scholarly journals SIMULATION OF ANTHROPOMORPHIC ROBOTS WITH ELASTIC DRIVES BY INTRODUCING VIRTUAL LINKS

2018 ◽  
Vol 22 (3) ◽  
pp. 59-66
Author(s):  
S. I. Savin ◽  
L. Yu. Vorochaeva
Keyword(s):  
Mathematical Models ◽  
Control Systems ◽  
Sagittal Plane ◽  
Equations Of Motion ◽  
Bipedal Walking ◽  
Walking Robots ◽  
Structure And Properties ◽  
Dynamics Model ◽  
Sit To Stand ◽  
Virtual Links

Anthropomorphic walking robots are among the most promising robot types, due to the possibility to introduce them into the urbane environment through the use of the existing infrastructure. Control systems developed for such robots require access to the exact mathematical models of these robots, taking into account the properties of actuators, gears and sensors. In this paper, we consider approaches to describing the model of a bipedal walking robot with elastic drives. The robot is a three-link mechanism that moves in the sagittal plane and performs verticalization (sit-to-stand transfer). Two variants of describing the dynamics of the robot are shown. In the first variant, the number of equations describing the movement of the robot is doubled due to the introduction of elastic drives, in comparison with the case when there are no elastic elements present. In the second variant, there is robot model and the elastic element dynamics model, and bothare described separately. The advantages of this method include the fact that it allows us to preserve the structure and properties of the equations of motion of the mechanism used in constructing control methods in cases when the elastic properties of the gears are not taken into account, and it also allows to conserve the structure of the generalized inertia matrix. The simulation results are presented in two described previously variants, their comparison is made. It is established that both mathematical models behave almost identically, with the most significant differences manifested in the formation of control actions generated by the regulator.

Study on Dynamics Model of Macro/Micro Mechanical Arm of the New Workover

2012 ◽  
Vol 538-541 ◽  
pp. 1002-1005
Author(s):  
Yan Wang ◽  
Yu Lian Chang ◽  
Sheng Gao ◽  
Jing Wang
Keyword(s):  
Rigid Body ◽  
Mathematical Models ◽  
Rate Equation ◽  
Theoretical Basis ◽  
Equations Of Motion ◽  
Kinematics And Dynamics ◽  
Dynamics Analysis ◽  
Dynamics Model ◽  
Constraint Equations ◽  
Working Principle

Macro/micro mechanical arm is an important component of workover mechanical system. According to its composition characteristics and working principle, the arm was simplified to a plane system that all components were working in the same plane. Based on rigid body kinematics and dynamics theories, the kinematics and dynamics mathematical models of arm lifting progress were established by using constraint equations, rate equation, acceleration equations, virtual principle work, lagrange multiplier and differential-algebraic mixed equations of motion. It provides theoretical basis for kinematics and dynamics analysis of the macro/micro mechanical arm in lifting process.

scholarly journals Development of the Lower Extremity Exoskeleton Dynamics Model Using in the Task of the Patient Verticalization

2021 ◽  
Vol 2096 (1) ◽  
pp. 012042
Author(s):  
M R Saypulaev ◽  
Yu Yu Zuev ◽  
G R Saypulaev
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Lower Extremity ◽  
Degrees Of Freedom ◽  
Sagittal Plane ◽  
Equations Of Motion ◽  
Viscous Friction ◽  
Dynamics Model ◽  
Supporting Surface ◽  
The Right

Abstract The object of the study is an exoskeleton of the lower extremities with a rigid structure of the power frame, which has 7 degrees of freedom. The movement of the exoskeleton in the sagittal plane is considered with the assumption of symmetrical movement of the right and left legs. The aim of the study is to develop a mathematical model of the dynamics of the exoskeleton, taking into account the forces of viscous friction in the joints. The equations of motion are obtained under the condition that there is no slippage of the points of contact with the supporting surface. Based on the results of numerical simulation, the control moments were obtained, which must be created by the drives to provide program movement.

Numerical Investigations of the Positive Effects of Vehicle Dynamics Control Systems on Vehicle Crash

2013 ◽  
Author(s):  
Mustafa Elkady ◽  
Ahmed Elmarakbi ◽  
John MacIntyre ◽  
Hicham El-Hage
Keyword(s):  
Control Systems ◽  
Vehicle Dynamics ◽  
Equations Of Motion ◽  
Vehicle Body ◽  
Dynamics Model ◽  
Pitch Control ◽  
Positive Effects ◽  
Front End ◽  
Vehicle Collision ◽  
Vehicle Dynamics Control

This paper focuses on the use of vehicle dynamics control systems (VDCS) to mitigate vehicle collisions in case of offset frontal vehicle-to-barrier crash scenario. A unique six-Degree-of-Freedom (6-DOF) vehicle dynamics/crash mathematical model is developed and analysed in this paper. The model is used to define the vehicle body crash parameters by integrating a vehicle dynamics model with a vehicle front-end structure model. In this model, the anti-lock braking system (ABS) and the active suspension control system (ASC) are co-simulated with the full car vehicle dynamics model and integrated with the front-end structure. The associated equations of motion of the model are developed and solved numerically. In this study, different crash scenarios are simulated with different cases of VDCS to investigate their influences on the vehicle collision improvement. ABS, ASC, and anti-pitch control (APC) systems as well as an under pitch control (UPC) technique are applied in this paper, and their results are compared with free rolling crash scenarios. This study shows that the vehicle dynamics/crash response is captured and analysed quickly and accurately. Furthermore, it is shown that the VDCS affect the crash characteristics positively.

