Free-body-diagram method for the uniqueness analysis of reactions and driving forces in redundantly constrained multibody systems with nonholonomic constraints

2019 ◽  
Vol 133 ◽  
pp. 329-346 ◽  
Author(s):  
Marcin Pękal ◽  
Marek Wojtyra ◽  
Janusz Frączek
Keyword(s):  
Multibody Systems ◽  
Driving Forces ◽  
Nonholonomic Constraints ◽  
Diagram Method ◽  
Constrained Multibody Systems ◽  
Free Body Diagram ◽  
Free Body

A Reduced and Linearized High Fidelity Waveboard Multibody Model for Stability Analysis

2022 ◽  
Author(s):  
Alfonso García-Agúndez Blanco ◽  
Daniel García Vallejo ◽  
Emilio Freire ◽  
Aki Mikkola
Keyword(s):  
Multibody Systems ◽  
Jacobian Matrix ◽  
Equations Of Motion ◽  
Linear Equations ◽  
Nonholonomic Constraints ◽  
Design Parameters ◽  
Constrained Multibody Systems ◽  
Multibody Model ◽  
The Stability ◽  
Nonlinear Equations Of Motion

Abstract In this paper, the stability of a waveboard, a human propelled two-wheeled vehicle consisting in two rotatable platforms, joined by a torsion bar and supported on two caster wheels, is analysed. A multibody model with holonomic and nonholonomic constraints is used to describe the system. The nonlinear equations of motion, which constitute a Differential-Algebraic system of equations (DAE system), are linearized along the steady forward motion resorting to a recently validated linearization procedure, which allows the maximum possible reduction of the linearized equations of motion of constrained multibody systems. The approach enables the generation of the Jacobian matrix in terms of the geometric and dynamic parameters of the multibody system, and the eigenvalues of the system are parameterized in terms of the design parameters. The resulting minimum set of linear equations leads to the elimination of spurious null eigenvalues, while retaining all the stability information in spite of the reduction of the Jacobian matrix. The linear stability results of the waveboard obtained in previous work are validated with this approach. The procedure shows an excellent computational efficiency with the waveboard, its utilization being highly advisable to linearize the equations of motion of complex constrained multibody systems.

On the Use of the Canonical Equations of Motion for the Dynamic Analysis of Constrained Multibody Systems

1992 ◽  
Author(s):  
E. Bayo ◽  
J. M. Jimenez
Keyword(s):  
Dynamic Analysis ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Numerical Algorithms ◽  
Constrained Multibody Systems ◽  
Constrained Mechanical Systems ◽  
First Order ◽  
Canonical Variables ◽  
Lagrange’S Multipliers

Abstract We investigate in this paper the different approaches that can be derived from the use of the Hamiltonian or canonical equations of motion for constrained mechanical systems with the intention of responding to the question of whether the use of these equations leads to more efficient and stable numerical algorithms than those coming from acceleration based formalisms. In this process, we propose a new penalty based canonical description of the equations of motion of constrained mechanical systems. This technique leads to a reduced set of first order ordinary differential equations in terms of the canonical variables with no Lagrange’s multipliers involved in the equations. This method shows a clear advantage over the previously proposed acceleration based formulation, in terms of numerical efficiency. In addition, we examine the use of the canonical equations based on independent coordinates, and conclude that in this second case the use of the acceleration based formulation is more advantageous than the canonical counterpart.

Dynamics of Flexible Beams and Plates in Large Overall Motions

1992 ◽  
Vol 59 (4) ◽  
pp. 991-999 ◽  
Author(s):  
Z. E. Boutaghou ◽  
Arthur G. Erdman ◽  
Henryk K. Stolarski
Keyword(s):  
Dynamic Response ◽  
Nonlinear Interaction ◽  
Multibody Systems ◽  
Present Theory ◽  
Rigid Body Dynamics ◽  
Flexible Beams ◽  
Constrained Multibody Systems ◽  
Dynamic Stiffening ◽  
Body Dynamics ◽  
Arbitrary Representation

The dynamic response of flexible beams, plates, and solids undergoing arbitrary spatial motions are systematically derived via a proposed approach. This formulation is capable of incorporating arbitrary representation of the kinematics of deformation, phenomenon of dynamic stiffening, and complete nonlinear interaction between elastic and rigid-body dynamics encountered in constrained multibody systems. It is shown that the present theory captures the phenomenon of dynamic stiffening due to the transfer of the axial and membrane forces to the bending equations of beams and plates, respectively. Examples are presented to illustrate the proposed formulations.

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
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