Efficient Impulse Momentum Formulation for Multi-Flexible Body Systems

2009 ◽  
Author(s):  
Rudranarayan M. Mukherjee ◽  
Kurt S. Anderson
Keyword(s):  
Equations Of Motion ◽  
Divide And Conquer ◽  
Flexible Bodies ◽  
Disassembly Process ◽  
Closed Loop Systems ◽  
Bilateral Constraints ◽  
Impulsive Loads ◽  
Tree Map ◽  
Unilateral And Bilateral Constraints ◽  
Kinematic Joint

This paper presents the generalization of the divide and conquer impulse momentum formulation to systems with flexible bodies. The approach utilizes a hierarchic assembly-disassembly process by traversing the system topology in a binary tree map to solve for the jumps in the system generalized speeds and the constraint impulsive loads in linear and logarithmic cost in serial and parallel implementations, respectively. The coupling between the unilateral and bilateral constraints is handled efficiently through the use of kinematic joint definitions. The equations of motion for the system are produced in a hierarchic sub-structured form. The generalized impulse momenta equations of flexible bodies are derived using a projection method. The equations are then cast into a format amenable to be incorporated in the basic divide and conquer form. The solution of the equations using the hierarchic assembly disassembly process by using the boundary conditions are discussed for free floating, anchored trees and kinematically closed loop systems.

Parallel Algorithm for Modeling Constrained Multi-Flexible Body System Dynamics

2013 ◽  
Author(s):  
Rudranarayan Mukherjee ◽  
Jeremy Laflin
Keyword(s):  
Parallel Implementation ◽  
Equations Of Motion ◽  
Small Deformation ◽  
The Body ◽  
Deformation Field ◽  
Flexible Body ◽  
Disassembly Process ◽  
Joint Constraints ◽  
Kinematic Loop ◽  
Kinematic Joint

This paper presents an algorithm for modeling the dynamics of multi-flexible body systems in closed kinematic loop configurations where the component bodies are modeled using the large displacement small deformation formulation. The algorithm uses a hierarchic assembly disassembly process in parallel implementation and a recursive assembly disassembly process in serial implementation to achieve highly efficient simulation turn-around times. The operational inertias arising from the rigid body modes of motion at the joint locations on a component body are modified to account for the nonlinear inertial effects and body forces arising from the body based deformations. Traditional issues, such as motion induced stiffness and temporal invariance of deformation field related inertia terms, are robustly addressed in this algorithm. The algorithm uses a mixed set of coordinates viz. (i) absolute coordinates for expressing the equations of motion of a body fixed reference frame, (ii) relative or internal coordinates to express the kinematic joint constraints and (iii) body fixed coordinates to account for the body’s deformation field. The kinematic joint constraints and the closed loop constraints are treated alike through the formalism of relative coordinates, joint motion spaces and their orthogonal complements. Verification of the algorithm is demonstrated using the planar fourbar mechanism problem that has been traditionally used in literature.

Using Nonlinear Recursive Formulation for the Kinematic Analysis of Human Biomechanical Systems

2012 ◽  
Vol 482-484 ◽  
pp. 938-941
Author(s):  
Yunn Lin Hwang ◽  
Wei Hsin Gau ◽  
Wen Huang Lin ◽  
Shen Jenn Hwang ◽  
Chien Hsin Chen
Keyword(s):  
Kinematic Analysis ◽  
Equations Of Motion ◽  
Open Loop ◽  
Body Motion ◽  
Displacement Fields ◽  
Flexible Bodies ◽  
Recursive Formulation ◽  
Closed Loop Systems ◽  
Generalized Newton ◽  
Time Invariant

Generally speaking, the human biomechanical systems can be classified into two main groups: open-loop and closed-loop systems. In this investigation, the nonlinear recursive formulation is developed for the kinematic analysis of human biomechanical systems. The nonlinear generalized Newton-Euler equations are developed for flexible bodies that undergo large translational and rotational displacements. These equations are formulated in terms of a set of time invariant scalars, vectors and matrices that depend on the spatial coordinates as well as the assumed displacement fields, and these time invariant quantities represent the dynamic coupling between the rigid body motion and elastic deformation. The formulation to solve equations of motion for human biomechanical systems consisting of interconnected rigid and flexible bodies is presented in this paper.

