot can achieve stable movement even in very complex scenes. Although the experiments are performed on a hexapod robot, our method is applicable to all forms of legged robots.

Descriptions of Attack Angle and Ideal Lift Coefficient for Various Airfoil Profiles in Wind Turbine Blade

The angle of attack is highly sensitive to pitch point in the airfoil shape and the decline of pitch point value induces smaller angle of attack, which implies that airfoil profile possessing closer pitch point to the airfoil tip reacts more sensitively to upcoming wind. The method of conformal transformation functions is employed for airfoil profiles and airfoil surfaces are expressed with a trigonometric series form. Attack angle and ideal lift coefficient distributions are investigated for various airfoil profiles in wind turbine blade regarding conformal transformation and pitch point. The conformed angle function representing the surface angle of airfoil shape generate various attack angle distributions depending on the choice of surface angle function. Moreover, ideal attack angle and ideal lift coefficient are susceptible to the choice of airfoil profiles and uniform loading area. High ideal attack angle signifies high pliability to upcoming wind, and high ideal lift coefficient involves high possibility to generate larger electric energy. According to results obtained pitch point, airfoil shape, uniform loading area, and the conformed airfoil surface angle function are crucial factors in the determination of angle of attack.

CALCULATION OF THE STABILITY OF A PLANE BENDING OF BEAMS WITH A VARIABLE CROSS-SECTIONAL WIDTH

The article proposes a technique for calculating the side buckling of beams of variable rectangular section based on the energy method. This method is considered on the example of a two-section cantilever beam of variable width under the action of a concentrated force. The twist angle function was set in the form of a trigonometric series. As a result, the problem is reduced to a generalized eigenvalue problem.

MATLAB® Functions for Numerical Analysis and Their Applications in M&T

The chapter presents the MATLAB® commands that realize numerical methods for solving problems arising in science and engineering in general and in the field of mechanics and tribology (M&T) in particular. The most commonly used commands along with some information on numerical methods are explained. The topics of the chapter include interpolation and extrapolation, solving nonlinear equations with one or more unknowns, finding minimum and maximum, integration, and differentiation. All described actions are explained by examples from the field of M&T. At the end of the chapter, applications are presented; they illustrate how to interpolate the friction coefficient data, calculate elongation of a scale with two springs, determine the maxima and minima of the pressure-angle function, and solve some other M&T problems.

MATHEMATICAL MODEL AND AREA OF EXISTENCE OF THE FAMILY CRANKS AND MOBILE MECHANISMS WITH THE MAXIMUM TRANSMISSION ANGLE

The article examines crank-rocker mechanisms. Such mechanisms are used in transport and technological machines. The article is devoted to the search for a new family of crank-rocker mechanisms. A mathematical model of a new family of crank-rocker mechanisms is obtained. In this family, the maximum transmission angle reaches 90 when the crank angle is 75. Thus, the new family of crank-rocker mechanisms differs from the known families by the position of the mechanism in which the maximum of the transmission angle function takes place. It is shown that, with a certain ratio of link lengths, the new family corresponds to the known families KKM-5 and KKM-7. The area of existence of a new family of crank-rocker mechanisms is established. This area is bounded by the arc of the circle of the unit radius and the curve. The mentioned curve is based on a joint solution of a mathematical model of a new family of mechanisms and the famous Kolchin straight line. The dependence for the minimum transmission angle is obtained. A formula for determining the angle of the rocker arm span is proposed. A graphical interpretation of the mentioned dependencies and formulas is constructed. The scope of existence of a new family of crank-rocker mechanisms and graphical interpretations are used in determining the geometric parameters of mechanisms. These mechanisms are part of a new family of mechanisms.

Asteroid models reconstructed from ATLAS photometry

Context. The Asteroid Terrestrial-impact Last Alert System (ATLAS) is an all-sky survey primarily aimed at detecting potentially hazardous near-Earth asteroids. Apart from the astrometry of asteroids, it also produces their photometric measurements that contain information about asteroid rotation and their shape. Aims. To increase the current number of asteroids with a known shape and spin state, we reconstructed asteroid models from ATLAS photometry that was available for approximately 180 000 asteroids observed between 2015 and 2018. Methods. We made use of the light-curve inversion method implemented in the Asteroids@home project to process ATLAS photometry for roughly 100 000 asteroids with more than a hundred individual brightness measurements. By scanning the period and pole parameter space, we selected those best-fit models that were, according to our setup, a unique solution for the inverse problem. Results. We derived ~2750 unique models, 950 of them were already reconstructed from other data and published. The remaining 1800 models are new. About half of them are only partial models, with an unconstrained pole ecliptic longitude. Together with the shape and spin, we also determined for each modeled asteroid its color index from the cyan and orange filter used by the ATLAS survey. We also show the correlations between the color index, albedo, and slope of the phase-angle function. Conclusions. The current analysis is the first inversion of ATLAS asteroid photometry, and it is the first step in exploiting the huge scientific potential that ATLAS photometry has. ATLAS continues to observe, and in the future, this data, together with other independent photometric measurements, can be inverted to produce more refined asteroid models.

Geometric Hardy and Hardy–Sobolev inequalities on Heisenberg groups

In this paper, we present geometric Hardy inequalities for the sub-Laplacian in half-spaces of stratified groups. As a consequence, we obtain the following geometric Hardy inequality in a half-space of the Heisenberg group with a sharp constant: [Formula: see text] which solves a conjecture in the paper [S. Larson, Geometric Hardy inequalities for the sub-elliptic Laplacian on convex domain in the Heisenberg group, Bull. Math. Sci. 6 (2016) 335–352]. Here, [Formula: see text] is the angle function. Also, we obtain a version of the Hardy–Sobolev inequality in a half-space of the Heisenberg group: [Formula: see text] where [Formula: see text] is the Euclidean distance to the boundary, [Formula: see text], and [Formula: see text]. For [Formula: see text], this gives the Hardy–Sobolev–Maz’ya inequality on the Heisenberg group.

Flat bending shape stability of the beams with variable section width

The paper proposes a methodology for calculating lateral buckling of beams of variable rectangular cross section based on the energy approach. The technique is considered on the example of a cantilever beam of variable width with two sections under the action of a concentrated force. The twist angle function was set in the form of a trigonometric series. As a result, the problem is reduced to a generalized secular equation.

The effects of Virtual Reality Training with Upper Limb Sensory Exercise Stimulation on the AROM of Upper Limb Joints, Function, and Concentration in Chronic Stroke Patients

Objective We investigated the effect of upper limb sensory stimulation and virtual reality rehabilitation (SMVR) on upper extremity active joint angle, function and cognitive ability in chronic stroke patients. Methods A total of 30 patients were randomly divided into SMVR group and CON group. SMVR group was performed 60 min three times a week for 8 weeks in upper limb sensory stimulation and robot virtual reality rehabilitation. CON group performed conservative treatment and peripheral joint movement for 60 min. The upper limb function was measured by the Jebsen-Taylor hand function test (JTT) and the cognitive ability test was performed by the Stroop test (ST) and Trail making test (TMT). Results There was a significant difference (P<0.05) between before and after training in both groups, and SMVR group showed significant improvement in both groups. Conclusions In this study, we confirmed that robot virtual reality training in combination with limb motion stimulation for stroke patients positively affects the angle, function, and concentration of upper extremity active joints in chronic stroke patients.