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Weakly and fully coupled methods for structural optimization of flexible mechanisms Tromme, Emmanuel ; Bruls, Olivier ; Duysinx, Pierre in Multibody System Dynamics (2015) The paper concerns a detailed comparison between two optimization methods that are used to perform the structural optimization of flexible components within a multibody system (MBS) simulation. The ... [more ▼] The paper concerns a detailed comparison between two optimization methods that are used to perform the structural optimization of flexible components within a multibody system (MBS) simulation. The dynamic analysis of flexible MBS is based on a nonlinear finite element formulation. The first method is a weakly coupled method, which reformulates the dynamic response optimization problem in a two-level approach. First, a rigid or flexible MBS simulation is performed, and second, each component is optimized independently using a quasi-static approach in which a series of equivalent static load (ESL) cases obtained from the MBS simulation are applied to the respective components. The second method, the fully coupled method, performs the dynamic response optimization using the time response obtained directly from the flexible MBS simulation. Here, an original procedure is proposed to evaluate the ESL from a nonlinear finite element simulation, contrasting with the floating reference frame formulation exploited in the standard ESL method. Several numerical examples are provided to support our position. It is shown that the fully coupled method is more general and accommodates all types of constraints at the price of a more complex optimization process. [less ▲] Detailed reference viewed: 18 (2 ULg)Sensitivity analysis for multibody systems formulated on a Lie group Sonneville, Valentin ; Bruls, Olivier in Multibody System Dynamics (2014), 31 A direct differentiation method and an adjoint variable method are proposed for the efficient semi-analytical evaluation of the sensitivities of multibody systems formulated in a matrix Lie group ... [more ▼] A direct differentiation method and an adjoint variable method are proposed for the efficient semi-analytical evaluation of the sensitivities of multibody systems formulated in a matrix Lie group framework. These methods rely on the linearization of the equations of motion and/or of the time integration procedure. The simpler structure of the equations of motion in the Lie group formalism appears as an advantage for that purpose. Lie bracket contributions and the non-linearity of the exponential map need to be taken into account in the sensitivity algorithms. Nevertheless, essential characteristics of formulations of the direct differentiation method and the adjoint variable method on linear spaces are recovered. Some implementation issues are discussed and two relevant examples illustrate the properties of these methods. [less ▲] Detailed reference viewed: 112 (31 ULg)Inverse dynamics of serial and parallel underactuated multibody systems using a DAE optimal control approach Guimaraes Bastos Junior, Guaraci ; ; Bruls, Olivier in Multibody System Dynamics (2013) The inverse dynamics analysis of underactuated multibody systems aims at determining the control inputs in order to track a prescribed trajectory. This paper studies the inverse dynamics of non-minimum ... [more ▼] The inverse dynamics analysis of underactuated multibody systems aims at determining the control inputs in order to track a prescribed trajectory. This paper studies the inverse dynamics of non-minimum phase underactuated multibody systems with serial and parallel planar topology, e.g. for end-effector control of flexible manipulators or manipulators with passive joints. Unlike for minimum phase systems, the inverse dynamics of non-minimum phase systems cannot be solved by adding trajectory constraints (servoconstraints) to the equations of motion and applying a forward time integration. Indeed, the inverse dynamics of a non-minimum phase system is known to be non-causal, which means that the control forces and torques should start before the beginning of the trajectory (preactuation phase) and continue after the end-point is reached (post-actuation phase). The existing stable inversion method roposed for general nonlinear non-minimum phase systems requires to derive explicitly the equations of the internal dynamics and to solve a boundary value problem. This paper proposes an alternative solution strategy which is based on an optimal control approach using a direct transcription method. The method is illustrated for the inverse dynamics of an underactuated serial manipulator with rigid links and four degrees-of-freedom and an underactuated parallel machine. An important advantage of the proposed approach is that it can be applied directly to the standard equations of motion of multibody systems either in ODE or in DAE form. Therefore, it is easier to implement this method