On higher-order differentiation in nonlinear mechanics

Charpentier, Isabelle

doi:10.1080/10556788.2011.577775

Cited by 18 publications

(21 citation statements)

References 47 publications

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“…The solutions for the under-determined system (4) define one-dimensional continua, hereafter called branches of solutions. Continuation methods and related software, see [26,24] enable to compute solution branches. Most of them rely on first order predictor-corrector principles described in [27,28,29,30] and approximate the solution branches as a collection of points satisfying (4).…”

Section: Mechanism Analysis Using Higher-order Continuation Methodsmentioning

confidence: 99%

“…A second main contribution is the ability that offers the method to determine workspace and kinematic properties of mechanisms that can be employed using only basic knowledge of a mechanism. It builds on the higher-order continuation method [23,24] for the continuous computation of joint angular positions along any parameterized end-effector path. The results are presented in the form of so-called bifurcation diagrams displaying joint positions as functions of the end-effector position.…”

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confidence: 99%

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Higher-order continuation method for the rigid-body kinematic design of compliant mechanisms

Rubbert

Charpentier

Henein

et al. 2017

Precision Engineering

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Compliant mechanisms are of great interest in precision engineering. In this paper we propose a higher-order continuation method to help their rigid-body kinematic design. Higher-order continuation method leads to direct accurate plotting of the input-output relationship of any mechanism using only its geometrical closed-loop equations, i.e. without complex derivation of any analytical model. These plots, called bifurcation diagrams, reveal essential information as joint velocity profile and the presence of singular configurations. Moreover, the continuous and accurate computation of the mechanism configuration in the vicinity of singularities provides detailed information about the kinematic behavior of the mechanism in its extreme positions. For the design of compliant mechanisms, the designer can advantageously use the bifurcation diagrams to first evaluate the relevance of the selected mechanism, then identify a working configuration in order to obtain adequate kinematic properties without the derivation of the inverse kinematic model (IKM) or the direct kinematic model (DKM). The method is exemplified with a 3 universal-joint and 3 spherical-joint mechanism (3-US) mechanism, the IKM and DKM of which cannot be derived analytically. The latter has a large workspace and special kinematic behaviors consisting of a screw-like motion and platform gyration, which have not been studied before and could lead to interesting novel devices. drawback during a mechanism synthesis when several designs have to be compared. It has been demonstrated that the workspace boundaries corresponds to singularity locii [19]. Haug et al. [20] and recently Hentz et al. [21,22] have consequently developed continuation-based methods to determine the workspace outer envelope by following onedimension paths on it. Any mechanism can be analyzed after simply deriving the geometrical closed-loop equations, and with a limited computation time. This constitutes very interesting features for a systematic evaluation of mechanism, but no information is obtained on accessible configurations within the workspace. In this paper, we introduce an evaluation method based on the same theoretical background but with a complementary approach giving information on the boundary and the inner properties of the workspace.Kinematic analysis to study the geometrical model and properties of robots have been developed using different methods including analytical [10,9] and geometrical approaches [11,8]. Both have their limitations since obtaining an analytical model is not always possible and the geometrical approach efficiency strongly depends on the mechanism and the user expertise. Moreover, considering the analysis of robot singular configurations, analytical approaches generally fail. For these particular situations, Grassman-Cayley algebra and screw theory can be used to prove the existence of singularity and to identify the nature of singular movements [14]. However, these methods lack generality and require advanced knowledge on the mechanism as well as d...

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Section: Mechanism Analysis Using Higher-order Continuation Methodsmentioning

confidence: 99%

mentioning

confidence: 99%

Higher-order continuation method for the rigid-body kinematic design of compliant mechanisms

Rubbert

Charpentier

Henein

et al. 2017

Precision Engineering

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“…In a nutshell, AD is a set of techniques designed to augment the source code of a software with derivative computations (Griewank & Walther, 2008;Naumann, 2011). It implements the chain rule in either a source to 260 source AD tool like Tapenade (Hascoet & Pascual, 2013) or an AD overloading library (Griewank et al, 1996;Charpentier, 2012) to be linked with the computer code. The AD tool (Hascoet & Pascual, 2013) is here applied to our MHFEM code.…”

Section: Inverse Modelingmentioning

confidence: 99%

Temporal estimation of hydrodynamic parameter variability in stormwater constructed wetlands – The hysteresis effect during multi-rainfall events

Moezzibadi

Charpentier

Wanko

et al. 2019

Ecological Engineering

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Constructed wetland (CW) systems are increasingly implemented as rustic water treatment facilities, the efficiency of which varies with time due to possible malfunctions such as clogging related to excessive loads of suspended solids or inadequate CW sizing. A numerical flow modeling can be used to evaluate filtering performance and to improve the design of CWs. Such a modeling usually involves the so-called van Genuchten-Mualem (vGM) soil hydrodynamic parameters which are notoriously difficult to measure. The meticulous attention brought to the sensitivity of the model to the vGM parameters reveals a predominant influence of the shape parameters and the saturated conductivity of the filter on the piezometric heads, during feeding and drainage. We then discuss a simple, robust and low-cost inverse modeling approach, deterministic and stochastic, for the identification of the soil hydrodynamic properties from piezometric heads measured during successive storm events. The temporal variability of hydrodynamic parameters is assessed and analyzed with regards to modeling efficiency. Principal component analysis shows that the estimated hydrodynamic parameters from the feeding and drainage sub-periods are significantly different.

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“…Nevertheless after taking into account these uncertainties, we see that the trace phase (not the initiation or termination of the phase) has an important impact on the runtime of each of the operations and that it clearly forms a bottleneck of the computation 8 . We attribute this to the fact that tracing tracks the sequence of operations dynamically, resulting in a lot of dynamic allocations, indirections, cache misses, pipeline stalls and far jumps through the binary executable.…”

Section: A Comparison To Adol-cmentioning

confidence: 99%

“…A list of packages that allow for the differentiation of C++ codes is provided on the AutoDiff site. Beyond that, the differentiation of linear solvers or linear transformations, fixed-point methods [7], nonlinear solvers [8,9] and special functions of mathematical physics [10] requires a careful study to be accurate and efficient. Although general developments were proposed and automated for most of these issues, they are not systematically included in the existing AD tools.…”

Section: Introduction and Overviewmentioning

confidence: 99%

`Arbogast`: Higher order automatic differentiation for special functions with Modular C

Charpentier

Gustedt

2018

Optimization Methods and Software

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On higher-order differentiation in nonlinear mechanics

Cited by 18 publications

References 47 publications

Higher-order continuation method for the rigid-body kinematic design of compliant mechanisms

Higher-order continuation method for the rigid-body kinematic design of compliant mechanisms

Temporal estimation of hydrodynamic parameter variability in stormwater constructed wetlands – The hysteresis effect during multi-rainfall events

`Arbogast`: Higher order automatic differentiation for special functions with Modular C

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On higher-order differentiation in nonlinear mechanics

Cited by 18 publications

References 47 publications

Higher-order continuation method for the rigid-body kinematic design of compliant mechanisms

Higher-order continuation method for the rigid-body kinematic design of compliant mechanisms

Temporal estimation of hydrodynamic parameter variability in stormwater constructed wetlands – The hysteresis effect during multi-rainfall events

Arbogast: Higher order automatic differentiation for special functions with Modular C

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Product

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`Arbogast`: Higher order automatic differentiation for special functions with Modular C