A New Order-N Order-N3 Hybrid Parallelizable Algorithm for a Multi-Rigid-Body Mechanical System

1999 ◽  
Author(s):  
Kurt S. Anderson ◽  
Shanzhong Duan
Keyword(s):  
Rigid Body ◽  
State Space ◽  
Mechanical System ◽  
Equations Of Motion ◽  
Parallel System ◽  
Body Motion ◽  
System Model ◽  
New Order ◽  
Constraint Equations ◽  
Floating Base

Abstract In this paper, a new hybrid parallelizable algorithm involving formulations of different computational orders is presented for chain systems. The parallel system model is constructed through the separation of certain system interbody joints so that largely independent multibody subchain systems are formed. These sub-chains in turn interact with one another through associated unknown constrain forces fc¯ at those separated joints. Within each of the floating subchains, equations of motion for the system of bodies are produced using a recursive state space O(n) formulation, while the equations associated specifically with the floating “composite” base body are formed using a more tradition O(n3) approach. Parallel strategies are used to form and solve constraint equations between subchains concurrently. 41% computational savings can be achieved for the floating base body motion description by using O(n3) approach relative to using sequential O(n) procedure.

Dynamic Modeling and Simulation of Flexible Robots With Prismatic Joints

1990 ◽  
Vol 112 (3) ◽  
pp. 307-314 ◽  
Author(s):  
Ye-Chen Pan ◽  
R. A. Scott ◽  
A. Galip Ulsoy
Keyword(s):  
Rigid Body ◽  
Equations Of Motion ◽  
Numerical Procedure ◽  
Differential Algebraic Equations ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Integration Scheme ◽  
System Response ◽  
Constraint Equations ◽  
Prismatic Joints

A dynamic model for flexible manipulators with prismatic joints is presented in Part I of this study. Floating frames following a nominal rigid body motion are introduced to describe the kinematics of the flexible links. A Lagrangian approach is used in deriving the equations of motion. The work done by the rigid body axial force through the axial shortening of the link due to transverse deformations is included in the Lagrangian function. Kinematic constraint equations are used to describe the compatibility conditions associated with revolute joints and prismatic joints, and incorporated into the equations of motion by Lagrange multipliers. The small displacements due to the flexibility of the links are then discretized by a displacement based finite element method. Equations of motion are derived for the cases of prescribed rigid body motion as well as prescribed joint torques/forces through application of Lagrange’s equations. The equations of motion and the constraint equations result in a set of differential algebraic equations. A numerical procedure combining a constraint stabilization method and a Newmark direct integration scheme is then applied to obtain the system response. An example, previously treated in the literature, is presented to validate the modeling and solution methods used in this study.

The Global Motion of a Rigid Body Subject to Periodic Body-Fixed Torques

1995 ◽  
Author(s):  
X. Tong ◽  
B. Tabarrok
Keyword(s):  
Rigid Body ◽  
Equations Of Motion ◽  
Melnikov Method ◽  
The Body ◽  
Body Motion ◽  
Heteroclinic Orbits ◽  
Coordinate Frame ◽  
Global Motion ◽  
Stable And Unstable Manifolds ◽  
Body Subject

Abstract In this paper the global motion of a rigid body subject to small periodic torques, which has a fixed direction in the body-fixed coordinate frame, is investigated by means of Melnikov’s method. Deprit’s variables are introduced to transform the equations of motion into a form describing a slowly varying oscillator. Then the Melnikov method developed for the slowly varying oscillator is used to predict the transversal intersections of stable and unstable manifolds for the perturbed rigid body motion. It is shown that there exist transversal intersections of heteroclinic orbits for certain ranges of parameter values.

