This paper presents a method of polynomial transition curve application for making agricultural aggregate movement paths during headland turn drives as well as within the field. Four types of agricultural aggregate paths in five different variant designs are discussed. Each path is composed of only two curves, making the so-called transition bi-curve. The curvature described by the linear function as well as the third, fifth, seventh, and ninth degree polynomials was designated. Moreover, a trajectory planning algorithm in which the movement proceeds along two transition curves composing the so-called bi-curve was proposed. The simulation was carried out applying the MATLAB program in which the 4th order Runge–Kutta method was used. The results were presented by means of figures showing the proposed paths and kinematic quantity courses in the displacement function. The obtained trajectories were compared regarding the size and kinematic quantities. The trajectories, whose curvature is described by the 3° polynomial, were found to possess the smallest absolute values of maximal acceleration and jerk and to lack jerk discontinuity. The proposed solutions can be applied for planning trajectory of not only agriculture machines and aggregates but also autonomous vehicles or mobile robots.

This paper presents planning of smooth trajectories using the asymmetric profiles of displacement, velocity, acceleration and jerk of described higher degree polynomials. The presented way of determination of polynomial and asymmetry coefficients as well as motion time includes the procedure at both constraints of single kinematic quantities, i.e., velocity, acceleration, jerk and introducing a few constraints simultaneously. Moreover, the paper presents a method of planning trajectories with intermediate points consisting in concatenation of the analyzed polynomials. The proposed method of trajectory planning was compared to that of using the S-curve. The results in the form of kinematic quantity courses are presented graphically. The discussed method guarantees continuity of displacement, velocity, acceleration and jerk. It can be used for planning trajectories of various technical objects (e.g., manipulators, mobile robots, CNC machine tools, optical disk drives, autonomous vehicles, etc.).

The investigations on the response of bone tissue under different loading conditions are important from clinical and engineering points of view. In this paper, the influence of nesfatin-1 administration on rat humerus mechanical properties was analyzed. The classical three-point bending and impact tests were carried out for three rat bone groups: control (SHO), the humerus of animals under the conditions of established osteopenia (OVX), and bones of rats receiving nesfatin-1 after ovariectomy (NES). The experiments proved that the bone strength parameters measured under various mechanical loading conditions increased after the nesfatin-1 administration. The OVX bones were most susceptible to deformation and had the smallest fracture toughness. The SEM images of humerus fracture surface in this group showed that ovariectomized rats had a much looser bone structure compared to the SHO and NES females. Loosening of the bone structure was also confirmed by the densitometric and qualitative EDS analysis, showing a decrease in the OVX bones’ mineral content. The samples of the NES group were characterized by the largest values of maximum force obtained under both quasi-static and impact conditions. The energies absorbed during the impact and the critical energy for fracture (from the three-point bending test) were similar for the SHO and NES groups. Statistically significant differences were observed between the mean F_{i max} values of all analyzed sample groups. The obtained results suggest that the impact test was more sensitive than the classical quasi-static three-point bending one. Hence, F_{i max} could be used as a parameter to predict bone fracture toughness.

The purpose of the study was to use reverse engineering to model biological products, especially sugar beet root. In the process of creating the solid model, the appropriate tools available in the 3D design environment were applied. The 3D scan of the beet, in the form of a spatial point cloud, was used to project the root geometry. This was, in turn, used to construct a triangulation grid that includes nodal points of triangles. The subsequent steps presented the process of creating a solid model using the Interpolation Spline tool. Attention has been paid to the possibility of modifying the geometry by inserting additional points into the existing interpolation spline and changing angular position as well as the distance of the structural planes. Geometry mapping error values were determined with regard to the reference model depending on the spread value of the Structural Planes. Error courses are non-linear with a logarithmic line trend (surface field error) and a linear line trend (volume error). The effects demonstrated the usefulness of geometry projection and its applicability to support the strength testing of biological materials, with particular emphasis on dynamic tests using whole roots.

Root damages due to mechanical impacts result in deterioration in commercial sugar beet quality. In order to determine the mechanical characteristics of roots, a stand equipped with a pendulum enabling impact investigations of whole beets was used. The roots were stored in a monitored environment for up to 5 days (temperature 15 ± 2 °C, 40 ± 2%). During the tests, the beets were struck against a flat steel resistant surface with the velocities V_imp = 0.5, 1.0 and 1.5 m·s⁻¹. The measurements of local root curvatures in three chosen impact areas and the deformation (d_max) allowed modelling of the volume of contact (CV) by means of the ellipsoid cap. These investigations enabled the determination of the relations between the maximal impact force, F_max, the impact energy, E_imp, and the absorbed energy, E_abs, as well as the contact volume and impact velocity, taking into account the root storage time, S_t. It was found that the maximal impact force increased with increasing impact velocity and decreased with the storage time for each group of roots. With increasing velocity, there were also increases in the following: impact energy, absorbed energy, contact volume and maximal deformation, as well as absorbed energy, referred to as the mass E_abs-v from V_imp. The mean values of the stresses (σ_max), being the quotients of the impact force (F_max) and the surface area of the ellipsoid cap base (A_BE), were 0.81–1.17 MPa, 1.064–1.59 MPa and 1.45–1.77 MPa for the velocities of 0.5, 1.0 and 1.5 m·s⁻¹, respectively. It was confirmed that the statistical significance of the mentioned parameters changes depending on the impact velocity.