Modeling of control forces for kinematical constraints in multibody systems dynamics—a new approach

1991 ◽  
Vol 38 (4) ◽  
pp. 409-414
Author(s):  
S.Kemal Ider
Keyword(s):  
Multibody Systems ◽  
Systems Dynamics ◽  
New Approach ◽  
Control Forces

scholarly journals Closed-form time derivatives of the equations of motion of rigid body systems

2021 ◽  
Author(s):  
Andreas Müller ◽  
Shivesh Kumar
Keyword(s):  
Rigid Body ◽  
Closed Form ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Alternative Formulation ◽  
Dynamics Of Rigid Body ◽  
Control Forces ◽  
And Control ◽  
Derivatives Of ◽  
Insight Into

AbstractDerivatives of equations of motion (EOM) describing the dynamics of rigid body systems are becoming increasingly relevant for the robotics community and find many applications in design and control of robotic systems. Controlling robots, and multibody systems comprising elastic components in particular, not only requires smooth trajectories but also the time derivatives of the control forces/torques, hence of the EOM. This paper presents the time derivatives of the EOM in closed form up to second-order as an alternative formulation to the existing recursive algorithms for this purpose, which provides a direct insight into the structure of the derivatives. The Lie group formulation for rigid body systems is used giving rise to very compact and easily parameterized equations.

scholarly journals Control Force Recalculation for Balancing Problems

2019 ◽  
Vol 19 (05) ◽  
pp. 1941010
Author(s):  
Bálint Bodor ◽  
László Bencsik ◽  
Tamás Insperger
Keyword(s):  
Optimization Problem ◽  
Control Mechanism ◽  
Numerical Differentiation ◽  
Open Loop ◽  
Second Step ◽  
Control Force ◽  
New Approach ◽  
Numerical Errors ◽  
Linearized System ◽  
Control Forces

Understanding the mechanism of human balancing is a scientifically challenging task. In order to describe the nature of the underlying control mechanism, the control force has to be determined experimentally. A main feature of balancing tasks is that the open-loop system is unstable. Therefore, reconstruction of the trajectories using the measured control force is difficult, since measurement inaccuracies, noise and numerical errors increase exponentially with time. In order to overcome this problem, a new approach is proposed in this paper. In the presented technique, first the solution of the linearized system is used. As a second step, an optimization problem is solved which is based on a variational principle. A main advantage of the method is that there is no need for the numerical differentiation of the measured data for the calculation of the control forces, which is the main source of the numerical errors. The method is demonstrated in case of a human stick balancing.

Coupled finite element and multibody systems dynamics modelling for the investigation of the bridge approach problem

2019 ◽  
Vol 233 (10) ◽  
pp. 1097-1111 ◽  
Author(s):  
AI El-Ghandour ◽  
CD Foster
Keyword(s):  
Finite Element ◽  
Multibody Systems ◽  
Sudden Change ◽  
Three Dimensional ◽  
Systems Dynamics ◽  
The Finite Element Method ◽  
Three Dimensional Model ◽  
Bridge Approach ◽  
Railroad System ◽  
Approach Problem

Railways are the most common mode of transportation for both people and cargo due to its advantages in economy, safety, and comfort. The finite element method has been broadly used for more than three decades to model the different components of the railroad system such as rails, sleepers (cross ties), and substructure and has been used to investigate a variety of problems associated with rail mechanics. Different multibody systems dynamics software programs have also been developed to investigate the dynamic performance and contact behaviour between the rails and the wheels and to determine the contact forces. In this work, a full three-dimensional model that couples both the finite element method and the multibody systems dynamics has been used to study the railroad system. The main focus of this study is to model the bridge approach problem under dynamic load. The bridge approach problem arises from the sudden change in the foundation's stiffness under the rails at the bridge entry and exit, leading to high levels of stress and settlement that can also cause further problems over time. The effect of using a concrete slab at the bridge entry is also investigated in this study, using two slab designs: rectangular and inclined. The results show the effectiveness of the three-dimensional model and slab implementation on the forces and the vertical deformation, especially the inclined slab that applies a gradual change in the stiffness rather than a sudden change.

