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Dynamic Analysis of Multibody Mechanical Systems
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Dynamic Analysis of Multibody Mechanical Systems

A special issue of Machines (ISSN 2075-1702). This special issue belongs to the section "Automation and Control Systems".

Deadline for manuscript submissions: closed (30 November 2023) | Viewed by 50542

Special Issue Editor

Dr. Carmine Maria Pappalardo

E-Mail Website
Guest Editor
Department of Industrial Engineering, Università di Salerno, 84135 Salerno, Italy
Interests: multibody dynamics; nonlinear control; system identification.

Special Issue Information

Multibody systems are formed by articulated systems composed of mechanical components. As a key feature, kinematic joints constrain the motion of multibody mechanical systems. Nonlinear forces and nonlinear force fields, which generate complex dynamic behaviors, are also applied to the bodies that form a multibody system. Furthermore, multibody mechanical systems can be either rigid or deformable, leading to two completely separated descriptions of the motion based on fundamental mathematical approaches that eventually may converge in a unified formulation. In general, multibody systems are mathematically modelled using nonlinear sets of Differential-Algebraic Equations (DAEs). Through the fundamental principles of analytical mechanics and employing modern linear algebra techniques, the mathematical description of the motion of a multibody system can be systematically formulated into a nonlinear set of differential-algebraic equations that must be then solved numerically. Therefore, the multibody approach to the analysis of constrained mechanical systems represents a fundamental tool suitable for performing the optimal design and the virtual prototyping of modern engineering systems.

The central goal of this Special Issue is to offer an overview of the state-of-the-art research in the kinematic, static, and dynamic analysis of multibody mechanical systems, on the development of effective and efficient algorithms to address these issues, and on the engineering applications that lie in this context. Consequently, the subjects covered in this Special Issue belong to a broad framework and encompass a wide range of fundamental aspects and engineering problems. The topics of interest for this Special Issue include, but are not limited to, mathematical modelling of articulated mechanical systems, dynamic and vibration analysis approaches, experimental model validation techniques, finite rotation and large deformation problems concerning rigid-flexible multibody systems, methodologies for formulating and solving the differential-algebraic equations of motion, nonlinear control techniques for controlling the dynamic behavior of multibody systems, developments in the finite element technologies, and advances in the kinematic and geometric description of the motion in general. 

Dr. Carmine Maria Pappalardo
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Machines is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Published Papers (17 papers)

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Research

20 pages, 11502 KiB  
Article
Research on Deployment Process Dynamics and Vibration for Replaceable Interface Mast
by Tongliang Liu, Jianmin Wen and Ping Zhang
Machines 2024, 12(4), 243; https://doi.org/10.3390/machines12040243 - 08 Apr 2024
Viewed by 344
Abstract
The mast of the rover is a device used to carry precision instruments such as cameras on the rover, and its performance directly affects the working quality of these devices. The replaceable interface mast can effectively solve the problems of a single structure [...] Read more.
The mast of the rover is a device used to carry precision instruments such as cameras on the rover, and its performance directly affects the working quality of these devices. The replaceable interface mast can effectively solve the problems of a single structure and poor maintenance of ordinary masts, so we study the deployment process dynamics properties and vibration for replaceable interface mast. Firstly, we analyzed the spatial motion of the reconfigurable rigid body module by the absolute node coordinate method and the natural coordinate method, and established the dynamic equation of the interface, the reconfigurable module without external constraints. Then, we established a dynamic model of the mast system deployment process. We analyzed the dynamic behavior of the replaceable interface mast and studied and compared the differences in the deployment behavior of the replaceable interface mast under different system configurations, flexible interface geometric parameters, and different driving rules. Finally, we built a model of the mast system and experimentally analyzed the deployment process of the replaceable interface mast. Using numerical solution and experimental verification, we proved that the established dynamic model of the mast system can correctly analyze the deployment behavior dynamics of the replaceable interface mast, and the study can provide a reference for the design and behavior analysis of the mast system. Full article
(This article belongs to the Special Issue Dynamic Analysis of Multibody Mechanical Systems)
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25 pages, 8612 KiB  
Article
A Unified Approach to Modeling and Simulation of Underwater Vehicle Multi-Manipulator Systems
by Gloria León-González, Rafael Stanley Núñez-Cruz, Elba Dolores Antonio-Yañez, Juan Herrera-Vidal, Giovanni Canales-Gómez and Clementina Rueda-Germán
Machines 2024, 12(2), 94; https://doi.org/10.3390/machines12020094 - 26 Jan 2024
Viewed by 948
Abstract
In this article, the model of a family of underwater vehicle multi-manipulator systems (UVMMS) is obtained by considering all its elements as parts of a unique system, the model includes the forces produced on the manipulators by the movement of the vehicle, as [...] Read more.
