A unified dynamic algorithm for wheeled multibody systems with passive joints and nonholonomic constraints

2017 ◽  
Vol 41 (4) ◽  
pp. 317-346 ◽  
Author(s):  
Shaukat Ali
Keyword(s):  
Multibody Systems ◽  
Nonholonomic Constraints ◽  
Dynamic Algorithm

scholarly journals Simulation of Multibody Systems with Nonholonomic Constraints

PAMM ◽  
2003 ◽  
Vol 2 (1) ◽  
pp. 132-133
Author(s):  
G. Kielau ◽  
P. Maißer
Keyword(s):  
Multibody Systems ◽  
Nonholonomic Constraints

An Ordinary Differential Equation Formulation for Multibody Dynamics: Nonholonomic Constraints

2016 ◽  
Vol 17 (1) ◽  
Author(s):  
Edward J. Haug
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Multibody Systems ◽  
Mass Matrix ◽  
Equations Of Motion ◽  
Computational Cost ◽  
Nonholonomic Constraints ◽  
State Variables ◽  
Well Conditioning ◽  
Fifth Order

A method is presented for formulating and numerically integrating ordinary differential equations of motion for nonholonomically constrained multibody systems. Tangent space coordinates are defined in configuration and velocity spaces as independent generalized coordinates that serve as state variables in the formulation, yielding ordinary differential equations of motion. Orthogonal-dependent coordinates and velocities are used to enforce constraints at position, velocity, and acceleration levels. Criteria that assure accuracy of constraint satisfaction and well conditioning of the reduced mass matrix in the equations of motion are used as the basis for updating local coordinates on configuration and velocity constraint manifolds, transparent to the user and at minimal computational cost. The formulation is developed for multibody systems with nonlinear holonomic constraints and nonholonomic constraints that are linear in velocity coordinates and nonlinear in configuration coordinates. A computational algorithm for implementing the approach is presented and used in the solution of three examples: one planar and two spatial. Numerical results using a fifth-order Runge–Kutta–Fehlberg explicit integrator verify that accurate results are obtained, satisfying all the three forms of kinematic constraint, to within error tolerances that are embedded in the formulation.

Selective Generalized Coordinates Partitioning Method for Multibody Systems With Non-Holonomic Constraints

2017 ◽  
Author(s):  
Ayman A. Nada ◽  
Abdullateef H. Bashiri
Keyword(s):  
Multibody Systems ◽  
Large Scale ◽  
Research Work ◽  
Nonholonomic Constraints ◽  
Integration Step ◽  
Large Scale Systems ◽  
Holonomic Constraints ◽  
Generalized Coordinates ◽  
Holonomic And Nonholonomic Constraints ◽  
Multi Body

The goal of this research work is to extend the method of generalized coordinates partitioning to include both holonomic and nonholonomic constraints. Furthermore, the paper proposes a method for selective coordinates for integration instead of identifying a set of independent coordinates at each integration step. The effectiveness of the proposed method is presented and compared with full-coordinates integration as well as generalized co-ordinates partitioning method. The proposed method can treat large-scale systems as one of the main advantages of multi-body systems.

Formulation and Implementation of Nonholonomic Constraints in the Analysis of Multibody Systems Using Joint Coordinates

1996 ◽  
Author(s):  
Claus Balling
Keyword(s):  
Multibody Systems ◽  
Relative Velocity ◽  
Nonholonomic Constraint ◽  
Nonholonomic Constraints ◽  
General Purpose ◽  
Mutual Interaction ◽  
Cartesian Coordinates ◽  
Joint Coordinates ◽  
Moving Points ◽  
Two Bodies

Abstract A general formulation for analysis of spatial multibody systems subjected to nonholonomic constraints is presented. Nonholonomic constraints are usually formulated in Cartesian coordinates constraining the relative velocity or acceleration between some (fixed or moving) points on two bodies in mutual interaction or a point on one body with respect to ground. The formulation involves a specific type of nonholonomic constraint (rolling disk on a surface) in terms of joint coordinates and perform the implementation in a general purpose program.

Quasi-velocities definition in Lagrangian multibody dynamics

2021 ◽  
pp. 095440622199585
Author(s):  
S Mohammad Mirtaheri ◽  
Hassan Zohoor
Keyword(s):  
Computational Efficiency ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Nonholonomic Constraints ◽  
Matrix Inversion ◽  
Lagrangian Mechanics ◽  
Holonomic Constraints ◽  
Velocity Constraints ◽  
Analytical Relations ◽  
Explicit Equations Of Motion

Based on Lagrangian mechanics, use of velocity constraints as a special set of quasi-velocities helps derive explicit equations of motion. The equations are applicable to holonomic and nonholonomic constrained multibody systems. It is proved that in proposed quasi-spaces, the Lagrange multipliers are eliminated from equations of motion; however, it is possible to compute these multipliers once the equations of motion have been solved. The novelty of this research is employing block matrix inversion to find the analytical relations between the parameters of quasi-velocities and equations of motion. In other words, this research identifies arbitrary submatrices and their effects on equations of motion. Also, the present study aimed to provide appropriate criteria to select arbitrary parameters to avoid singularity, reduce constraints violations, and improve computational efficiency. In order to illustrate the advantage of this approach, the simulation results of a 3-link snake-like robot with nonholonomic constraints and a four-bar mechanism with holonomic constraints are presented. The effectiveness of the proposed approach is demonstrated by comparing the constraints violation at the position and velocity levels, conservation of the total energy, and computational efficiency with those obtained via the traditional methods.

Energy Consistent Time Integration of Non-Conservative Hybrid Multibody Systems

2009 ◽  
Author(s):  
Stefan Uhlar ◽  
Peter Betsch
Keyword(s):  
Multibody Systems ◽  
Time Integration ◽  
Nonholonomic Constraints ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Hybrid Energy ◽  
Joint Friction ◽  
Time Stepping ◽  
Time Integrators ◽  
Coupling Constraints

The contribution at hand deals with the energy-consistent time integration of hybrid multibody systems. The coupling of both rigid and flexible components is facilitated by the introduction of so called coupling constraints, leading to a set of differential algebraic equations governing the motion of the hybrid system. For the modeling of rigid components we rely on the so called rotationless formulation which makes possible the design of mechanical time integrators. In this connection modeling techniques such as the coordinate augmentation, nonholonomic constraints, control issues and modeling of joint friction will be addressed. This leads to a unified approach for the modeling of rigid and flexible bodies, rendering a hybrid-energy-momentum-consistent time stepping scheme. The performance will be demonstrated with the example of a spatial nonholonomic manipulator.

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