scholarly journals Dynamical Analysis of the Mechanical System with Two Degrees of Freedom Applied to the Transmission of the Wind Turbine

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Maria Luminiţa Scutaru ◽  
Bogdan Mitrica
Keyword(s):  
Mathematical Model ◽  
Dynamic Response ◽  
Mechanical System ◽  
Degrees Of Freedom ◽  
Physical Mechanism ◽  
Dynamical Analysis ◽  
Mechanical Parameters ◽  
Two Degrees Of Freedom ◽  
Innovative Solution ◽  
Water Pumps

The authors develop a mathematical model to analyze the transmission of wind-driven water pumps in order to determine their dynamic response, stability, and stresses occurring in the transmission elements. The authors propose, as an innovative solution, the use of a mechanism with two degrees of freedom that provides automatically a flexibility of the transmission ratio and the harmonization of the turbine operation with the wind velocity. To verify the results a stand was carried out as physical mechanism on which measurements and recordings of the significant mechanical parameters of the system are made.

Computer Modelling of Wrist Biomechanics: Translation into Specific Tasks and Injuries

2020 ◽  
Vol 16 (3) ◽  
pp. 178-183
Author(s):  
Michael J. Sandow
Keyword(s):  
Mathematical Model ◽  
Reverse Engineering ◽  
Mechanical System ◽  
Virtual Environment ◽  
Degrees Of Freedom ◽  
Carpal Bones ◽  
Ulnar Deviation ◽  
Two Degrees Of Freedom ◽  
Flexion Extension ◽  
Four Bar Linkage

Background: The carpus is a complicated and functionally challenged mechanical system, advancements in the understanding of which have been compromised by the recognition that there is no standard carpal mechanical system and no typical wrist. This paper covers components of a larger project that seeks to develop a kinetic model of wrist mechanics to allow reverse analysis of the specific biomechanical controls or rules of a specific patient’s carpus. Those rules, unique to each patient, could be used to create a forward synthesis mathematical model to reproduce the individual’s anatomical motion in a virtual environment. Objective and Methods: Based on the previous observations, the carpus essentially moves with only two degrees of freedom-pitch (flexion/extension) and yaw (radial deviation/ulnar deviation)-while largely preventing roll (pronation/supination). The objective of this paper is, therefore, to present the background and justification to support the rules-based motion (RBM) concept, which states that the motion of a mechanical system, such as the wrist, is the net interplay of four rules: morphology, constraint, interaction, and load. The stable central column theory (SCCT) of wrist mechanics applies the concept of RBM to the carpus, and by using a reverse engineering computational analysis model, a consistent pattern of isometric constraints was identified, creating a “two-gear four-bar” linkage. This study assessed the motion of the carpus using a 3D (three-dimensional) dynamic visualization model. The hypothesis was that the pattern and direction of motion of the proximal row and the distal row with respect to the immediately cephalad carpal bones or radius would be similar in all directions of wrist motion. To identify the unique motion segments, 3D models were created from five normal wrists that underwent CT scanning in multiple positions of radial and ulnar deviation as well as flexion and extension. Each carpal row (proximal and distal) was animated in a virtual environment with the cephalad carpal bones or radius held immobile. The rotational axis and position of each bone and each row were then compared in sagittal (flexion-extension) and coronal (radial and ulnar deviation) motion. Results: The carpus appeared to have only two degrees of freedom, and yet was stable in those arcs with the loads applied proximally in the forearm. The proximal row moved in a singular arc, but with a varying extent during sagittal and coronal motion. The isometric constraints were consistent in both directions. The distal row moved on an axis formed by a pivot joint laterally (between the trapezium and scaphoid) and a saddle joint medially (between hamate and triquetrum). The sagittal and coronal alignment of this axis changed as the proximal row moved. This created a distinct pattern of row motion to achieve the various required positions of wrist function. On wrist radial deviation, the scaphoid (with the proximal row) was flexed and the distal row was extended, whereas, in wrist flexion, the scaphoid flexed (with the proximal row) and so did the distal row. The pattern was reversed in the opposite wrist movements. While the general direction of motion of each row was consistent, the extent was quite variable. Conclusion: This review supports the SCCT of carpal mechanics and the carpus acting as a twogear four-bar linkage, as well as the concept of RBM as a means to understand the biomechanics of the wrist, and how this is translated into specific functional tasks. More sophisticated 3D modelling will be required to further understand the specifics of carpal motion; however, reverse engineering of the specific rules that define each individual wrist can also be applied to a mathematical model to provide a “what if” test of particular surgical interventions for a variety of wrist injuries. The use of quantitative 3D Computed Tomography Scan (CT) analysis, surgical planning and virtual surgical intervention allows potential surgical solutions to be applied to a computer model of an injured wrist to test the possible outcomes and prognosis of a proposed treatment.

scholarly journals Analysis of Dynamic Response of a Two Degrees of Freedom (2-DOF) Ball Bearing Nonlinear Model