In this article, the model of a family of underwater vehicle multi-manipulator systems (UVMMS) is obtained by considering all its elements as parts of a unique system, the model includes the forces produced on the manipulators by the movement of the vehicle, as well as the reaction forces on the vehicle produced by the movement of the manipulators. The modeling process is completed using the Newton–Euler approach through the mobile arborescent kinematic chain. This work also presents different approaches to the use of numerical implementations of the proposed model, and simulation results are included to demonstrate that the model is capable to represent the interaction between the vehicle and the manipulators. The proposed model and simulations are important because they allow the design of control strategies that consider all the elements of the system instead of neglecting the interaction forces or considering the vehicle and the arms as uncoupled elements. Full article
(This article belongs to the Special Issue Dynamic Analysis of Multibody Mechanical Systems)
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20 pages, 10518 KiB  
Article
Vibration Modeling and Analysis of a Flexible 3-PRR Planar Parallel Manipulator Based on Transfer Matrix Method for Multibody System
by Guoning Si, Wenkai Li, Hanjing Lu, Zhuo Zhang and Xuping Zhang
Machines 2023, 11(5), 505; https://doi.org/10.3390/machines11050505 - 22 Apr 2023
Cited by 1 | Viewed by 1229
Abstract
This paper presents the vibration model of a 3-prismatic–revolute–revolute (PRR) planar parallel manipulator (PPM) with three flexible intermedia links, utilizing the linear transfer matrix method for multibody systems (MSTMM). The dynamic characteristics of the PRR PPM are also investigated. The dynamic model of [...] Read more.
This paper presents the vibration model of a 3-prismatic–revolute–revolute (PRR) planar parallel manipulator (PPM) with three flexible intermedia links, utilizing the linear transfer matrix method for multibody systems (MSTMM). The dynamic characteristics of the PRR PPM are also investigated. The dynamic model of the 3-PRR PPM is derived, and the transfer matrix and transfer equation of each component in the system, as well as the overall transfer equation and transfer matrix of the system are obtained. The vibration characteristics of the whole system are determined using the MSTMM and verified through ANSYS simulation. Furthermore, the relationship between the natural frequencies and the flexible PPM configurations is analyzed under a specific circular trajectory. The results demonstrate that the natural frequency of the system changes constantly with the configurations, and the trends of the first six orders are similar. This novel modeling approach does not require global dynamic equations and is both efficient and accurate. Moreover, it can be easily extended to other parallel manipulators with flexible components. Full article
(This article belongs to the Special Issue Dynamic Analysis of Multibody Mechanical Systems)
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48 pages, 13458 KiB  
Article
Computer-Aided Design, Multibody Dynamic Modeling, and Motion Control Analysis of a Quadcopter System for Delivery Applications
by Carmine Maria Pappalardo, Marco Del Giudice, Emanuele Baldassarre Oliva, Littorino Stieven and Alessandro Naddeo
Machines 2023, 11(4), 464; https://doi.org/10.3390/machines11040464 - 08 Apr 2023
Cited by 1 | Viewed by 3740
Abstract
This paper elaborates on the modeling and control of an Unmanned Aerial Vehicle (UAV) for delivery purposes, thereby integrating computer-aided design, multibody dynamic modeling, and motion control analysis in a unified framework. The UAV system designed in this study and utilized for item [...] Read more.
