Generalized coordinate partitioning for complex mechanisms based on kinematic substructuring

Wehage, Kristopher; Wehage, R. A.; Ravani, Bahram

doi:10.1016/j.mechmachtheory.2015.06.006

Cited by 26 publications

(9 citation statements)

References 22 publications

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“…The multibody dynamic equations of the triple pendulum system form a system of differential-algebraic dynamic equations that are analytically derived by using the RPCF-EP and the NACF. Subsequently, the Robust Generalized Coordinate Partitioning (RGCP) method is used for stabilizing constraint drift of the triple pendulum system as well as to enforce the kinematic constraints at both the position and velocity levels [60,61]. The constraint tolerance used in the Newton-Raphson (NR) numerical procedure implemented in the RGCP algorithm is equal to ε = 10 −9 .…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

On the Computational Methods for Solving the Differential-Algebraic Equations of Motion of Multibody Systems

Pappalardo

Guida

2018

Machines

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In this investigation, different computational methods for the analytical development and the computer implementation of the differential-algebraic dynamic equations of rigid multibody systems are examined. The analytical formulations considered in this paper are the Reference Point Coordinate Formulation based on Euler Parameters (RPCF-EP) and the Natural Absolute Coordinate Formulation (NACF). Moreover, the solution approaches of interest for this study are the Augmented Formulation (AF) and the Udwadia-Kalaba Equations (UKE). As shown in this paper, the combination of all the methodologies analyzed in this work leads to general, effective, and efficient multibody algorithms that can be readily implemented in a general-purpose computer code for analyzing the time evolution of mechanical systems constrained by kinematic joints. This study demonstrates that multibody algorithm based on the combination of the NACF with the UKE turned out to be the most effective and efficient computational method. The conclusions drawn in this paper are based on the numerical results obtained for a benchmark multibody system analyzed by means of dynamical simulations.

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Section: Numerical Results and Discussionmentioning

confidence: 99%

On the Computational Methods for Solving the Differential-Algebraic Equations of Motion of Multibody Systems

Pappalardo

Guida

2018

Machines

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“…This way of solving the problem can arise some numerical difficulties and efficiency, as it has been addressed in the thematic literature [32,80,91]. Nevertheless, the proposed approach is quite efficiency from computational point of view, because for the simulations performed within the goals of the present work, in general, no more the 2 iterations are needed to obtained a good convergence of the method.…”

Section: Demonstrative Examples Of Applicationmentioning

confidence: 99%

“…It must be highlighted that the coordinate partitioning methods are effective and very useful [83][84][85] and a good number of investigations haven been carried out on the establishment of the sets of independent and dependent coordinates. In fact, over the last few decades, several approaches that allows for the selection of the independent set of coordinates have been proposed [86][87][88][89][90][91]. Recently, Carpinelli et al [92] studied the problem of the accuracy and efficiency of the implicit Euler approach when switching from dependent to independent coordinates.…”

Section: Introductionmentioning

confidence: 99%

On the constraints violation in forward dynamics of multibody systems

2016

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It is known that the dynamic equations of motion for constrained mechanical multibody systems are frequently formulated using the Newton-Euler's approach, which is augmented with the acceleration constraint equations. This formulation results in the establishment of a mixed set of partial differential and algebraic equations, which are solved in order to predict the dynamic behavior of general multibody systems. The classical resolution of the equations of motion is highly prone to constraints violation because the position and velocity constraint equations are not fulfilled. In this work, a general and comprehensive methodology to eliminate the constraints violation at the position and velocity levels is offered. The basic idea of the described approach is to add corrective terms to the position and velocity vectors with the intent to satisfy the corresponding kinematic constraint equations. These corrective terms are evaluated as function of the Moore-Penrose generalized inverse of the Jacobian matrix and of the kinematic constraint equations. The described methodology is embedded in the standard method to solve the equations of motion based on the technique of Lagrange multipliers. Finally, the effectiveness of the described methodology is demonstrated through the dynamic modeling and simulation of different planar and spatial multibody systems. The outcomes in terms of constraints violation at the position and velocity levels, conservation of the total energy and computational efficiency are analyzed and compared with those obtained with the standard Lagrange multipliers method, the Baumgarte stabilization method, the augmented Lagrangian formulation, the index-1 augmented Lagrangian and the coordinate partitioning method.

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“…The velocity of the general coordinates (̇⃗), using coordinate partitioning method (Wehage, Wehage, & Ravani, 2015), can be express in function of the independent coordinates as:…”

Section: �⃗mentioning

confidence: 99%

Optimal Reconfiguration of a Limited Parallel Robot for Forward Singularities Avoidance

Llopis-Albert

Valero

Mata

et al. 2020

Mult.J.Edu.Soc.Tec.Sci.

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The positioning of the anchoring points of a Parallel Kinematic Manipulator has an important impact on its later performance. This paper presents an optimization problem to deal with the reconfiguration of a Parallel Kinematic manipulator with four degrees of freedom and the corresponding algorithms to address such problem, with the subsequent test on an actual robot.The cost function minimizes the forces applied by the actuators along the trajectory and considers singular positions and the feasibility of the active generalized coordinates. Results are compared among different algorithms, including evolutionary, heuristics, multi-strategy and gradient-based optimizers.

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Generalized coordinate partitioning for complex mechanisms based on kinematic substructuring

Cited by 26 publications

References 22 publications

On the Computational Methods for Solving the Differential-Algebraic Equations of Motion of Multibody Systems

On the Computational Methods for Solving the Differential-Algebraic Equations of Motion of Multibody Systems

On the constraints violation in forward dynamics of multibody systems

Optimal Reconfiguration of a Limited Parallel Robot for Forward Singularities Avoidance

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