Dynamic Modeling of a Multi-Legged Robotic Vehicle: Part 1 — Kinematic Analysis

1987 ◽  
Author(s):  
R. A. Hart ◽  
N. D. Ebrahimi
Keyword(s):  
Dynamic Model ◽  
Dynamic Modeling ◽  
Dynamic Equilibrium ◽  
Contact Forces ◽  
System Response ◽  
Kinematic Chains ◽  
Locomotion System ◽  
Robotic Vehicle ◽  
Ground Profile ◽  
Legged Vehicle

Abstract This two-part paper presents a dynamic model of a legged vehicle for travel on a variable-topographic terrain. In Part 1 of the paper, we develop expressions for the kinematics of the vehicular system. These expressions, in turn, form the foundation for the dynamic analysis of the robotic vehicle presented in Part 2 of the paper. The model applies to a system composed of a cargocarrying body supported by four multi-degree-of-freedom linkage assemblies whose configurations are adjustable to accommodate terrain irregularities. The mobility of the locomotion system is provided by four rigid wheels which serve as a base to the kinematic chains that extend from the platform of the vehicle. To assure dynamic equilibrium of all members in the system, torque actuators are employed at the joints between inter-connecting bodies to facilitate the adjustment of each articulated chain configuration without reducing the adaptability of the vehicle to ground profile variations. The dynamic model used for determining the system response to environmental contact forces is based on a Newton-Euler recursive formulation.

Dynamic Modeling of a Multi-Legged Robotic Vehicle: Part 2 — Dynamic Analysis

1987 ◽  
Author(s):  
R. A. Hart ◽  
N. D. Ebrahimi
Keyword(s):  
Dynamic Analysis ◽  
Dynamic Model ◽  
Dynamic Modeling ◽  
Kinetic Equations ◽  
Euler Method ◽  
Degree Of Freedom ◽  
Time Response ◽  
Robotic Vehicle

Abstract In Part 1 of this report, we described the overall objective of the investigation; that is, the formulation of a dynamic model for determining the time response of a multi-legged robotic vehicle traveling on a variable-topographic terrain. Specifically, we developed expressions for the joint variables, and their rates, which are essential for describing the system’s links orientations, velocities, and accelerations. This procedure enabled us to determine the kinematic quantities associated with the entire vehicular system in accordance with the Newton-Euler method. In the present paper, we formulate the kinetic equations for the multi-degree-of-freedom leg assemblies, the rigid wheels, and the platform of the vehicle to achieve the prescribed motion and corresponding configuration of the system.

scholarly journals A Dynamic Modeling Method for the Bi-Directional Pneumatic Actuator Using Dynamic Equilibrium Equation

Actuators ◽  
2021 ◽  
Vol 11 (1) ◽  
pp. 7
Author(s):  
Yiqing Li ◽  
Wen Zhou ◽  
Junwu Wu ◽  
Guoxu Hu
Keyword(s):  
Dynamic Model ◽  
Dynamic Modeling ◽  
Equilibrium Equation ◽  
Dynamic Equilibrium ◽  
Research Field ◽  
Modeling Method ◽  
Pneumatic Actuator ◽  
Pneumatic Actuators ◽  
Challenging Research ◽  
Rubber Block

Dynamic modeling of soft pneumatic actuators are a challenging research field. In this paper, a dynamic modeling method used for a bi-directionaly soft pneumatic actuator with symmetrical chambers is proposed. In this dynamic model, the effect of uninflated rubber block on bending deformation is considered. The errors resulting from the proposed dynamic equilibrium equation are analyzed, and a compensation method for the dynamic equilibrium equation is proposed. The equation can be solved quickly after simplification. The results show that the proposed dynamic model can describe the motion process of the bi-directional pneumatic actuator effectively.

Predictive Dynamic Model of a Deep Groove Ball Bearing With a Flexible Outer Ring

2008 ◽  
Author(s):  
Alexandre Laurent ◽  
David Lenoir ◽  
Louis Jezequel ◽  
Bruno Mevel
Keyword(s):  
Dynamic Model ◽  
Ball Bearing ◽  
Dynamic Equilibrium ◽  
Rigid Bodies ◽  
Contact Forces ◽  
Hertzian Contact ◽  
Outer Ring ◽  
Integration Scheme ◽  
Deep Groove ◽  
Deep Groove Ball Bearing

An explicit dynamic model of a deep groove ball bearing under a radial load is proposed. All components are treated as rigid bodies whereas the bearing outer ring flexibility is taken into account using fixed interface component mode synthesis (CMS). The classical lubricated Hertzian contact theory is used to calculate elastic deflections and non-linear contact forces. The dynamic loading of the outer ring interface nodes is ensured using C2-continuous rational cubic splines. A Runge-Kutta-Felhberg 4th/5th order integration scheme is used to solve the dynamic equilibrium of all components. Time and frequency domain analyses are then carried out to investigate the dynamic behaviour of the ball bearing. The accuracy of these works is validated by comparison with the results of an analytical model and a model based on finite elements proposed in prior researchs.