This paper elaborates on the modeling and control of an Unmanned Aerial Vehicle (UAV) for delivery purposes, thereby integrating computer-aided design, multibody dynamic modeling, and motion control analysis in a unified framework. The UAV system designed in this study and utilized for item delivery has a quadcopter structure composed of four arms connected to a central trunk. In this investigation, the proposed design of the delivery drone is systematically modeled employing the multibody approach, while SIMSCAPE MULTIBODY is the software used for performing the dynamic analysis and for devising the final design of the control system. To this end, starting from the CAD model designed using SOLIDWORKS, the control system of the quadcopter is developed by performing dynamic simulations in the MATLAB/SIMULINK environment. Additionally, another fundamental contribution of this paper is the analytical derivation of the nonlinear set of algebraic constraint equations peculiar to the present multibody system, which characterizes the kinematics of the delivery drone and describes the relative angular velocity imposed between two rigid bodies as nonholonomic constraints. Furthermore, as discussed in detail in this paper, the choice of the propulsion system and the design of the individual components heavily depends on the structural and functional needs of the UAV under study. On the other hand, the control system devised in this work is based on cascaded Proportional-Integral-Derivative (PID) controllers, which are suitable for achieving different maneuvers that are fundamental for the motion control of the delivery drone. Therefore, the final performance of the UAV system is a consequence of the regulation of the feedback parameters that characterize the PID controllers. In this respect, the paper presents the refining of the parameters characterizing the PID controllers by using both an internal MATLAB tool, which automatically tunes the controller gains of single-input single-output systems, and by observing the resulting transient behavior of the UAV system, which is obtained through extensive dynamical simulations. The set of numerical results found in this investigation demonstrates the high performance of the dynamical behavior of the UAV system designed in this work. Full article
(This article belongs to the Special Issue Dynamic Analysis of Multibody Mechanical Systems)
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19 pages, 1580 KiB  
Article
Quasi-Coordinates-Based Closed-Form Dynamic Modeling and Analysis for a 2R1T PKM with a Rigid–Flexible Structure
by Renfeng Zhu, Guilin Yang, Zaojun Fang, Chin-Yin Chen, Huamin Li and Chi Zhang
Machines 2023, 11(2), 260; https://doi.org/10.3390/machines11020260 - 09 Feb 2023
Viewed by 1138
Abstract
This work derives a closed-form dynamic model for a two rotational and one translational degrees-of-freedom (2R1T) parallel kinematic mechanism (PKM) with a hybrid rigid–flexible structure for force-control applications. Based on the three-prismatic-prismatic-spherical (3PPS) kinematic configuration of the 2R1T PKM and its zero-torsion motion [...] Read more.
This work derives a closed-form dynamic model for a two rotational and one translational degrees-of-freedom (2R1T) parallel kinematic mechanism (PKM) with a hybrid rigid–flexible structure for force-control applications. Based on the three-prismatic-prismatic-spherical (3PPS) kinematic configuration of the 2R1T PKM and its zero-torsion motion characteristics, a symbolic formulation approach is proposed to establish closed-form kinematic models for both forward and inverse kinematics analysis. As the moving platform pose of the 2R1T 3PPS PKM can be readily determined by the three active prismatic joint variables and the three passive prismatic joint variables, these six joint variables are selected as the quasi-coordinates so as to systematically develop the closed-form dynamic model with a Lagrangian formulation, in which the stiffness and deformation of the three flexure-based passive prismatic joints are uniformly taken into consideration. Through eliminating the three passive prismatic joint variables based on the principle of virtual work and the relationships between the active and passive prismatic joint variables, a closed-form dynamic model for the 2R1T 3PPS PKM with a rigid–flexible structure is finally obtained. The correctness of the closed-form dynamic model was validated with the commercial dynamic simulation software. Utilizing the closed-form dynamic model, the effects of different flexure stiffness in driving directions on the required active joint force were investigated, which indicated that little flexure stiffness in driving directions is desired. Full article
(This article belongs to the Special Issue Dynamic Analysis of Multibody Mechanical Systems)
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16 pages, 779 KiB  
Article
Complex Eigenvalue Analysis of Multibody Problems via Sparsity-Preserving Krylov–Schur Iterations
by Dario Mangoni, Alessandro Tasora and Chao Peng
Machines 2023, 11(2), 218; https://doi.org/10.3390/machines11020218 - 02 Feb 2023
Cited by 2 | Viewed by 1168
Abstract
In this work, we discuss the numerical challenges involved in the computation of the complex eigenvalues of damped multi-flexible-body problems. Aiming at the highest generality, the candidate method must be able to deal with arbitrary rigid body modes (free–free mechanisms), arbitrary algebraic constraints, [...] Read more.
