Efficient Direct Differentiation Sensitivity Analysis for General Multi-Rigid-Body Dynamic Systems

2001 ◽  
Author(s):  
Yuhung Hsu ◽  
Kurt S. Anderson
Keyword(s):  
Sensitivity Analysis ◽  
Rigid Body ◽  
Design Optimization ◽  
Dynamic Systems ◽  
Computationally Efficient ◽  
Rigid Body Dynamic ◽  
Direct Differentiation ◽  
Computational Performance ◽  
Analysis Scheme ◽  
Body Dynamic

Abstract Sensitivity analysis plays an important role in modern engineering applications where design optimization is desired. A computationally efficient sensitivity analysis scheme is presented in this paper in an effort to facilitate design optimization as it pertains to general, complex multi-rigid-body dynamic systems. Based on the underlying velocity space projection, state space formulation, and direct differentiation approach, the first-order sensitivity information can be efficiently determined in a fully recursive manner for general multi-rigid-body dynamic systems involving an arbitrary number of closed loops. The overall computational expense of this method is bilinear in the number of design variables and the number of system generalized coordinates. The solution accuracy and the computational performance are demonstrated by several numerical examples.

Improved “Order-N” Performance Algorithm for the Simulation of Constrained Multi-Rigid-Body Dynamic Systems

2001 ◽  
Author(s):  
Kurt S. Anderson
Keyword(s):  
Rigid Body ◽  
Dynamic Systems ◽  
Constraint Violation ◽  
Closed Loops ◽  
Rigid Body Dynamic ◽  
Large N ◽  
Computing Performance ◽  
Algebraic Constraints ◽  
Coordinate Partitioning ◽  
Body Dynamic

Abstract This paper presents an algorithm for the efficient numerical analysis and simulation of modest to heavily constrained multi-rigid-body dynamic systems. The algorithm can accommodate the spatial motion of general multi-rigid-body systems containing arbitrarily many closed loops in O(n + m) operations overall for systems containing n generalized coordinates, and m independent algebraic constraints. The presented approach does not suffer from the performance (speed) penalty encountered by most other of the so-called “O(n)” state-space formulations, when dealing with constraints which tend to actually show O(n + m + nm + nm2 + m3) performance. Additionally, these latter formulations may require additional constraint violation stablization procedures (e.g. Baumgarte’s method, coordinate partitioning, etc.) which can contribute significant additional computation. The presented method suffers less from this difficulty because the loop closure constraints at both the velocity and acceleration level are directly embedded within the formulation. Due to these characteristics, the presented algorithm should offer superior computing performance relative to other methods in situations involving both large n and m.

Recursive Coordinate Reduction: An Addendum

2005 ◽  
Author(s):  
Michael J. Sadowski ◽  
Kurt S. Anderson
Keyword(s):  
Rigid Body ◽  
Dynamic Systems ◽  
Closed Loops ◽  
Rigid Body Dynamic ◽  
Large N ◽  
Computing Performance ◽  
Algebraic Constraints ◽  
Coordinate Reduction ◽  
Coordinate Partitioning ◽  
Body Dynamic

This paper presents an addendum to the Recursive Coordinate Reduction (RCR) algorithm for the efficient numerical analysis and simulation of modest to heavily constrained multi-rigid-body dynamic systems. The RCR algorithm can accommodate the spatial motion of broad categories of multi-rigid-body systems containing arbitrarily many closed loops in O(n + m) operations overall for systems containing n generalized coordinates, and m independent algebraic constraints. The presented approach does not suffer from the performance (speed) penalty encountered by most other of the so-called “(n)” state-space formulations, and does not require additional constraint violation stabilization procedures (e.g. Baumgartes method, coordinate partitioning, etc.). Due to these characteristics, the presented algorithm should offer superior computing performance relative to other methods in many situations involving both large n and m. This paper will specifically address an unpublished recursive step in the handling of “floating” loop base bodies, as well as present an extension to “spur” topologies.

Direct Differentiation Methods for the Design Sensitivity of Multibody Dynamic Systems

1996 ◽  
Author(s):  
Radu Serban ◽  
Jeffrey S. Freeman
Keyword(s):  
Sensitivity Analysis ◽  
Dynamic Systems ◽  
Design Sensitivity ◽  
Differential Algebraic Equations ◽  
Mechanism Analysis ◽  
Algebraic Equations ◽  
First Order ◽  
Direct Differentiation ◽  
Multibody Dynamic ◽  
Standard Techniques

Abstract Methods for formulating the first-order design sensitivity of multibody systems by direct differentiation are presented. These types of systems, when formulated by Euler-Lagrange techniques, are representable using differential-algebraic equations (DAE). The sensitivity analysis methods presented also result in systems of DAE’s which can be solved using standard techniques. Problems with previous direct differentiation sensitivity analysis derivations are highlighted, since they do not result in valid systems of DAE’s. This is shown using the simple pendulum example, which can be analyzed in both ODE and DAE form. Finally, a slider-crank example is used to show application of the method to mechanism analysis.