Probabilistic Performance of Helical Compound Planetary System in Wind Turbine

2015 ◽  
Vol 10 (4) ◽  
Author(s):  
Fisseha M. Alemayehu ◽  
Stephen Ekwaro-Osire
Keyword(s):  
Wind Turbine ◽  
Multibody Systems ◽  
Planetary System ◽  
Design Parameters ◽  
Wind Turbine Gearbox ◽  
New Approach ◽  
Highly Nonlinear ◽  
Multibody Dynamic ◽  
Input Variables ◽  
Maintenance Process

The dynamics of contact, stress and failure analysis of multibody systems is highly nonlinear. Nowadays, several commercial and other analysis software dedicated for this purpose are available. However, these codes do not consider the uncertainty involved in loading, design, and assembly parameters. One of these systems with a combined high nonlinearity and uncertainty of parameters is the gearbox of wind turbines (WTs). Wind turbine gearboxes (WTG) are subjected to variable torsional and nontorsional loads. In addition, the manufacturing and assembly process of these devices results in uncertainty of the design parameters of the system. These gearboxes are reported to fail in their early life of operation, within three to seven years as opposed to the expected twenty years of operation. Their downtime and maintenance process is the most costly of any failure of subassembly of WTs. The objective of this work is to perform a probabilistic multibody dynamic analysis (PMBDA) of a helical compound planetary stage of a selected wind turbine gearbox that considers ten random variables: two loading (the rotor speed, generator side torque), and eight design parameters. The reliability or probabilities of failure of each gear and probabilistic sensitivities of the input variables toward two performance functions have been measured and conclusions have been drawn. The results revealed that PMBDA has demonstrated a new approach of gear system design beyond a traditional deterministic approach. The method demonstrated the components' reliability or probability of failure and sensitivity results that will be used as a tool for designers to make sound decisions.

Comparative reduction of theories — or over-simplification?

1996 ◽  
Vol 19 (2) ◽  
pp. 301-302 ◽  
Author(s):  
Edgar Koerner
Keyword(s):  
Phase Transitions ◽  
State Space ◽  
Functional Diversity ◽  
Chaotic Systems ◽  
General Scheme ◽  
Systems Dynamics ◽  
Rapid Phase ◽  
Cortical Dynamics ◽  
Control Forces

AbstractTo model the organization of levels' of cortical dynamics, at least some general scheme for hierarchy, functional diversity, and proper intrinsic control must be provided. Rhythmic control forces the system to iterate its state by short trajectories, which makes it much more stable and predictable without discarding the desirable ability of chaotic systems to make rapid phase transitions. Rhythmic control provides a fundamentally different systems dynamics, one not provided by models that allow the emergence of continuous trajectories in the systems state space.

Globally Independent Coordinates for Real-Time Vehicle Simulation

1998 ◽  
Vol 122 (4) ◽  
pp. 575-582 ◽  
Author(s):  
Radu Serban ◽  
Edward J. Haug
Keyword(s):  
State Space ◽  
Real Time ◽  
Multibody Systems ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Vehicle Simulation ◽  
Generalized Coordinates ◽  
Dynamics Of Multibody Systems ◽  
Improved Performance ◽  
Control Forces

Models of the dynamics of multibody systems generally result in a set of differential-algebraic equations (DAE). State-space methods for solving the DAE of motion are based on reduction of the DAE to ordinary differential equations (ODE), by means of local parameterizations of the constraint manifold that must be often modified during a simulation. In this paper it is shown that, for vehicle multibody systems, generalized coordinates that are dual to suspension and/or control forces in the model are independent for the entire range of motion of the system. Therefore, these additional coordinates, together with Cartesian coordinates describing the position and orientation of the chassis, form a set of globally independent coordinates. In addition to the immediate advantage of avoiding the computationally expensive redefinition of local parameterization in a state-space formulation, the existence of globally independent coordinates leads to efficient algorithms for recovery of dependent generalized coordinates. A topology based approach to identify efficient computational sequences is presented. Numerical examples with realistic vehicle handling models demonstrate the improved performance of the proposed approach, relative to the conventional Cartesian coordinate formulation, yielding real-time for vehicle simulation. [S1050-0472(00)00404-9]

Generalized Vector-Network Formulation for the Dynamic Simulation of Multibody Systems

1986 ◽  
Vol 108 (4) ◽  
pp. 322-329 ◽  
Author(s):  
M. J. Richard ◽  
R. Anderson ◽  
G. C. Andrews
Keyword(s):  
Multibody Systems ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Rigid Bodies ◽  
New Approach ◽  
System Description ◽  
Nonlinear Equations Of Motion ◽  
Systematic Formulation ◽  
Multi Body ◽  
Entire Procedure

This paper describes the vector-network approach which is a comprehensive mathematical model for the systematic formulation of the nonlinear equations of motion of dynamic three-dimensional constrained multi-body systems. The entire procedure is a basic application of concepts of graph theory in which laws of vector dynamics have been combined. The main concepts of the method have been explained in previous publications but the work described herein is an appreciable extension of this relatively new approach. The method casts simultaneously the three-dimensional inertia equations associated with each rigid body and the geometrical expressions corresponding to the kinematic restrictions into a symmetrical format yielding the differential equations governing the motion of the system. The algorithm is eminently well suited for the computer-aided simulation of arbitrary interconnected rigid bodies; it serves as the basis for a “self-formulating” computer program which can simulate the response of a dynamic system, given only the system description.

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