In this work, we discuss the numerical challenges involved in the computation of the complex eigenvalues of damped multi-flexible-body problems. Aiming at the highest generality, the candidate method must be able to deal with arbitrary rigid body modes (free–free mechanisms), arbitrary algebraic constraints, and must be able to exploit the sparsity pattern of Jacobians of large systems. We propose a custom implementation of the Krylov–Schur method, proving its robustness and its accuracy in a variety of different complex test cases. Full article
(This article belongs to the Special Issue Dynamic Analysis of Multibody Mechanical Systems)
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17 pages, 17174 KiB  
Article
An Elaborate Dynamic Model of the Dual-Motor Precision Transmission Mechanism for Performance Optimization
by Jieji Zheng, Xin Xie, Ruoyu Tan, Lingyu Chen, Baoyu Li and Dapeng Fan
Machines 2022, 10(12), 1181; https://doi.org/10.3390/machines10121181 - 07 Dec 2022
Viewed by 1089
Abstract
The dual-motor precision transmission mechanism (DMPTM) is an alternative way to eliminate backlash while ensuring the stiffness of the servo system. However, most of the established models of DMPTM are not accurate enough, and are not conducive to the optimization of system performance [...] Read more.
The dual-motor precision transmission mechanism (DMPTM) is an alternative way to eliminate backlash while ensuring the stiffness of the servo system. However, most of the established models of DMPTM are not accurate enough, and are not conducive to the optimization of system performance and the design of high-precision controllers. In this paper, based on the detailed linear model of the single components of the DMPTM, the dead-zone model, considering the time-varying stiffness, is proposed to describe the backlash of the two transmission chains, and the friction of the mechanism is depicted by the Stribeck model. Then, a high-precision dynamic model of the DMPTM is formed. Finally, the model validation experiments for the open-loop and closed-loop are carried out in the time domain and frequency domain. The experimental results show that the proposed model can accurately describe the nonlinear characteristics of the mechanism. The Pearson correlation coefficient between the proposed model and the actual system is ropen-loop > 99.41%, for the open-loop, and rclosed-loop > 83.7%, for the closed-loop, and these results are both better than those of the existing model. In the frequency domain, whether it is the open-loop or closed-loop model, the frequency response of the proposed model also reproduces the actual system well, which verifies the accuracy of the model. Full article
(This article belongs to the Special Issue Dynamic Analysis of Multibody Mechanical Systems)
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11 pages, 2665 KiB  
Article
The Design and Control of a Footplate-Based Gait Robo-Assisted System for Lower Limb Actuator
by Seyed Mohammadali Rahmati and Alireza Karimi
Machines 2022, 10(7), 546; https://doi.org/10.3390/machines10070546 - 06 Jul 2022
Cited by 1 | Viewed by 1470
Abstract
Stroke causes disability in the lower-limb symmetry gait pattern in affected patients. The patients would not be able to regain their usual walking ability independently unless they benefit from rehabilitation therapies. Footplate-based gait robo-assisted systems can help patients to conduct effective training/exercising while [...] Read more.
Stroke causes disability in the lower-limb symmetry gait pattern in affected patients. The patients would not be able to regain their usual walking ability independently unless they benefit from rehabilitation therapies. Footplate-based gait robo-assisted systems can help patients to conduct effective training/exercising while tracking their progress of recovery and can dramatically reduce the clinical labor costs of physiotherapy. In the sense of simulation and not the design of the mechanical structure, this study aims to perform a combination of dynamic and control simulation of a five degrees-of-freedom footplate-based gait robo-assisted system established according to the Stewart platform structure for use in lower limb rehabilitation of stroke patients. The effectiveness and performance of the proposed mechanism were assessed through a clinical gait pattern of a healthy male individual. The proposed robo-assisted system enables the simulation of the hip and knee flexion/extension as well as the ankle dorsiflexion/plantar flexion of stroke patients to reproduce their typical symmetry gait pattern. The results were interpreted as the dynamic movement characteristics of the right and left thigh, leg, and foot compared to the clinical gait pattern with a mean percentage error of 6.70% to show the effectiveness and accuracy of the developed robo-assisted system for lower limb actuation in the simulation process. Full article
(This article belongs to the Special Issue Dynamic Analysis of Multibody Mechanical Systems)
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16 pages, 6325 KiB  
Article
Dynamic Characteristic Analysis and Structural Optimization Design of the Large Mining Headframe
by Yue Liu, Min Huang, Qi An, Long Bai and Deyong Shang
Machines 2022, 10(7), 510; https://doi.org/10.3390/machines10070510 - 24 Jun 2022
Cited by 2 | Viewed by 2026
Abstract
A large headframe is the core structure of a mine hoisting system. In the traditional design, only the static analysis under load is considered, resulting in the resonance phenomenon of the large headframe in later applications. In order to restrain the resonance phenomenon, [...] Read more.