Steady-State Rigid-Body Dynamic Response of Cam-Follower Mechanisms

1994 ◽  
Author(s):  
Andi I. Mahyuddin ◽  
Ashok Midha
Keyword(s):  
Steady State ◽  
Dynamic Response ◽  
Rigid Body ◽  
Angular Speed ◽  
Integration Scheme ◽  
Rigid Body Dynamic ◽  
Speed Variation ◽  
Cam Follower ◽  
Speed Fluctuation ◽  
Body Dynamic

Abstract The camshaft of a cam-follower mechanism experiences a position-dependent moment due to the force exerted on the cam by the follower, causing the angular speed of the camshaft to fluctuate. In this work, a method to expediently predict the camshaft speed fluctuation is developed. The governing equation of motion is derived assuming that the cam-follower system is an ideal one wherein all members are treated as rigid. An existing closed-form numerical algorithm is used to obtain the steady-state rigid-body dynamic response of a machine system. The solution considers a velocity-dependent moment; specifically, a resisting moment is modeled as a velocity-squared damping. The effects of flywheel size and resisting moment on camshaft speed fluctuation are studied. The results compare favorably with those obtained from transient response using a direct integration scheme. The analytical result also shows excellent agreement with the camshaft speed variation of an experimental cam-follower mechanism. The steady-state rigid-body dynamic response obtained herein also serves as a first approximation to the input camshaft speed variation in the dynamic analysis of flexible cam-follower mechanisms in a subsequent research.

Pseudo-rigid-body dynamic modeling and analysis of compliant mechanisms

2017 ◽  
Vol 232 (9) ◽  
pp. 1665-1678 ◽  
Author(s):  
Yue-Qing Yu ◽  
Qian Li ◽  
Qi-Ping Xu
Keyword(s):  
Rigid Body ◽  
Dynamic Model ◽  
Dynamic Modeling ◽  
Dynamic Models ◽  
Compliant Mechanisms ◽  
Lagrange Equation ◽  
Dynamic Responses ◽  
Modeling And Analysis ◽  
Rigid Body Dynamic ◽  
Body Dynamic

An intensive study on the dynamic modeling and analysis of compliant mechanisms is presented in this paper based on the pseudo-rigid-body model. The pseudo-rigid-body dynamic model with single degree-of-freedom is proposed at first and the dynamic equation of the 1R pseudo-rigid-body dynamic model for a flexural beam is presented briefly. The pseudo-rigid-body dynamic models with multi-degrees-of-freedom are then derived in detail. The dynamic equations of the 2R pseudo-rigid-body dynamic model and 3R pseudo-rigid-body dynamic model for the flexural beams are obtained using Lagrange equation. Numerical investigations on the natural frequencies and dynamic responses of the three pseudo-rigid-body dynamic models are made. The effectiveness and superiority of the pseudo-rigid-body dynamic model has been shown by comparing with the finite element analysis method. An example of a compliant parallel-guiding mechanism is presented to investigate the dynamic behavior of the mechanism using the 2R pseudo-rigid-body dynamic model.

SPHERE ENCAPSULATED ORIENTED-DISCRETE ORIENTATION POLYTOPES (S-DOP) COLLISION CULLING FOR MULTI-, RIGID BODY DYNAMIC

2015 ◽  
Vol 75 (2) ◽  
Author(s):  
Norhaida Mohd Suaib ◽  
Abdullah Bade ◽  
Dzulkifli Mohamad
Keyword(s):  
Rigid Body ◽  
Collision Detection ◽  
Simulation System ◽  
Improve Performance ◽  
Excellent Performance ◽  
Approximation Techniques ◽  
Rigid Body Dynamic ◽  
Rigid Body Simulation ◽  
Body Dynamic

This paper discusses on sphere encapsulated oriented-discrete orientation polytopes (therefore will be referred to as S-Dop) collision culling for multiple rigid body simulation. In order to improve performance of the whole simulation system, there are available options in sacrificing the accuracy over speed by using certain approximation techniques. The aim of this research is to achieve excellent performance through implementation of suitable culling technique, without jeopardizing the resulting behavior so that the simulation will still be physically plausible. The basic idea is to identify the highly probable pairs to collide and test the pair with a more accurate collision test in broad-phase collision detection, before the pair is passed to a more costly stage. Results from the experiments showed that there are a number of ways to implement the sphere encapsulated or-Dops (S-Dop) collision culling on a multiple rigid body simulation depending on the level of performance needed.  

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