Seismic Analysis of Structures With Coulomb Friction

1983 ◽  
Vol 105 (2) ◽  
pp. 171-178 ◽  
Author(s):  
V. N. Shah ◽  
C. B. Gilmore
Keyword(s):  
Rigid Body ◽  
Coulomb Friction ◽  
Seismic Event ◽  
Seismic Analysis ◽  
Equations Of Motion ◽  
Relative Displacement ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Superposition Method ◽  
Modal Superposition Method

A modal superposition method for the dynamic analysis of a structure with Coulomb friction is presented. The finite element method is used to derive the equations of motion, and the nonlinearities due to friction are represented by pseudo-force vector. A structure standing freely on the ground may slide during a seismic event. The relative displacement response may be divided into two parts: elastic deformation and rigid body motion. The presence of rigid body motion necessitates the inclusion of the higher modes in the transient analysis. Three single degree-of-freedom problems are solved to verify this method. In a fourth problem, the dynamic response of a platform standing freely on the ground is analyzed during a seismic event.

The Dynamics of a Deformable Body Experiencing Large Displacements

1988 ◽  
Vol 55 (3) ◽  
pp. 676-680 ◽  
Author(s):  
W. P. Koppens ◽  
A. A. H. J. Sauren ◽  
F. E. Veldpaus ◽  
D. H. van Campen
Keyword(s):  
Rigid Body ◽  
Mass Matrix ◽  
Deformable Body ◽  
Equations Of Motion ◽  
Body Motion ◽  
General Description ◽  
Large Displacements ◽  
Displacement Fields ◽  
Cpu Time ◽  
Time Savings

A general description of the dynamics of a deformable body experiencing large displacements is presented. These displacements are resolved into displacements due to deformation and displacements due to rigid body motion. The former are approximated with a linear combination of assumed displacement fields. D’Alembert’s principle is used to derive the equations of motion. For this purpose, the rigid body displacements and the displacements due to deformation have to be independent. Commonly employed conditions for achieving this are reviewed. It is shown that some conditions lead to considerably simpler equations of motion and a sparser mass matrix, resulting in CPU time savings when used in a multibody program. This is illustrated with a uniform beam and a crank-slider mechanism.

Steady-State Responses of an RSRC-Type Spatial Flexible Linkage

1994 ◽  
Vol 116 (1) ◽  
pp. 264-269 ◽  
Author(s):  
R. Y. Chang ◽  
C. K. Sung
Keyword(s):  
Steady State ◽  
Equations Of Motion ◽  
Body Motion ◽  
Flexible Link ◽  
Predictive Capability ◽  
Kinematic Constraint ◽  
Constraint Equations ◽  
Steady State Responses ◽  
State Responses ◽  
Flexible Linkage

This paper presents an analytical and experimental investigation on the steady-state responses of an RSRC-type spatial flexible linkage. The kinematic analysis of the spatial rigid-body motion is performed using kinematic constraint equations to yield the linear and angular positions, velocities, and accelerations of the linkage. A mixed variational principle is, then, employed to derive the equations of motion governing the longitudinal, transverse, and torsional vibrations of the flexible link and the associated boundary conditions. Based on these equations, the steady-state responses are predicted. Finally, an RSRC-type four-bar spatial flexible linkage is constructed and the experimental study is performed to examine the predictive capability proposed in this investigation. Favorable comparisons between the analytical and experimental results are obtained.

Small Vibrations Superimposed on Non-Linear Rigid Body Motion

1997 ◽  
Author(s):  
A. L. Schwab ◽  
J. P. Meijaard
Keyword(s):  
Rigid Body ◽  
Equations Of Motion ◽  
Harmonic Balance Method ◽  
Rigid Motion ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Connecting Rod ◽  
Non Linear ◽  
Linear Differential

Abstract In the case of small elastic deformations in a flexible multi-body system, the periodic motion of the system can be modelled as a superposition of a small linear vibration and a non-linear rigid body motion. For the small deformations this analysis results in a set of linear differential equations with periodic coefficients. These equations give more insight in the vibration phenomena and are computationally more efficient than a direct non-linear analysis by numeric integration. The realization of the method in a program for flexible multibody systems is discussed which requires, besides the determination of the periodic rigid motion, the determination of the linearized equations of motion. The periodic solutions for the linear equations are determined with a harmonic balance method, while transient solutions are obtained by averaging. The stability of the periodic solution is considered. The method is applied to a pendulum with a circular motion of its support point and a slider-crank mechanism with flexible connecting rod. A comparison is made with previous non-linear results.