A large headframe is the core structure of a mine hoisting system. In the traditional design, only the static analysis under load is considered, resulting in the resonance phenomenon of the large headframe in later applications. In order to restrain the resonance phenomenon, a novel method for dynamic characteristic analysis and structural optimization design of a large headframe is proposed. First, the eigenfrequencies and vibration modes of the large headframe were obtained through modal analysis. The results showed that the numerical values of the multi-order eigenfrequencies of the system are relatively close. When subjected to alternating loads of similar frequencies, a large headframe is prone to the resonance phenomenon. Second, the steady-state vibration response of the large headframe was obtained through harmonic response analysis. The results showed that when the frequency of the alternating load is close to the first-order eigenfrequency, the vibration amplitude increases. Meanwhile, the fourth-order and the fifth-order eigenfrequencies are very close. When subjected to alternating loads of similar frequencies, the fourth-order and the fifth-order vibration modes of the headframe will be excited simultaneously. At this time, the headframe will have a strong resonance, which may cause structural damage and other problems. Finally, based on the above analysis, nine different structural optimization schemes are proposed in this paper. Through modal analysis and harmonic response analysis, the nine schemes were compared and analyzed, and the optimal scheme was eventually determined as scheme 9. The method proposed in this paper provides a new concept for the structural optimization design of a large mining headframe, and it has great significance for restraining the resonance phenomenon and ensuring the safety of mining operations. Full article
(This article belongs to the Special Issue Dynamic Analysis of Multibody Mechanical Systems)
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14 pages, 2370 KiB  
Article
Using Pose-Dependent Model Predictive Control for Path Tracking with Bounded Tensions in a 3-DOF Spatial Cable Suspended Parallel Robot
by Jason Bettega, Dario Richiedei and Alberto Trevisani
Machines 2022, 10(6), 453; https://doi.org/10.3390/machines10060453 - 08 Jun 2022
Cited by 4 | Viewed by 1785
Abstract
This paper proposes the preliminary results on a novel control architecture based on model predictive control (MPC) for cable-driven parallel robots (CDPRs) and applies them to a three degrees of freedom (3-DOF) robot with a suspended configuration, leading to a cable-suspended parallel robot [...] Read more.
This paper proposes the preliminary results on a novel control architecture based on model predictive control (MPC) for cable-driven parallel robots (CDPRs) and applies them to a three degrees of freedom (3-DOF) robot with a suspended configuration, leading to a cable-suspended parallel robot (CSPR). The goal of the control scheme is ensuring accurate path tracking of the reference end-effector path, while imposing a priori positive cable tensions. To handle the nonlinearities characterizing the dynamic model that governs this kind of multibody system and to keep the computational effort low, a position-dependent MPC algorithm with an embedded integrator is designed to compute the optimal cable tensions required to track the end-effector commanded path. Such tensions must belong to the feasible domain defined through a lower bound, which is slightly greater than zero, to ensure that cables pull the end-effector, and an upper bound, to represent the maximum stress that cables can withstand without breaking. The resulting controller is nonlinear, although it performs a local linearization in the prediction at each time step to reduce the computational effort. The optimal tensions are then transformed into the commanded motor torques through the inverse dynamic model of the servomotors driving the winches, since no force measurement is adopted in the controller implementation. The control architecture is designed and numerically validated through a spatial CSPR with lumped end-effector, and driven by three cables (i.e., with a non-redundant configuration). Four different paths are assumed to highlight various features of the proposed controller. Full article
(This article belongs to the Special Issue Dynamic Analysis of Multibody Mechanical Systems)
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15 pages, 3278 KiB  
Article
Multibody Model for the Design of a Rover for Agricultural Applications: A Preliminary Study
by Filippo Califano, Chiara Cosenza, Vincenzo Niola and Sergio Savino
Machines 2022, 10(4), 235; https://doi.org/10.3390/machines10040235 - 27 Mar 2022
Cited by 4 | Viewed by 3852
Abstract
The employment of vehicles such as rovers equipped with automictic and robotic systems in agriculture is an emerging field. The development of suitable simulation models can aid in the design and testing of agricultural rovers before prototyping. Here, we propose a simulation test [...] Read more.
