Contact/Impact in Hybrid Parameter Multiple Body Mechanical Systems—Extensions for Higher-Order Continuum Models

1998 ◽  
Vol 120 (1) ◽  
pp. 142-144 ◽  
Author(s):  
Alan A. Barhorst
Keyword(s):  
Mechanical Systems ◽  
Nonholonomic Constraints ◽  
Higher Order ◽  
Constrained Motion ◽  
Momentum Exchange ◽  
Contact Impact ◽  
Systematic Formulation ◽  
Impact Motion ◽  
Boundary Equations ◽  
Hybrid Differential Equations

In recent work the author presented a systematic formulation of hybrid parameter multiple body mechanical systems (HPMBS) undergoing contact/impact motion. The method rigorously models all motion regimes of hybrid multiple body systems (i.e., free motion, contact/impact motion, and constrained motion), utilizing minimal sets of hybrid differential equations; Lagrange multipliers are not required. The contact/impact regime was modeled via the idea of instantaneously applied nonholonomic constraints. The technique previously presented did not include the possibility of continuum assumptions along the lines of Timoshenko beams, higher order plate theories, or rational theories considering intrinsic spin-inertia. In this technical brief, the above-mentioned method is extended to include the higher-order continuum assumptions which eliminates the continuum shortfalls from the previous work. The main contributions of this work include: 1) the previous work is rigorously extended, and 2) the fact that coefficients of restitution are not required for modeling the momentum exchange between motion regimes of HPMBS. The field and boundary equations provide the needed extra equations that are used to supply post-collision pointwise relationships for the generalized velocities and velocity fields.

Modeling Contact/Impact in Hybrid Parameter Multiple Body Mechanical Systems: Extensions for Higher Order Continuum Models

1995 ◽  
Author(s):  
Alan A. Barhorst
Keyword(s):  
Mechanical Systems ◽  
Higher Order ◽  
Continuum Models ◽  
Timoshenko Beams ◽  
Constrained Motion ◽  
Contact Impact ◽  
Systematic Formulation ◽  
Impact Motion ◽  
Hybrid Differential Equations ◽  
The Continuum

Abstract In recent work the author presented a systematic formulation of hybrid parameter multiple body mechanical systems undergoing contact/impact motion. The method rigorously modeled all motion regimes of hybrid multiple body systems (i.e. free motion, contact/impact motion, and constrained motion), utilizing minimal sets of hybrid differential equations. The contact/impact regime was modeled via the idea of instantaneous non-holonomic constraint application. The technique previously presented did not include the possibility of continuum assumptions along the lines of Timoshenko beams, higher order plate theories, or rational theories considering intrinsic spin-inertia. In this paper, the above mentioned method is extended to include the higher order continuum assumptions which eliminates some of the continuum shortfalls from the previous work.

Simulation of Constrained Mechanical Systems—Part II: Explicit Numerical Integration

2012 ◽  
Vol 79 (4) ◽  
Author(s):  
David J. Braun ◽  
Michael Goldfarb
Keyword(s):  
Mechanical Systems ◽  
Nonholonomic Constraints ◽  
Direct Consequence ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Constrained Motion ◽  
Constrained Mechanical Systems ◽  
Holonomic And Nonholonomic Constraints ◽  
Long Time ◽  
Constraint Correction

This paper presents an explicit to integrate differential algebraic equations (DAEs) method for simulations of constrained mechanical systems modeled with holonomic and nonholonomic constraints. The proposed DAE integrator is based on the equation of constrained motion developed in Part I of this work, which is discretized here using explicit ordinary differential equation schemes and applied to solve two nontrivial examples. The obtained results show that this integrator allows one to precisely solve constrained mechanical systems through long time periods. Unlike many other implicit DAE solvers which utilize iterative constraint correction, the presented DAE integrator is explicit, and it does not use any iteration. As a direct consequence, the present formulation is simple to implement, and is also well suited for real-time applications.

