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In this paper, a detailed and comprehensive linear stability analysis of a rolling toroidal wheel is performed. The wheel is modeled as a rigid toroid-shaped body rolling without slipping on a horizontal surface. The nonlinear equations of motion constitute a Differential-Algebraic Equations system, given by the dynamic equilibrium equations augmented with the nonholonomic constraints, which arise from the no-slip condition. The circular steady motion and the linearized equations of motion along this relative equilibrium are obtained, for both the solid and hollow tori. The expressions of the linearized equations and the corresponding eigenvalues are derived analytically as a function of the torus aspect ratio. The variation of the stability boundary with the torus aspect ratio is shown. A comparison of the results obtained in the solid and hollow scenarios is included, and all the results are validated with the rolling hoop, which corresponds to a degenerate torus with zero aspect ratio. In the particular case of the steady straight-line rolling and spinning about a vertical diameter, which constitute limit motions of the circular steady motion, the critical rotational and angular speeds required for stabilization are obtained.

In this paper, the handling of the dependent coordinates in the linearization of constrained multibody systems is clarified. To this end, a brief but comprehensive overview of linearization approaches used in the field of Multibody System Dynamics is presented. These procedures are illustrated by using a common notation and classified into four groups, depending on the initial form of the nonlinear equations of motion and the selection of the generalized coordinates (a redundant or a minimal set). The handling of the dependent coordinates in each of the procedures is discussed. The linearized equations of motion of constrained multibody systems are of great importance in several applications, such as linear stability and modal analyses, the design of linear state feedback controllers or the building of state and input estimators, like Kalman filters. When modeling a constrained multibody system, a number of coordinates greater than the number of degrees of freedom of the system is usually used. While some linearization approaches make use of the complete set of coordinates, several procedures are based on a coordinate partition in terms of independent and dependent coordinates to reduce the number of linearized equations of motion. In this latter scenario, the role of the dependent coordinates in the linearization is important and, in a general case, these dependent coordinates cannot be ignored to obtain the correct linearized equations of motion. This aspect, which may seem obvious, is not straightforward and is addressed in this work. The importance of considering the set of dependent coordinates in the linearization is demonstrated with a well-acknowledged bicycle benchmark multibody model and an electric kickscooter multibody model with rear and front suspensions. To this end, the Jacobian matrix and the linear stability results of these case studies are computed by considering different choices of independent and dependent coordinates.

In this work, a detailed multibody model of an electric kickscooter is presented. The model includes toroidal wheels as well as rear and front suspensions. The equations of motion are derived and linearized along the steady forward motion of the vehicle. Using an efficient linearization approach, suitable for complex multibody systems with holonomic and nonholonomic constraints, allows for obtaining the reduced linearized equations of motion as a function of the geometric, dynamic, wheels’, and suspensions’ parameters. The proposed electric kickscooter multibody model is validated with the stability results of a previously presented electric kickscooter benchmark. Since the resulting eigenvalues are parameterized regarding the design parameters, a detailed linear stability analysis of the system is performed. In particular, the influence on the stability of the toroidal geometry of the wheels, the elliptic cross-section of the toroidal wheels, the rider model, the steering axis inclination angle, the inertia tensor of the front frame, and the rear and front suspensions is analyzed. The model presented, together with the linearized equations of motion obtained in this work, enables a systematic analysis of the stability of these vehicles, which helps design new electric kickscooters with improved vehicle safety conditions and oriented to a wider range of potential users.

This PhD thesis aims to develop a methodology that contributes to the modelling of nonholonomic multibody systems, the study of their linear stability and the design of linear feedback controllers. The ultimate objective is on single-person nonholonomic vehicles, particularly in terms of safety in urban transportation. By understanding how critical design parameters affect stability, it will be possible to carry out design modifications that result in safer vehicles and reduce accidents. These modifications will also cater to a wider range of potential users, including elderly and physically impaired individuals. From a regulatory perspective, understanding stability conditions will play a crucial role in formulating rules for the use of these vehicles within cities. Moreover, advancements focused on enhancing safety will promote the adoption of electric single-person vehicles, leading to a reduction in environmental degradation and aiding in the accomplishment of pollution reduction objectives. The methodology consists of the following phases. First, multibody models of a class of nonholonomic systems are developed. Subsequently, in order to carry out the linear stability analyses of these multibody systems, efficient and accurate linearization approaches are required. To this end, novel linearization procedures, for multibody systems with holonomic and nonholonomic constraints, are proposed. The correctness of the linearization approaches is validated with the linear stability results of a well-acknowledged bicycle benchmark. The results show that the procedures are completely accurate, efficient, valid for any multibody system (regardless of its complexity) and powerful, obtaining the linearized equations of motion along an arbitrary reference solution as a function of the design parameters of the multibody system. Next, by varying these parameters over a wide range of values, a detailed sensitivity analysis of the eigenvalues can be performed to assess the linea