The employment of vehicles such as rovers equipped with automictic and robotic systems in agriculture is an emerging field. The development of suitable simulation models can aid in the design and testing of agricultural rovers before prototyping. Here, we propose a simulation test rig based on a multibody model to investigate the main issues connected with agricultural rover designs. The results of the simulations show significant differences between the two structures, especially regarding the energy savings, which is a key aspect for the applicability of a rover in field operations. The modular structure of the proposed simulation model can be easily adapted to other vehicle structures. Full article
(This article belongs to the Special Issue Dynamic Analysis of Multibody Mechanical Systems)
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18 pages, 1994 KiB  
Article
A Variable-Length Rational Finite Element Based on the Absolute Nodal Coordinate Formulation
by Zhishen Ding and Bin Ouyang
Machines 2022, 10(3), 174; https://doi.org/10.3390/machines10030174 - 25 Feb 2022
Cited by 9 | Viewed by 2038
Abstract
The variable-length arbitrary Lagrange–Euler absolute nodal coordinate formulation (ALE-ANCF) finite element, which employs nonrational interpolating polynomials, cannot exactly describe rational cubic Bezier curves such as conic and circular curves. The rational absolute nodal coordinate formulation (RANCF) finite element, whose reference length (undeformed length) [...] Read more.
The variable-length arbitrary Lagrange–Euler absolute nodal coordinate formulation (ALE-ANCF) finite element, which employs nonrational interpolating polynomials, cannot exactly describe rational cubic Bezier curves such as conic and circular curves. The rational absolute nodal coordinate formulation (RANCF) finite element, whose reference length (undeformed length) is constant, can exactly represent rational cubic Bezier curves. A new variable-length finite element called the ALE-RANCF finite element, which is capable of accurately describing rational cubic Bezier curves, is proposed and was formed by combining the desirable features of the ALE-ANCF and RANCF finite elements. To control the reference length of the ALE-RANCF element within a suitable range, element segmentation and merging schemes are proposed. It is demonstrated that the exact geometry and mechanics are maintained after the ALE-RANCF element is divided into two shorter ones, and compared with the ALE-ANCF elements, there are smaller deviations and oscillations after two ALE-RANCF elements are merged into a longer one. Numerical examples are presented, and the feasibility and advantages of the ALE-RANCF finite element are demonstrated. Full article
(This article belongs to the Special Issue Dynamic Analysis of Multibody Mechanical Systems)
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40 pages, 15945 KiB  
Article
Detachment Detection in Cam Follower System Due to Nonlinear Dynamics Phenomenon
by Louay S. Yousuf
Machines 2021, 9(12), 349; https://doi.org/10.3390/machines9120349 - 09 Dec 2021
Cited by 10 | Viewed by 2513
Abstract
The detachment between the cam and the follower was investigated for different cam speeds (N) and different internal distance of the follower guide from inside (I.D.). The detachment between the cam and the follower were detected using largest Lyapunov exponent parameter, power density [...] Read more.