Multibody Dynamic Model of Web Guiding System With Moving Web

2010 ◽  
Vol 132 (5) ◽  
Author(s):  
Lei Yu ◽  
Zhihua Zhao ◽  
Gexue Ren
Keyword(s):  
Dynamic Model ◽  
Lateral Displacement ◽  
Dynamical Behavior ◽  
Contact Forces ◽  
Lagrangian Formulation ◽  
Pi Control ◽  
Control Law ◽  
Reference Surface ◽  
Multibody Dynamic ◽  
Guiding System

In this paper, a multibody dynamic model is established to simulate the dynamics and control of moving web with its guiding system, where the term moving web is used to describe thin materials, which are manufactured and processed in a continuous, flexible strip form. In contrast with available researches based on Eulerian description and beam assumption, webs are described by Lagrangian formulation with the absolute nodal coordinate formulation (ANCF) plate element, which is based on Kirchhoff’s assumptions that material normals to the original reference surface remain straight and normal to the deformed reference surface, and the nonlinear elasticity theory that accounts for large displacement, large rotation, and large deformation. The rollers and guiding mechanism are modeled as rigid bodies. The distributed frictional contact forces between rollers and web are considered by Hertz contact model and are evaluated by Gauss quadrature. The proportional integral (PI) control law for web guiding is also embedded in the multibody model. A series of simulations on a typical web-guide system is carried out using the multibody dynamics approach for web guiding system presented in this study. System dynamical information, for example, lateral displacement, stress distribution, and driving moment for web guiding, are obtained from simulations. Parameter sensitivity analysis illustrates the effect of influence variables and effectiveness of the PI control law for lateral movement control of web that are verified under different gains. The present Lagrangian formulation of web element, i.e., ANCF element, is not only capable of describing the large movement and deformation but also easily adapted to capture the distributed contact forces between web and rollers. The dynamical behavior of the moving web can be accurately described by a small number of ANCF thin plate elements. Simulations carried out in this paper show that the present approach is an effective method to assess the design of web guiding system with easily available desktop computers.

Urban Dynamics and Urban Cycles

1978 ◽  
Vol 10 (1) ◽  
pp. 43-49 ◽  
Author(s):  
D S Dendrinos
Keyword(s):  
Dynamic Model ◽  
Urban Area ◽  
Catastrophe Theory ◽  
Dynamic Equilibrium ◽  
Urban System ◽  
Type A ◽  
Parameter Control ◽  
Economic Activities ◽  
Urban Dynamics ◽  
Behavioral Variables

Some basic elements of catastrophe theory are discussed insofar as they relate to discontinuities observed in the allocation of economic activities in urban settings. The case of a dynamic model of the allocation of manufacturing and residential activities is presented in an open urban area as a model of a hyperbolic umbilic catastrophe. The dynamic equilibrium allocations of these two activities are identified as possible paths in the bifurcation set of the three parameter (control variables) and two behavioral-variables catastrophe type. A regulating function governing the urban system at the macroscale is discussed.

scholarly journals Planetary Gearbox Dynamic Modeling Considering Bearing Clearance and Sun Gear Tooth Crack

Sensors ◽  
2021 ◽  
Vol 21 (8) ◽  
pp. 2638
Author(s):  
Xianhua Chen ◽  
Xingkai Yang ◽  
Ming J. Zuo ◽  
Zhigang Tian
Keyword(s):  
Dynamic Model ◽  
Dynamic Modeling ◽  
Failure Modes ◽  
Gear Tooth ◽  
Working Environment ◽  
The Sun ◽  
Planetary Gearbox ◽  
Bearing Clearance ◽  
Vibration Responses ◽  
Planet Gear

Planetary gearbox systems are critical mechanical components in heavy machinery such as wind turbines. They may suffer from various failure modes, due to the harsh working environment. Dynamic modeling is a useful method to support early fault detection for enhancing reliability and reducing maintenance costs. However, reported studies have not considered the sun gear tooth crack and bearing clearance simultaneously to analyze their combined effect on vibration characteristics of planetary gearboxes. In this paper, a dynamic model is developed for planetary gearboxes considering the clearance of planet gear, sun gear, and carrier bearings, as well as sun gear tooth crack levels. Bearing forces are calculated considering bearing clearance, and the dynamic model equations are updated accordingly. The results reveal that the combination of bearing clearances can affect the vibration response with sun gear tooth crack by increasing the kurtosis. It is found that the effect of planet gear bearing clearance is very small, while the sun gear and carrier bearing clearance has clear impact on the vibration responses. These findings suggest that the incorporation of bearing clearance is important for planetary gearbox dynamic modeling.