Operational Space Impulse Momentum Algorithm for Flexible Multibody Systems With Generalized Topologies

2011 ◽  
Author(s):  
Rudranarayan M. Mukherjee
Keyword(s):  
Multibody Systems ◽  
Divide And Conquer ◽  
Closed Loops ◽  
Operational Space ◽  
Bilateral Constraints ◽  
Tree Topologies ◽  
Rigid Multibody Systems ◽  
Divide And Conquer Scheme ◽  
Tree Map ◽  
Rigid Multibody

This paper presents a new methodology for modeling discontinuous dynamics of flexible and rigid multibody systems based on the impulse momentum formulation. The new methodology is based on the seminal idea of the divide and conquer scheme for modeling the forward dynamics of rigid multibody systems. While a similar impulse momentum approach has been demonstrated for multibody systems in tree topologies, this paper presents the generalization of the approach to systems in generalized topologies including many coupled kinematically closed loops. The approach utilizes a hierarchic assembly-disassembly process by traversing the system topology in a binary tree map to solve for the jumps in the system generalized speeds and the constraint impulsive loads in linear and logarithmic cost in serial and parallel implementations, respectively. The coupling between the unilateral and bilateral constraints is handled efficiently through the use of kinematic joint definitions. The generalized impulse momenta equations of flexible bodies are derived using a projection method.

Parallel Algorithm for Modeling Multi-Rigid Body System Dynamics With Nonholonomic Constraints

2013 ◽  
Author(s):  
Rudranarayan Mukherjee ◽  
Pawel Malczyk
Keyword(s):  
Rigid Body ◽  
Parallel Implementation ◽  
Equations Of Motion ◽  
Numerical Test ◽  
Nonholonomic Constraints ◽  
Test Case ◽  
Central Idea ◽  
Acceleration Level ◽  
Disassembly Process ◽  
Kinematic Joint

This paper presents a new algorithm for serial or parallel implementation of computer simulations of the dynamics of multi-rigid body systems subject to nonholonomic and holonomic constraints. The algorithm presents an elegant approach for eliminating the nonholonomic constraints explicitly from the equations of motion and implicitly expressing them in terms of nonlinear coupling in the operational inertias of the bodies subject to these constraints. The resulting equations are in the same form as those of a body subject to kinematic joint constraints. This enables the nonholohomic constraints to be seamlessly treated in either a (i) recursive or (ii) hierarchic assembly-disassembly process for solving the equations of motion of generalized multi-rigid body systems in serial or parallel implementations. The algorithm is non-iterative and although the nonholonomic constraints are imposed at the acceleration level, constraint satisfaction is excellent as demonstrated by the numerical test case implemented to verify the algorithm. The paper presents procedures for handling both cases where the nonholonomic constraints are imposed between terminal bodies of a system and the environment as well as when the constraints are imposed between bodies in the interior of the system topology. The algorithm uses a mixed set of coordinates and is built on the central idea of eliminating either constraint loads or relative accelerations from the equations of motion by projecting the equations of motion into the motion subspaces or their orthogonal complements.

Recursive Method for the Dynamic Analysis of Open-Loop Flexible Multibody Systems

2003 ◽  
Author(s):  
Yunn-Lin Hwang
Keyword(s):  
Dynamic Analysis ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Open Loop ◽  
Flexible Multibody Systems ◽  
Recursive Method ◽  
Flexible Bodies ◽  
System Equations ◽  
Generalized Newton ◽  
Time Invariant

The main objective of this paper is to develop a recursive method for the dynamic analysis of open-loop flexible multibody systems. The nonlinear generalized Newton-Euler equations are used for flexible bodies that undergo large translational and rotational displacements. These equations are formulated in terms of a set of time invariant scalars, vectors and matrices that depend on the spatial coordinates as well as the assumed displacement fields, and these time invariant quantities represent the dynamic coupling between the rigid body motion and elastic deformation. The method to solve for the equations of motion for open-loop systems consisting of interconnected rigid and flexible bodies is presented in this investigation. This method applies recursive method with the generalized Newton-Euler method for flexible bodies to obtain a large, loosely coupled system equations of motion. The solution techniques used to solve for the system equations of motion can be more efficiently implemented in the vector or digital computer systems. The algorithms presented in this investigation are illustrated by using cylindrical joints that can be easily extended to revolute, slider and rigid joints. The basic recursive formulations developed in this paper are demonstrated by two numerical examples.

A Recursive Hybrid Time-Stepping Scheme for Intermittent Contact in Multi-Rigid-Body Dynamics

2009 ◽  
Vol 4 (4) ◽  
Author(s):  
Kishor D. Bhalerao ◽  
Kurt S. Anderson ◽  
Jeffrey C. Trinkle
Keyword(s):  
Rigid Body ◽  
Linear Complementarity Problem ◽  
Complementarity Problem ◽  
Linear Complementarity ◽  
Rigid Body Dynamics ◽  
Divide And Conquer ◽  
Double Pendulum ◽  
Time Stepping ◽  
Bilateral Constraints ◽  
Intermittent Contact

This paper describes a novel method for the modeling of intermittent contact in multi-rigid-body problems. We use a complementarity based time-stepping scheme in Featherstone’s divide and conquer framework to efficiently model the unilateral and bilateral constraints in the system. The time-stepping scheme relies on impulse-based equations and does not require explicit collision detection. A set of complementarity conditions is used to model the interpenetration constraint and a linearized friction cone is used to yield a linear complementarity problem. The divide and conquer framework ensures that the size of the resulting mixed linear complementarity problem is independent of the number of bilateral constraints in the system. This makes the proposed method especially efficient for systems where the number of bilateral constraints is much greater than the number of unilateral constraints. The method is demonstrated by applying it to a falling 3D double pendulum.