The detachment between the cam and the follower was investigated for different cam speeds (N) and different internal distance of the follower guide from inside (I.D.). The detachment between the cam and the follower were detected using largest Lyapunov exponent parameter, power density function of Fast Fourier Transform (FFT), and Poincare’ maps due to the nonlinear dynamics phenomenon of the follower. The follower displacement and the contact force between the cam and the follower were used in the detection of the detachment heights. Multi-degrees of freedom (spring-damper-mass) systems at the very end of the follower were used to improve the dynamic performance and to reduce the detachment between the cam and the follower. Nonlinear response of the follower displacement was calculated at different cam speeds, different coefficient of restitution, different contact conditions, and different internal distance of the follower guide from inside. SolidWorks program was used in the numerical solution while high speed camera at the foreground of the OPTOTRAK 30/20 equipment was used to catch the follower position. The friction and impact were considered between the cam and the follower and between the follower and its guide. The peak of nonlinear response of the follower displacement was reduced to (15%, 32%, 45%, and 62%) after using multiple degrees of freedom systems. Full article
(This article belongs to the Special Issue Dynamic Analysis of Multibody Mechanical Systems)
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17 pages, 4935 KiB  
Article
Dynamic Modeling of a Front-Loading Type Washing Machine and Model Reliability Investigation
by Jungjoon Park, Sinwoo Jeong and Honghee Yoo
Machines 2021, 9(11), 289; https://doi.org/10.3390/machines9110289 - 15 Nov 2021
Cited by 3 | Viewed by 2646
Abstract
A linear dynamic model of a front-loading type washing machine was developed in this study. The machine was conceptualized with three moving rigid bodies, revolute joints, springs, and dampers along with prescribed rotational drum motion. Kane’s method was employed for deriving the equations [...] Read more.
A linear dynamic model of a front-loading type washing machine was developed in this study. The machine was conceptualized with three moving rigid bodies, revolute joints, springs, and dampers along with prescribed rotational drum motion. Kane’s method was employed for deriving the equations of motion of the idealized washing machine. Since the modal and transient characteristics can be conveniently investigated with a linear dynamic model, the linear model can be effectively used for the design of an FL type washing machine. Despite the convenience, however, the reliability of the linear dynamic model is often restricted to a certain range of system parameters. Parameters relevant to the reliability of the linear dynamic model were identified and the parameters’ ranges that could guarantee the reliability of the proposed linear dynamic model were numerically investigated in this study. Full article
(This article belongs to the Special Issue Dynamic Analysis of Multibody Mechanical Systems)
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34 pages, 1779 KiB  
Article
A Multibody System Approach for the Systematic Development of a Closed-Chain Kinematic Model for Two-Wheeled Vehicles
by Camilo Andres Manrique-Escobar, Carmine Maria Pappalardo and Domenico Guida
Machines 2021, 9(11), 245; https://doi.org/10.3390/machines9110245 - 20 Oct 2021
Cited by 25 | Viewed by 2456
Abstract
In this investigation, a closed-chain kinematic model for two-wheeled vehicles is devised. The kinematic model developed in this work is general and, therefore, it is suitable for describing the complex geometry of the motion of both bicycles and motorcycles. Since the proposed kinematic [...] Read more.
In this investigation, a closed-chain kinematic model for two-wheeled vehicles is devised. The kinematic model developed in this work is general and, therefore, it is suitable for describing the complex geometry of the motion of both bicycles and motorcycles. Since the proposed kinematic model is systematically developed in the paper by employing a sound multibody system approach, which is grounded on the use of a straightforward closed-chain kinematic description, it allows for readily evaluating the effectiveness of two alternative methods to formulate the wheel-road contact constraints. The methods employed for this purpose are a technique based on the geometry of the vector cross-product and a strategy based on a simple surface parameterization of the front wheel. To this end, considering a kinematically driven vehicle system, a comparative analysis is performed to analyze the geometry of the contact between the front wheel of the vehicle and the ground, which represents a fundamental problem in the study of the motion of two-wheeled vehicles in general. Subsequently, an exhaustive and extensive numerical analysis, based on the systematic multibody approach mentioned before, is carried out in this work to study the system kinematics in detail. Furthermore, the orientation of the front assembly, which includes the frontal fork, the handlebars, and the front wheel in a seamless subsystem, is implicitly formulated through the definition of three successive rotations, and this approach is used to propose an explicit formulation of its inherent set of Euler angles. In general, the numerical results developed in the present work compare favorably with those found in the literature about vehicle kinematics and contact geometry. Full article
(This article belongs to the Special Issue Dynamic Analysis of Multibody Mechanical Systems)
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23 pages, 10289 KiB  
Article
Dynamic Handling Characterization and Set-Up Optimization for a Formula SAE Race Car via Multi-Body Simulation
by Matteo Balena, Giacomo Mantriota and Giulio Reina
Machines 2021, 9(6), 126; https://doi.org/10.3390/machines9060126 - 21 Jun 2021
Cited by 7 | Viewed by 6962
Abstract
There is a growing interest towards multi-body modelling and simulation that play a critical role in the development and testing of new mechanical systems, in general, and formula cars specifically to avoid expensive and time-consuming experimental track testing. Recent advances in computer-aided engineering [...] Read more.