Equations of Motion for Nonholonomic, Constrained Dynamical Systems via Gauss’s Principle

1993 ◽  
Vol 60 (3) ◽  
pp. 662-668 ◽  
Author(s):  
R. E. Kalaba ◽  
F. E. Udwadia
Keyword(s):  
Dynamical Systems ◽  
Closed Form ◽  
Programming Problem ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Closed Form Solution ◽  
Nonholonomic Constraints ◽  
Form Solution ◽  
Constrained Motion ◽  
Constraint Forces

In this paper we develop an analytical set of equations to describe the motion of discrete dynamical systems subjected to holonomic and/or nonholonomic Pfaffian equality constraints. These equations are obtained by using Gauss’s Principle to recast the problem of the constrained motion of dynamical systems in the form of a quadratic programming problem. The closed-form solution to this programming problem then explicitly yields the equations that describe the time evolution of constrained linear and nonlinear mechanical systems. The direct approach used here does not require the use of any Lagrange multipliers, and the resulting equations are expressed in terms of two different classes of generalized inverses—the first class pertinent to the constraints, the second to the dynamics of the motion. These equations can be numerically solved using any of the standard numerical techniques for solving differential equations. A closed-form analytical expression for the constraint forces required for a given mechanical system to satisfy a specific set of nonholonomic constraints is also provided. An example dealing with the position tracking control of a nonlinear system shows the power of the analytical results and provides new insights into application areas such as robotics, and the control of structural and mechanical systems.

Contact/Impact in Hybrid Parameter Multiple Body Mechanical Systems

1995 ◽  
Vol 117 (4) ◽  
pp. 559-569 ◽  
Author(s):  
A. A. Barhorst ◽  
L. J. Everett
Keyword(s):  
Initial Conditions ◽  
System Modeling ◽  
Variational Calculus ◽  
Nonholonomic Constraints ◽  
Modeling Methodology ◽  
Starting Point ◽  
Holonomic And Nonholonomic Constraints ◽  
Contact Impact ◽  
Nature Of Time ◽  
Hybrid Differential Equations

The multiple motion regime (free/constrained) dynamics of hybrid parameter multiple body (HPMB) systems is addressed. Impact response has characteristically been analyzed using impulse-momentum techniques. Unfortunately, the classical methods for modeling complex HPMB systems are energy based and have proven ineffectual at modeling impact. The problems are exacerbated by the problematic nature of time varying constraint conditions. This paper outlines the reformulation of a recently developed HPMB system modeling methodology into an impulse-momentum formulation, which systematically handles the constraints and impact. The starting point for this reformulation is a variational calculus based methodology. The variational roots of the methodology allows rigorous equation formulation which includes the complete nonlinear hybrid differential equations and boundary conditions. Because the methodology presented in this paper is formulated in the constraint-free subspace of the configuration space, both holonomic and nonholonomic constraints are automatically satisfied. As a result, the constraint-addition/deletion algorithms are not needed. Generalized forces of constraint can be directly calculated via the methodology, so the condition for switching from one motion regime to another is readily determined. The resulting equations provides a means to determine after impact velocities (and velocity fields for distributed bodies) which provide the after collision initial conditions. Finally the paper demonstrates, via example, how to apply the methodology to contact/impact in robotic manipulators and structural systems.

New Formulations on Acceleration Energies in Analytical Dynamics

2016 ◽  
Vol 823 ◽  
pp. 43-48
Author(s):  
Iuliu Negrean ◽  
Kalman Kacso ◽  
Claudiu Schonstein ◽  
Adina Duca ◽  
Florina Rusu ◽  
...  
Keyword(s):  
Dynamic Behavior ◽  
Fast Moving ◽  
Mechanical Systems ◽  
Higher Order ◽  
Dynamic Study ◽  
Final Part ◽  
Transient Phase ◽  
Dynamic Aspect ◽  
Analytical Dynamics ◽  
Time Variations

This paper presents new formulations on the higher order motion energies that are applied in the dynamic study of multibody mechanical systems in keeping with the researches of the main author. The analysis performed in this paper highlights the importance of motion energies of higher order in the study of dynamic behavior of fast moving mechanical systems, as well as in transient phase of motion. In these situations, are developed higher order time variations of the linear and angular accelerations. As a result, in the final part of this paper is presented an application that emphasizes this essential dynamic aspect regarding the higher order acceleration energies.

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