This study investigates the discrete extended Kalman filter as applied to multibody systems and focuses on accurate formulation of the state-transition model in the framework. The proposed state-transition model is based on the coordinate-partitioning method and linearization of the multibody equations of motion. The approach utilizes the synergies between the integration of states and estimator covariances without overly simplifying the integrator structure. The proposed method is analyzed with a forward dynamics analysis of a four-bar mechanism. The results show that the stability of the state-transition model in the forward dynamics analysis is significantly enhanced with the proposed method compared with the forward Euler-based methods. The computational efficiency of the novel method was significantly lower in comparison to forward Euler-based methods, which was found to be mainly due to the computation of the Jacobian matrix of the nonlinear state equation. However, the increase in computational cost can be considered acceptable in Kalman-filtering applications, where the exact Jacobian of the state equation is needed.

Hydraulics is often used to actuate mechanisms in the applications of heavy machinery. In this work, a linearization approach for hydraulically driven multibody systems is presented. The approach allows linearizing the equations of motion of general multibody systems with holonomic and nonholonomic constraints, augmented with the hydraulic equations of the hydraulic subsystem. The derivation of this linearization approach is of interest in many applications, such as the performance of linear stability analyses. The procedure is tested with a three-dimensional multibody model of a hydraulically actuated four-bar mechanism. The validation of the approach is performed by means of the forward dynamics simulation of the linear and nonlinear systems. The results show the power of the approach, obtaining the linearized equations of motion around the equilibrium position of the four-bar mechanism multibody model in terms of the mechanical and hydraulic parameters. A comparison of the proposed procedure with a conventional counterpart approach is included, demonstrating the great accuracy and computational efficiency of the approach developed in this work.

Background: Uveal melanoma is a poor prognosis cancer. Ergolide, a sesquiterpene lactone isolated from Inula Brittanica, exerts anti-cancer properties. The objective of this study was to 1) evaluate whether ergolide reduced metastatic uveal melanoma (MUM) cell survival/viability in vitro and in vivo; and 2) to understand the molecular mechanism of ergolide action. Methods: Ergolide bioactivity was screened via long-term proliferation assay in UM/MUM cells and in zebrafish MUM xenograft models. Mass spectrometry profiled proteins modulated by ergolide within whole cell or extracellular vesicle (EVs) lysates of the OMM2.5 MUM cell line. Protein expression was analyzed by immunoblots and correlation analyses to UM patient survival used The Cancer Genome Atlas (TCGA) data. Results: Ergolide treatment resulted in significant, dose-dependent reductions (48.5 to 99.9%; p<0.0001) in OMM2.5 cell survival in vitro and of normalized primary zebrafish xenograft fluorescence (56%; p<0.0001) in vivo, compared to vehicle controls. Proteome-profiling of ergolide-treated OMM2.5 cells, identified 5023 proteins, with 52 and 55 proteins significantly altered at 4 and 24 hours, respectively (p<0.05; fold-change >1.2). Immunoblotting of heme oxygenase 1 (HMOX1) and growth/differentiation factor 15 (GDF15) corroborated the proteomic data. Additional proteomics of EVs isolated from OMM2.5 cells treated with ergolide, detected 2931 proteins. There was a large overlap with EV proteins annotated within the Vesiclepedia compendium. Within the differentially expressed proteins, the proteasomal pathway was primarily altered. Interestingly, BRCA2 and CDKN1A Interacting Protein (BCCIP) and Chitinase Domain Containing 1 (CHID1), were the only proteins significantly differentially expressed by ergolide in both the OMM2.5 cellular and EV isolates and they displayed inverse differential expression in the cells versus the EVs. Conclusions: Ergolide is a novel, promising anti-proliferative a