There is a growing interest towards multi-body modelling and simulation that play a critical role in the development and testing of new mechanical systems, in general, and formula cars specifically to avoid expensive and time-consuming experimental track testing. Recent advances in computer-aided engineering packages, allows one not only to evaluate the basic properties that define the dynamic behavior of a newly-designed formula car, but as well as to investigate the impact on the performance of the many adjustable parameters that collectively are referred to as the car set-up. Therefore, by providing a rapid feedback of a given set-up expectation, optimal configurations can be obtained ensuring the highest level of performance. In this paper, a Formula SAE vehicle is expressly targeted. First, a full multi-body model of the prototype is described detailing the properties of each subassembly, e.g., suspensions and antiroll bars, steering system, and powertrain. Then, the basic handling characteristics are obtained via simulated track testing. Based on vehicle dynamics principles, the fine tuning of the vehicle setup is thoroughly discussed to gain the best performance in each of the contest events of the Formula SAE competition. For example, in the skidpad event where cars are required to drive along an eight-shaped track, an almost 2 km/h gain in the maximum travel velocity can be achieved by adjusting the camber angles of all tires. Full article
(This article belongs to the Special Issue Dynamic Analysis of Multibody Mechanical Systems)
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16 pages, 4932 KiB  
Article
Development and Testing of a High-Frequency Dynamometer for High-Speed Milling Process
by Yanlin Lyu, Muhammad Jamil, Ning He, Munish Kumar Gupta and Danil Yurievich Pimenov
Machines 2021, 9(1), 11; https://doi.org/10.3390/machines9010011 - 12 Jan 2021
Cited by 9 | Viewed by 2820
Abstract
Cutting forces are strongly associated with the mechanics of the cutting process. Hence, machining forces measurements are very important to investigate the machining process, and numerous methods of cutting forces measurements have been applied. Nowadays, a dynamometer is the most popular tool for [...] Read more.
Cutting forces are strongly associated with the mechanics of the cutting process. Hence, machining forces measurements are very important to investigate the machining process, and numerous methods of cutting forces measurements have been applied. Nowadays, a dynamometer is the most popular tool for cutting forces measurements. However, the natural frequency of a dynamometer has a direct impact on the accuracy of measured cutting forces in the machining process. Therefore, few dynamometers are appropriate and reliable to measure the cutting forces at high frequencies. In this work, a new strain-gauge-based dynamometer (SGBD) with a special structure was designed, manufactured, and put to the test to ensure the measurement of high-frequency dynamic forces in the milling process. The main structure of the SGBD is symmetrical and mainly consists of a center quadrangular prism surrounded by four force sensing elastic elements, an upper support plate, and a lower support plate. The dynamic identification test was conducted and indicated that the SGBD′s natural frequency could be stabilized at a high value of 9.15 kHz. To automatically obtain the milling force data with a computer during high rotational speed milling, a data acquisition system was devised for the dynamometer. To reduce the effects of cross-sensitivity and acting point of force, an innovative model based on a conversion matrix was established for the dynamometer. Furthermore, the cutting tests were conducted at high rotational speeds (10,000–18,000 rpm), and it was found that the difference of cutting forces between the SGBD and a Kistler dynamometer are 2.3–5.8% in the X direction and 3.5–8.8% in the Y direction. The experimental findings disclosed that the new kind of dynamometer is reliably for the measurement of high-frequency dynamic forces in milling at high rotational speeds. Full article
(This article belongs to the Special Issue Dynamic Analysis of Multibody Mechanical Systems)
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