DETERMINATION OF THE JUICE EVAPORATION MATHEMATICAL MODELS EFFICIENCY FOR AUTOMATED PROCESS CONTROL SYSTEMS

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
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Keyword(s):  
Process Control ◽  
Mathematical Models ◽  
Control Systems ◽  
Process Control Systems ◽  
Automated Process

scholarly journals Mathematical models of supersonic and intersonic crack propagation in linear elastodynamics

2021 ◽  
Author(s):  
Javier Bonet ◽  
Antonio J. Gil
Keyword(s):  
Kinetic Energy ◽  
Crack Propagation ◽  
Mathematical Models ◽  
Linear Elasticity ◽  
Strain Energy ◽  
Equations Of Motion ◽  
Two Dimensions ◽  
Discontinuous Solutions ◽  
Linear Elasticity Theory ◽  
Intersonic Crack Propagation

AbstractThis paper presents mathematical models of supersonic and intersonic crack propagation exhibiting Mach type of shock wave patterns that closely resemble the growing body of experimental and computational evidence reported in recent years. The models are developed in the form of weak discontinuous solutions of the equations of motion for isotropic linear elasticity in two dimensions. Instead of the classical second order elastodynamics equations in terms of the displacement field, equivalent first order equations in terms of the evolution of velocity and displacement gradient fields are used together with their associated jump conditions across solution discontinuities. The paper postulates supersonic and intersonic steady-state crack propagation solutions consisting of regions of constant deformation and velocity separated by pressure and shear shock waves converging at the crack tip and obtains the necessary requirements for their existence. It shows that such mathematical solutions exist for significant ranges of material properties both in plane stress and plane strain. Both mode I and mode II fracture configurations are considered. In line with the linear elasticity theory used, the solutions obtained satisfy exact energy conservation, which implies that strain energy in the unfractured material is converted in its entirety into kinetic energy as the crack propagates. This neglects dissipation phenomena both in the material and in the creation of the new crack surface. This leads to the conclusion that fast crack propagation beyond the classical limit of the Rayleigh wave speed is a phenomenon dominated by the transfer of strain energy into kinetic energy rather than by the transfer into surface energy, which is the basis of Griffiths theory.

Numerical modelling of swirling momentumless turbulent wake dynamics

2018 ◽  
pp. 37-48
Author(s):  
Андрей Геннадьевич Деменков ◽  
Геннадий Георгиевич Черных
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Mathematical Models ◽  
Equations Of Motion ◽  
Turbulent Wake ◽  
The Body ◽  
Jet Flows ◽  
Reynolds Stresses ◽  
Bodies Of Revolution ◽  
Averaged Equations

С применением математической модели, включающей осредненные уравнения движения и дифференциальные уравнения переноса нормальных рейнольдсовых напряжений и скорости диссипации, выполнено численное моделирование эволюции безымпульсного закрученного турбулентного следа с ненулевым моментом количества движения за телом вращения. Получено, что начиная с расстояний порядка 1000 диаметров от тела течение становится автомодельным. На основе анализа результатов численных экспериментов построены упрощенные математические модели дальнего следа. Swirling turbulent jet flows are of interest in connection with the design and development of various energy and chemical-technological devices as well as both study of flow around bodies and solving problems of environmental hydrodynamics, etc. An interesting example of such a flow is a swirling turbulent wake behind bodies of revolution. Analysis of the known works on the numerical simulation of swirling turbulent wakes behind bodies of revolution indicates lack of knowledge on the dynamics of the momentumless swirling turbulent wake. A special case of the motion of a body with a propulsor whose thrust compensates the swirl is studied, but there is a nonzero integral swirl in the flow. In previous works with the participation of the authors, a numerical simulation of the initial stage of the evolution of a swirling momentumless turbulent wake based on a hierarchy of second-order mathematical models was performed. It is shown that a satisfactory agreement of the results of calculations with the available experimental data is possible only with the use of a mathematical model that includes the averaged equations of motion and differential equations for the transfer of normal Reynolds stresses along the rate of dissipation. In the present work, based on the above mentioned mathematical model, a numerical simulation of the evolution of a far momentumless swirling turbulent wake with a nonzero angular momentum behind the body of revolution is performed. It is shown that starting from distances of the order of 1000 diameters from the body the flow becomes self-similar. Based on the analysis of the results of numerical experiments, simplified mathematical models of the far wake are constructed. The authors dedicate this work to the blessed memory of Vladimir Alekseevich Kostomakha.

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