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    A General Multibody Approach for the Linear and Nonlinear Stability Analysis of Bicycle Systems. Part II: Application to the Whipple-Carvallo Bicycle Model

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    This paper represents the second contribution of a two-part research work presenting the application of the proposed multibody analysis approach to bicycle systems and the relative numerical results found. In this work, a nonlinear multibody model of a bicycle system is developed and implemented to perform a parametric analysis to understand the influence of the variation of the principal model parameters on the system stability under investigation. To demonstrate the effectiveness of the proposed approach, the case study considered in this paper is the dynamic analysis of the Whipple-Carvallo bicycle model. Considering the combined use of a robust numerical technique for nonlinear dynamical simulations with a specifically devised linearization procedure, the effects of the different geometric parameters and inertial properties on the bicycle stability are investigated. The numerical results obtained in this work using the proposed multibody techniques are useful to gain insight information about the dynamic behavior of the bicycle system in a straight motion. The proposed multibody methodology also demonstrated a high potential for analyzing complex multibody mechanical systems in virtue of the generality of the analytical and computational approaches adopted

    A General Multibody Approach for the Linear and Nonlinear Stability Analysis of Bicycle Systems. Part I: Methods of Constrained Dynamics

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    This investigation is the first contribution of a two-part research work concerning the theoretical development of a multibody approach to analyze the constrained dynamics of articulated mechanical systems. In this paper, a method for investigating the linear and nonlinear stability of the dynamic behavior of mechanical systems modeled as multibody systems subjected to holonomic and nonholonomic constraints is presented. To this end, the nonlinear equations of motions that assume a complex index-three differential-algebraic form are systematically formulated and directly linearized by using an automatic procedure based on a hybrid symbolic-numeric approach devised in this work. The proposed stability analysis method, therefore, is based on the formulation of a generalized eigenvalue problem and represents a viable computer-aided approach suitable for analyzing multibody mechanical systems having different degrees of complexity. Furthermore, an extension of the generalized coordinate partitioning algorithm is introduced in this paper for handling nonholonomic multibody systems leading to a robust and general multibody computational procedure referred to as the Robust Generalized Coordinate Partitioning Algorithm (RGCPA). Since the methodologies employed in this paper to study the stability of multibody mechanical systems are general and versatile, they can be easily implemented in general-purpose multibody computer programs and readily used to analyze several mechanical applications having engineering interest

    Identification of a Dynamical Model of the Latching Mechanism of an Aircraft Hatch Door using the Numerical Algorithms for Subspace State-Space System Identification

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    In this paper, the main objective is to underline the possibility of identifying simplified mechanical models of complex mechanical systems through the numerical techniques of applied system identification to develop control actions. For this purpose, the system identification theory and, in particular, the Numerical Algorithms for Subspace State-Space System Identification, shortened in N4SID, are employed in this work considering a mathematical model as the test rig instead of using a real system and the data gathered from real sensors. In particular, the mechanical model of the latch system of the ATR 42/72 cargo door is the case study considered in this investigation to integrate the CAD (Computer-Aided Design) model and the dynamical simulations carried out within the MBD (Multi-Body Dynamics) virtual environments. Thus, the software SOLIDWORKS is used for the CAD interface, whereas, at the same time, the software SIMSCAPE is chosen to carry out the numerical simulations of the corresponding multibody model, and the system identification process is performed employing the N4SID suite implemented in MATLAB. When compared with the original nonlinear multibody model, the numerical results found from the dynamical simulations generated in SIMSCAPE, starting from the model developed in SOLIDWORKS, are used to identify a simpler linear dynamical model of the latch system of the hatch door, which could be effectively used in subsequent developments to analyze further the real prototype and for the design of effective control strategies

    Stability analysis of rigid multibody mechanical systems with holonomic and nonholonomic constraints

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    In this paper, a new analytical approach suitable for the stability analysis of multibody mechanical systems is introduced in the framework of Lagrangian mechanics. The approach developed in this work is based on the direct linearization of the index-three form of the differential-algebraic dynamic equations that describe the motion of mechanical systems subjected to nonlinear constraints. One of the distinguishing features of the proposed method is that it can handle general sets of nonlinear holonomic and/or nonholonomic constraints without altering the original mathematical structure of the equations of motion. While the typical state-space dynamic description associated with multibody systems leads to the definition of a standard eigenproblem, which is impractical, if not impossible, to implement in the case of complex systems, the method developed in this paper involves a generalized state-space representation of the dynamic equations and allows for the formulation of a generalized eigenvalue problem that extends the scope of applicability of the stability analysis to complex mechanical systems. As demonstrated in this investigation employing simple numerical examples, the proposed methodology can be readily implemented in general-purpose multibody computer programs and compares favorably with several other reference computational approaches already available in the multibody literature

    Experimental Identification of a Car Dynamic Model Using the Numerical Algorithms for Subspace State-Space System Identification

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    In this paper, a system identification numerical procedure is used to perform an experimental work based on the System Identification Toolbox available in MATLAB. This work aims to show the possibility of identifying a mathematical model of a car using low-cost sensors. The instrumentation used to reach this goal is composed of an Arduino Mega2560, a GPS receiver module, and an inertial measurement unit. The Arduino is used to handle the sensors and to save the measured data. The inertial platform is used to get the linear acceleration and angular rates of the system, while the GPS is used to get the trajectory of the car. By employing the N4SID algorithm, a discrete state-space model of the system can be identified and used to predict the behavior of the car system. It is also possible to obtain a continuous model from the discrete one and to identify the natural frequencies and the system damping factors. The results show the possibility to easily identify a mathematical model of a complex system using a limited set of experimental data
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