Steady-State Responses of an RSRC-Type Spatial Flexible Linkages

1992 ◽  
Author(s):  
R. Y. Chang ◽  
C. K. Sung
Keyword(s):  
Steady State ◽  
Equations Of Motion ◽  
Body Motion ◽  
Flexible Link ◽  
Predictive Capability ◽  
Kinematic Constraint ◽  
Constraint Equations ◽  
Steady State Responses ◽  
State Responses ◽  
Flexible Linkage

Abstract This paper presents an analytical and experimental investigation on the steady-state responses of an RSRC-type spatial flexible linkage. The kinematic analysis of the spatial rigid-body motion is performed using kinematic constraint equations to yield linear and angular positions, velocities and accelerations of the linkage. A mixed variational principle is, then, employed to derive the equations of motion governing the longitudinal, transversal and torsional vibrations of the flexible link and the associated boundary conditions. Based on these equations, the steady-state responses are predicted. Finally, an RSRC-type four-bar spatial flexible linkage is constructed and the experimental study is performed to examine the predictive capability proposed in this investigation. Favorable comparisons between the analytical and experimental results are obtained.

On the Dynamics of Elastic Multibody Systems

1999 ◽  
Vol 52 (9) ◽  
pp. 275-303 ◽  
Author(s):  
Hartmut Bremer
Keyword(s):  
Rigid Body ◽  
Equations Of Motion ◽  
Complex Structure ◽  
Body Motion ◽  
Plate Vibrations ◽  
Elastic Bodies ◽  
Elastic Multibody Systems ◽  
Moving Beam ◽  
Dynamical Coupling ◽  
Left And Right

Due to the highly complex structure of the equations of motion, there exists a basic demand for procedures with minimum effort. This is achieved by the projection method applied to systems consisting of rigid and elastic bodies which undergo fast rigid body motions with superimposed small elastic deflections. The outlined method leads to different left and right Jacobians for the partial differential equations along with simple operators for determination of corresponding boundary conditions. When a Ritz series expansion is used for approximate solution, the left and right Jacobians become identical. The procedure is demonstrated for plate vibrations without rigid body motion and then applied to a single moving beam and finally augmented to multi beam systems. Special attention is hereby given to the effects of dynamical coupling which influence bending stiffness and connect bending with torsion. This review article has 55 references.

scholarly journals An Efficient Modelling of Flexible Airships

2006 ◽  
Author(s):  
Selima Bennaceur ◽  
Naoufel Azouz ◽  
Djaber Boukraa
Keyword(s):  
Rigid Body ◽  
Equations Of Motion ◽  
General System ◽  
Rigid Body Motion ◽  
The Body ◽  
Body Motion ◽  
Modal Synthesis ◽  
Stiffness Matrices ◽  
Updated Lagrangian ◽  
Convenient Technique

This paper presents an efficient modelling of airships with small deformations moving in an ideal fluid. The formalism is based on the Updated Lagrangian Method (U.L.M.). This formalism proposes to take into account the coupling between the rigid body motion and the deformation as well as the interaction with the surrounding fluid. The resolution of the equations of motion is incremental. The behaviour of the airship is defined relatively to a virtual non-deformed reference configuration moving with the body. The flexibility is represented by a deformation modes issued from a Finite Elements Method analysis. The increment of rigid body motion is represented similarly by rigid modes. A modal synthesis is used to solve the general system equations of motion. Time constant matrices appears (i.e. mass and structural stiffness matrices), and we show a convenient technique to actualise the time dependant matrices.

A Variationally Consistent Approach to Constrained Motion

2016 ◽  
Vol 83 (5) ◽  
Author(s):  
John T. Foster
Keyword(s):  
Rigid Body ◽  
Equations Of Motion ◽  
A Priori ◽  
Nonholonomic Systems ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Constrained Motion ◽  
Consistent Approach ◽  
Holonomic And Nonholonomic Systems ◽  
D'alembert's Principle

A variationally consistent approach to constrained rigid-body motion is presented that extends D'Alembert's principle in a way that has a form similar to Kane's equations. The method results in minimal equations of motion for both holonomic and nonholonomic systems without a priori consideration of preferential coordinates.

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