in a general purpose simulation software. [less ▲] Detailed reference viewed: 86 (18 ULg)Multiphysics modeling and optimization of mechatronic multibody systems ; Bruls, Olivier ; et al in Multibody System Dynamics (2007), 18(3), 345-373 Modeling mechatronic multibody systems requires the same type of methodology as for designing and prototyping mechatronic devices: a unified and integrated engineering approach. Various formulations are ... [more ▼] Modeling mechatronic multibody systems requires the same type of methodology as for designing and prototyping mechatronic devices: a unified and integrated engineering approach. Various formulations are currently proposed to deal with multiphysics modeling, e.g., graph theories, equational approaches, co-simulation techniques. Recent works have pointed out their relative advantages and drawbacks, depending on the application to deal with: model size, model complexity, degree of coupling, frequency range, etc. This paper is the result of a close collaboration between three laboratories, and aims at showing that for "non-academic" mechatronic applications (i.e., issuing from real industrial issues), multibody dynamics formulations can be generalized to mechatronic systems, for the model generation as well as for the numerical analysis phases. Model portability being also an important aspect of the work, they must be easily interfaced with control design and optimization programs. A global "demonstrator", based on an industrial case, is discussed: multiphysics modeling and mathematical optimization are carried out to illustrate the consistency and the efficiency of the proposed approaches. [less ▲] Detailed reference viewed: 72 (6 ULg)Convergence of the generalized-alpha scheme for constrained mechanical systems ; Bruls, Olivier in Multibody System Dynamics (2007), 18(2), 185-202 A variant of the generalized-alpha scheme is proposed for constrained mechanical systems represented by index-3 DAEs. Based on the analogy with linear multistep methods, an elegant convergence analysis is ... [more ▼] A variant of the generalized-alpha scheme is proposed for constrained mechanical systems represented by index-3 DAEs. Based on the analogy with linear multistep methods, an elegant convergence analysis is developed for this algorithm. Second-order convergence is demonstrated both for the generalized coordinates and the Lagrange multipliers, and those theoretical results are illustrated by numerical tests. [less ▲] Detailed reference viewed: 197 (9 ULg)A model reduction method for the control of rigid mechanisms Bruls, Olivier ; Duysinx, Pierre ; Golinval, Jean-Claude in Multibody System Dynamics (2006), 15(3), 213-227 This paper presents a reduction method to build closed-form dynamic equations for rigid multibody systems with a minimal kinematic description. Relying on an initial parameterization with absolute ... [more ▼] This paper presents a reduction method to build closed-form dynamic equations for rigid multibody systems with a minimal kinematic description. Relying on an initial parameterization with absolute displacements and rotations, the method is able to tackle complex topologies with closed-loops in a systematic way and its extension to flexible multibody systems will be investigated in the future. Thus, it would be of great use in the framework of model-based control of mechanisms. The method is based on an interpolation strategy. The initial model is built and reduced for a number of selected points in the configuration space. Then, a piecewise polynomial model is adjusted to match the collected data. After the presentation of the reduction procedure and of the interpolation strategy, two applications of the reduction method are considered: a four-bar mechanism and a parallel kinematic machine-tool called "Orthoglide". [less ▲] Detailed reference viewed: 44 (12 ULg)Contribution to the optimization of closed-loop multibody systems: Application to parallel manipulators ; ; Duysinx, Pierre in Multibody System Dynamics (2005), 13(1), 69-84 This paper describes an original and robust method to optimize the design of closed-loop mechanisms, especially parallel manipulators. These mechanisms involve non linear assembling constraints. During ... [more ▼] This paper describes an original and robust method to optimize the design of closed-loop mechanisms, especially parallel manipulators. These mechanisms involve non linear assembling constraints. During optimization, the Newton-Raphson algorithm we use to solve these constraints may fail when the Jacobian matrix of the constraints is ill-conditioned and stops the redesign process. To circumvent the difficulty, the technique we propose takes advantage of numerical conditioning to penalize the objective function. Applications to an academic example and parallel robots demonstrate the capabilities of the methodology. [less ▲] Detailed reference viewed: 41 (2 ULg) |
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