2021 ◽  
Vol 11 (2) ◽  
pp. 787
Author(s):  
Bartłomiej Ambrożkiewicz ◽  
Grzegorz Litak ◽  
Anthimos Georgiadis ◽  
Nicolas Meier ◽  
Alexander Gassner
Keyword(s):  
Mathematical Model ◽  
Degrees Of Freedom ◽  
Ball Bearing ◽  
Hertzian Contact ◽  
Two Degrees Of Freedom ◽  
Wide Range ◽  
Shape Errors ◽  
Nonlinear Features ◽  
Fourier Transform Phase ◽  
Hertzian Contact Theory

Often the input values used in mathematical models for rolling bearings are in a wide range, i.e., very small values of deformation and damping are confronted with big values of stiffness in the governing equations, which leads to miscalculations. This paper presents a two degrees of freedom (2-DOF) dimensionless mathematical model for ball bearings describing a procedure, which helps to scale the problem and reveal the relationships between dimensionless terms and their influence on the system’s response. The derived mathematical model considers nonlinear features as stiffness, damping, and radial internal clearance referring to the Hertzian contact theory. Further, important features are also taken into account including an external load, the eccentricity of the shaft-bearing system, and shape errors on the raceway investigating variable dynamics of the ball bearing. Analysis of obtained responses with Fast Fourier Transform, phase plots, orbit plots, and recurrences provide a rich source of information about the dynamics of the system and it helped to find the transition between the periodic and chaotic response and how it affects the topology of RPs and recurrence quantificators.

A Novel 4D Chaotic System Based on Two Degrees of Freedom Nonlinear Mechanical System

2018 ◽  
Vol 73 (7) ◽  
pp. 595-607 ◽  
Author(s):  
Sezgin Kacar ◽  
Zhouchao Wei ◽  
Akif Akgul ◽  
Burak Aricioglu
Keyword(s):  
Mechanical System ◽  
Chaotic System ◽  
Degrees Of Freedom ◽  
Electronic Circuit ◽  
Chaotic Behaviour ◽  
Two Degrees Of Freedom ◽  
Nonlinear Mechanical System ◽  
Linear Mechanical System ◽  
Low Amplitude ◽  
The Mathematical Model

AbstractIn this study, a non-linear mechanical system with two degrees of freedom is considered in terms of chaos phenomena and chaotic behaviour. The mathematical model of the system was moved to the state space and presented as a four dimensional (4D) chaotic system. The system’s chaotic behaviour was investigated by performing dynamic analyses of the system such as equilibria, Lyapunov exponents, bifurcation analyses, etc. Also, the electronic circuit realisation is implemented as a real-time application. This system exhibited vibration along with noise-like behaviour because of its very low amplitude values. Thus, the system is scaled to increase the amplitude values. As a result, the electronic circuit implementation of the 4D chaotic system derived from the model of a physical system is realised.

scholarly journals Mathematical model of pantograph cooperation with two degrees of freedom with a catenary system

2019 ◽  
Vol 294 ◽  
pp. 05005
Author(s):  
Marek Kaniewski ◽  
Michał Cichoński
Keyword(s):  
Mathematical Model ◽  
Discrete Model ◽  
Degrees Of Freedom ◽  
Variable Stiffness ◽  
System Model ◽  
Dynamic State ◽  
Rolling Stock ◽  
Two Degrees Of Freedom ◽  
Technical Specifications ◽  
Catenary System

The authors present a method of modeling pantograph cooperation with a catenary system by means of a computer program based on a pantograph discrete model with two degrees of freedom and a catenary system model as a focused mass that in the dynamic state has variable stiffness along the span. After performing the appropriate tests, the validation was carried out according to the proposed method in the PN EN 50318:2019-02 standard required in the Technical Specifications for the interoperability of the subsystem “Energy” and “Rolling stock -locomotives and passenger rolling stock” of the trans-European rail system in Europe.

Mathematical Model of the Servo Drive with Friction Wheals. Simulations and Real Object Examination Results

2013 ◽  
Vol 198 ◽  
pp. 15-20 ◽  
Author(s):  
Lukasz Fracczak
Keyword(s):  
Mathematical Model ◽  
Cardiac Surgery ◽  
Control System ◽  
Simulation Model ◽  
Degrees Of Freedom ◽  
Point Of View ◽  
Real Object ◽  
Servo Drive ◽  
Two Degrees Of Freedom ◽  
The Mathematical Model

In this paper the servo drive with friction wheels is presented. The servo drive is designed to move the automatic laparoscope tool or laparoscope camera (thereinafter laparoscope sleeve or sleeve) in two Degrees of Freedom (DOF). The description of the drive mechanism, operating principle and mathematical model of this drive is presented. Based on this model, the Control System (CS) has been created, and used to the construction of a simulation model. The simulation illustrates the proper functionality of the mathematical model of the servo drive with the described CS. This paper also presents the servo drive test stand and the most important examination results from the point of view of using them in the cardiac surgery Robin Heart robot.

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