Constraint Wrench Formulation for Closed-Loop Systems Using Two-Level Recursions

2007 ◽  
Vol 129 (12) ◽  
pp. 1234-1242 ◽  
Author(s):  
Himanshu Chaudhary ◽  
Subir Kumar Saha
Keyword(s):  
Lagrange Multipliers ◽  
Spanning Tree ◽  
Closed Loop ◽  
Equations Of Motion ◽  
Constraint Forces ◽  
Minimal Set ◽  
Closed Loops ◽  
Closed Loop Systems ◽  
Subsystem Level ◽  
Body Level

In order to compute the constraint moments and forces, together referred here as wrenches, in closed-loop mechanical systems, it is necessary to formulate a dynamics problem in a suitable manner so that the wrenches can be computed efficiently. A new constraint wrench formulation for closed-loop systems is presented in this paper using two-level recursions, namely, subsystem level and body level. A subsystem is referred here as the serial- or tree-type branches of a spanning tree obtained by cutting the appropriate joints of the closed loops of the system at hand. For each subsystem, unconstrained Newton–Euler equations of motion are systematically reduced to a minimal set in terms of the Lagrange multipliers representing the constraint wrenches at the cut joints and the driving torques/forces provided by the actuators. The set of unknown Lagrange multipliers and the driving torques/forces associated to all subsystems are solved in a recursive fashion using the concepts of a determinate subsystem. Next, the constraint forces and moments at the uncut joints of each subsystem are calculated recursively from one body to another. Effectiveness of the proposed algorithm is illustrated using a multiloop planar carpet scraping machine and the spatial RSSR (where R and S stand for revolute and spherical, respectively) mechanism.

Fast Far-Field Potential Evaluation in Multibody-Based Simulations of Biopolymers

2013 ◽  
Author(s):  
Mohammad Poursina ◽  
Kurt S. Anderson
Keyword(s):  
Potential Field ◽  
Equations Of Motion ◽  
Charged Particles ◽  
Field Potential ◽  
Divide And Conquer ◽  
Coarse Grained ◽  
Mathematical Framework ◽  
Far Field ◽  
Geometrical Properties ◽  
Divide And Conquer Scheme

A novel algorithm to approximate the long-range potential field in multiscale simulations of biopolymers is presented. These models contain various domains including single particles, as well as regions with coarse-grained clusters in which high frequency modes of motion are suppressed. Herein, coarse-grained regions are formed via treating groups of atoms as rigid and/or flexible bodies/clusters connected together via kinematic joints, and as such, multibody dynamic techniques are used to form and solve the equations of motion. In such simulations with n particles, the evaluation of the potential field with computational complexity of O(n2), if not performed wisely, may become a bottleneck. This paper presents the approximation of the potential field due to the interaction between a charged particle and a body containing charged particles. This approximation is expressed in terms of physical and geometrical properties of the bodies such as the entire charge of the cluster and a pseudo-inertia tensor. Further, a divide-and-conquer scheme is introduced to implement the presented far-field potential evaluations. In this scheme adjacent charged bodies are combined together to form new bodies. The mathematical framework to create these new assemblies is presented. Then the potential of the resulting bodies on the charged particles which are far from them are recursively calculated.

Divide-and-Conquer Based Adaptive Coarse Grained Simulation of RNA

2010 ◽  
Author(s):  
Mohammad Poursina ◽  
Kishor Bhalerao ◽  
Kurt Anderson
Keyword(s):  
Molecular Modeling ◽  
Degrees Of Freedom ◽  
Traditional Approach ◽  
Equations Of Motion ◽  
Critical Role ◽  
Divide And Conquer ◽  
Coarse Grained ◽  
Biomolecular Systems ◽  
Spatial And Temporal Scales ◽  
O 10

Molecular modeling has gained increasing importance in recent years for predicting important structural properties of large biomolecular systems such as RNA which play a critical role in various biological processes. Given the complexity of biopolymers and their interactions within living organisms, efficient and adaptive multi-scale modeling approaches are necessary if one is to reasonably perform computational studies of interest. These studies nominally involve multiple important physical phenomena occurring at different spatial and temporal scales. These systems are typically characterized by large number of degrees of freedom O(103) – O(107). The temporal domains range from sub-femto seconds (O(10−16)) associated with the small high frequency oscillations of individual tightly bonded atoms to milliseconds (O(10−3)) or greater for the larger scale conformational motion. The traditional approach for molecular modeling involved fully atomistic models which results in fully decoupled equations of motion. The problems with this approach are well documented in literature.

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