Macro-op scheduling: relaxing scheduling loop constraints

2004 ◽  
Author(s):  
I. Kim ◽  
M. Lipasti
Keyword(s):  
Loop Constraints

Dynamic Modeling and Simulation of Parallel Mechanisms Using the Virtual Spring Approach

2000 ◽  
Author(s):  
Jiegao Wang ◽  
Clément M. Gosselin ◽  
Li Cheng
Keyword(s):  
Closed Loop ◽  
Differential Algebraic Equations ◽  
Parallel Mechanisms ◽  
Algebraic Equations ◽  
New Approach ◽  
Flexible Links ◽  
Simulation Results ◽  
Loop Constraints ◽  
Virtual Springs ◽  
Good Agreement

Abstract A new approach for the dynamic simulation of parallel mechanisms or mechanical systems is presented in this paper. This approach uses virtual springs and dampers to include the closed-loop constraints thereby avoiding the solution of differential-algebraic equations. Examples illustrating the approach are given and include the four-bar mechanism with both rigid and flexible links as well as the 6-dof Gough-Stewart platform. Simulation results are given for the four-bar linkages and the 6-dof manipulator. The results achieve a good agreement with the results obtained from other conventional approaches.

scholarly journals Implementation of A Geometric Constraint Regularization For Multibody System Models

2014 ◽  
Vol 61 (2) ◽  
pp. 365-383 ◽  
Author(s):  
Andreas Müller
Keyword(s):  
Multibody System ◽  
Time Integration ◽  
Simulation Method ◽  
Dynamics Simulation ◽  
Computational Performance ◽  
Kinematic Loops ◽  
Computationally Expensive ◽  
Technical Systems ◽  
Loop Constraints

Abstract Redundant constraints in MBS models severely deteriorate the computational performance and accuracy of any numerical MBS dynamics simulation method. Classically this problem has been addressed by means of numerical decompositions of the constraint Jacobian within numerical integration steps. Such decompositions are computationally expensive. In this paper an elimination method is discussed that only requires a single numerical decomposition within the model preprocessing step rather than during the time integration. It is based on the determination of motion spaces making use of Lie group concepts. The method is able to reduce the set of loop constraints for a large class of technical systems. In any case it always retains a sufficient number of constraints. It is derived for single kinematic loops.

A Second-Order Method for Assembly Tolerance Analysis

1999 ◽  
Author(s):  
Charles G. Glancy ◽  
Kenneth W. Chase
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Nonlinear Analysis ◽  
Closed Loop ◽  
Tolerance Analysis ◽  
Linear Analysis ◽  
Tolerance Allocation ◽  
Input And Output ◽  
Loop Constraints ◽  
Geometric Effects

Abstract Linear analysis and Monte Carlo simulation are two well-established methods for statistical tolerance analysis of mechanical assemblies. Both methods have advantages and disadvantages. The Linearized Method, a form of linear analysis, provides fast analysis, tolerance allocation, and the capability to solve closed loop constraints. However, the Linearized Method does not accurately approximate nonlinear geometric effects or allow for non-normally distributed input or output distributions. Monte Carlo simulation, on the other hand, does accurately model nonlinear effects and allow for non-normally distributed input and output distributions. Of course, Monte Carlo simulation can be computationally expensive and must be re-run when any input variable is modified. The second-order tolerance analysis (SOTA) method attempts to combine the advantages of the Linearized Method with the advantages of Monte Carlo simulation. The SOTA method applies the Method of System Moments to implicit variables of a system of nonlinear equations. The SOTA method achieves the benefits of speed, tolerance allocation, closed-loop constraints, non-linear geometric effects and non-normal input and output distributions. The SOTA method offers significant benefits as a nonlinear analysis tool suitable for use in design iteration. A comparison was performed between the Linearized Method, Monte Carlo simulation, and the SOTA method. The SOTA method provided a comparable nonlinear analysis to Monte Carlo simulation with 106 samples. The analysis time of the SOTA method was comparable to the Linearized Method.

Symbolic Linearized Equations for Nonholonomic Multibody Systems With Closed-Loop Kinematics

2018 ◽  
Author(s):  
Márton Kuslits ◽  
Dieter Bestle
Keyword(s):  
Lagrange Multipliers ◽  
Multibody Systems ◽  
Closed Loop ◽  
Equations Of Motion ◽  
Linear Equations ◽  
Algebraic Equations ◽  
Computationally Efficient ◽  
Linearized Equations ◽  
Nonlinear Equations Of Motion ◽  
Loop Constraints

Multibody systems and associated equations of motion may be distinguished in many ways: holonomic and nonholonomic, linear and nonlinear, tree-structured and closed-loop kinematics, symbolic and numeric equations of motion. The present paper deals with a symbolic derivation of nonlinear equations of motion for nonholonomic multibody systems with closed-loop kinematics, where any generalized coordinates and velocities may be used for describing their kinematics. Loop constraints are taken into account by algebraic equations and Lagrange multipliers. The paper then focuses on the derivation of the corresponding linear equations of motion by eliminating the Lagrange multipliers and applying a computationally efficient symbolic linearization procedure. As demonstration example, a vehicle model with differential steering is used where validity of the approach is shown by comparing the behavior of the linearized equations with their nonlinear counterpart via simulations.

Solving Square Jigsaw Puzzle by Hierarchical Loop Constraints

2019 ◽  
Vol 41 (9) ◽  
pp. 2222-2235 ◽  
Author(s):  
Kilho Son ◽  
James Hays ◽  
David B. Cooper
Keyword(s):  
Jigsaw Puzzle ◽  
Loop Constraints

scholarly journals LOOP CONSTRAINTS: A HABITAT AND THEIR ALGEBRA

1998 ◽  
Vol 07 (02) ◽  
pp. 299-330 ◽  
Author(s):  
JERZY LEWANDOWSKI ◽  
DONALD MAROLF
Keyword(s):  
Quantum Gravity ◽  
Poisson Bracket ◽  
Large Class ◽  
Hamiltonian Constraint ◽  
Natural Domain ◽  
New Space ◽  
Loop Constraints ◽  
Quantum Constraints

This work introduces a new space [Formula: see text] of 'vertex-smooth' states for use in the loop approach to quantum gravity. Such states provide a natural domain for Euclidean Hamiltonian constraint operators of the type introduced by Thiemann (and using certain ideas of Rovelli and Smolin). In particular, such operators map [Formula: see text] into itself, and so are actual operators in this space. Their commutator can be computed on [Formula: see text] and compared with the classical hypersurface deformation algebra. Although the classical Poisson bracket of Hamiltonian constraints yields an inverse metric times an infinitesimal diffeomorphism generator, and despite the fact that the diffeomorphism generator has a well-defined nontrivial action on [Formula: see text], the commutator of quantum constraints vanishes identically for a large class of proposals.

Sign in / Sign up

Export Citation Format

Share Document