Sensor Dynamic Modeling Based on LS-SVM and NGA

2008 ◽  
Vol 381-382 ◽  
pp. 439-442
Author(s):  
Qi Wang ◽  
Zhi Gang Feng ◽  
K. Shida
Keyword(s):  
Genetic Algorithm ◽  
Neural Networks ◽  
Support Vector Machine ◽  
Least Squares ◽  
Dynamic Model ◽  
Dynamic Modeling ◽  
Support Vector ◽  
Local Minima ◽  
Highly Nonlinear ◽  
Sharing Function

Least squares support vector machine (LS-SVM) combined with niche genetic algorithm (NGA) are proposed for nonlinear sensor dynamic modeling. Compared with neural networks, the LS-SVM can overcome the shortcomings of local minima and over fitting, and has higher generalization performance. The sharing function based niche genetic algorithm is used to select the LS-SVM parameters automatically. The effectiveness and reliability of this method are demonstrated in two examples. The results show that this approach can escape from the blindness of man-made choice of LS-SVM parameters. It is still effective even if the sensor dynamic model is highly nonlinear.

scholarly journals Modeling and Dynamic Analysis of Spherical Roller Bearing with Localized Defects: Analytical Formulation to Calculate Defect Depth and Stiffness

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Behnam Ghalamchi ◽  
Jussi Sopanen ◽  
Aki Mikkola
Keyword(s):  
Dynamic Model ◽  
Contact Stiffness ◽  
Roller Bearing ◽  
Measurement Data ◽  
Contact Forces ◽  
Hertzian Contact ◽  
Radial Clearance ◽  
Outer Race ◽  
Rolling Elements ◽  
Localized Defects

Since spherical roller bearings can carry high load in both axial and radial direction, they are increasingly used in industrial machineries and it is becoming important to understand the dynamic behavior of SRBs, especially when they are affected by internal imperfections. This paper introduces a dynamic model for an SRB that includes an inner and outer race surface defect. The proposed model shows the behavior of the bearing as a function of defect location and size. The new dynamic model describes the contact forces between bearing rolling elements and race surfaces as nonlinear Hertzian contact deformations, taking radial clearance into account. Two defect cases were simulated: an elliptical surface on the inner and outer races. In elliptical surface concavity, it is assumed that roller-to-race-surface contact is continuous as each roller passes over the defect. Contact stiffness in the defect area varies as a function of the defect contact geometry. Compared to measurement data, the results obtained using the simulation are highly accurate.

Dynamic Behavior Analysis of Three-Span Rotor-Bearing System with Rub-Impact Fault

2012 ◽  
Vol 460 ◽  
pp. 160-164 ◽  
Author(s):  
Song He Zhang ◽  
Yue Gang Luo ◽  
Bin Wu ◽  
Bang Chun Wen
Keyword(s):  
Nonlinear Dynamics ◽  
Behavior Analysis ◽  
Dynamic Model ◽  
Dynamic Behavior ◽  
Rotor System ◽  
System Response ◽  
Rotor Bearing ◽  
Set Up ◽  
Bearing System ◽  
Main Influence

The dynamic model of the three-span rotor-bearing system with rub-impact fault was set up. The influence to nonlinear dynamics behaviors of the rotor-bearing system that induced by rub-impact of one disc, two discs and three discs were numerically studied. The main influence of the rotor system response by the rub-impact faults are in the supercritical rotate speed. There are mutations of amplitudes in the responses of second and third spans in supercritical rotate speed when rub-impact with one disc, and there are chaotic windows in the response of first span, and jumping changes in second and third spans when rub-impact with two or three discs.

scholarly journals Walking Gait of a Biped with a Wearable Walking Assist Device

2015 ◽  
Vol 12 (04) ◽  
pp. 1550018 ◽  
Author(s):  
Yannick Aoustin
Keyword(s):  
Dynamic Model ◽  
Unique Solution ◽  
Energy Cost ◽  
Assist Device ◽  
Double Support ◽  
Kinematic Chains ◽  
Walking Gait ◽  
Time Period ◽  
Single Support Phase ◽  
Support Phase

A ballistic walking gait is designed for a planar biped equipped with a wearable walking assist device. The biped is a seven-link planar biped with two legs, two feet, and a trunk. The wearable walking assist device is composed of a bodyweight support, two upper legs, two lower legs, and two shoes. The dynamic model of the biped with its walking assist device, containing two closed kinematic chains, is calculated by virtually cutting each of both loops at one of their point. In the single support phase, the biped with its assist device moves due to the existence of a momentum, produced mechanically, without applying active torques in the inter-link joints. The biped and this assist device are controlled with impulsive torques at the instantaneous double support to obtain a cyclic gait. The impulsive torques are applied in the six inter-link joints of the biped and in several inter-link joints of the wearable walking assist device. The following distributions of impulsive torques, in the knees or the ankles, hips and knees, hips and ankles, or knees and ankles and the fully assist device, are compared with the case of no assistance for the biped. Each time, an infinity of solutions exists to find the impulsive torques. An energy cost functional defined from these impulsive torques is minimized to determine a unique solution. Numerical results show that for a given time period and a given length of the walking gait step, the assistance of the hips is a good compromise to help the biped.

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