Experimental Validation of Jacobian-Based Stiffness Analysis Method for Parallel Manipulators With Nonredundant Legs

Hoevenaars, A.G.L.; Gosselin, Clément; Lambert, Patrice; Herder, Just L.

doi:10.1115/1.4032204

Cited by 12 publications

(6 citation statements)

References 27 publications

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“…In earlier publications it was argued by the authors that the Jacobian-derivative term, which represents the effect loading, is an essential part of a Jacobian-based stiffness analysis [12], and that this term improves the accuracy of the resulting stiffness model [37]. However, if inclusion of this term could lead to asymmetric stiffness matrices, then it cannot be considered part of a stiffness analysis.…”

Section: Discussionmentioning

confidence: 95%

“…On the other hand, the numerical method used by Huang and Li [36] resulted in a stiffness matrix in which part of the asymmetry had disappeared. Moreover, when Hoevenaars et al [37] included the Jacobian-derivative term in the analysis of two different compliant mechanisms, of which one is similar to the planar mechanism analyzed in Ref. [29], they found only symmetric stiffness matrices.…”

Section: Introductionmentioning

confidence: 97%

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Consistent modeling resolves asymmetry in stiffness matrices

Hoevenaars

Gosselin

Lambert

et al. 2016

Mechanism and Machine Theory

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Section: Discussionmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 97%

Consistent modeling resolves asymmetry in stiffness matrices

Hoevenaars

Gosselin

Lambert

et al. 2016

Mechanism and Machine Theory

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“…This paper used the linearised model of the protein backbone kinematics for the analysis of conformational change, but the opportunities are broader. In the field of robotics, the linear algebra that is at the heart of this paper is extensively used for dynamic analyses such as stiffness analysis and natural frequency analysis [7,47,45,23,21] and has also been applied for the analysis of mechanisms with more complex, internally connected, kinematic networks [28,22]. Such internally connected mechanisms are not unlike protein segments that are interconnected via hydrogen bonds, as for example investigated by Budday et al [8], and may proof a new source of inspiration.…”

Section: Discussionmentioning

confidence: 99%

Linearised loop kinematics to study pathways between conformations

Hoevenaars

André²

2021

Preprint

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Conformational changes are central to the function of many proteins. Characterization of these changes using molecular simulation requires methods to effectively sample pathways between protein conformational states. In this paper we present an iterative algorithm that samples conformational transitions in protein loops, referred to as the Jacobian-based Loop Transition (JaLT) algorithm. The method uses internal coordinates to minimise the sampling space, while Cartesian coordinates are used to maintain loop closure. Information from the two representations is combined to push sampling towards a desired target conformation. The innovation that enables the simultaneous use of Cartesian coordinates and internal coordinate is the linearisation of the inverse kinematics of a protein backbone. The algorithm uses the Rosetta all-atom energy function to steer sampling through low-energy regions and uses Rosetta's side-chain energy minimiser to update side-chain conformations along the way. Because the JaLT algorithm combines a detailed energy function with a low-dimensional conformational space, it is positioned in between molecular dynamics (MD) and elastic network model (ENM) methods. As a proof of principle, we apply the JaLT algorithm to study the conformational transition between the open and occluded state in the MET20 loop of the Escherichia coli dihydrofolate reductase enzyme. Our results show that the algorithm generates semi-continuous pathways between the two states with realistic energy profiles. These pathways can be used to identify energy barriers along the transition. The effect of a single point mutation of the MET20 loop was also investigated and the predicted increase in energy barrier is consistent with the experimentally observed reduction in catalytic rate of the enzyme. Additionally, it is demonstrated how the JaLT algorithm can be used to identify dominant degrees of freedom during a transition. This can be valuable input for a more extensive characterization of the free energy pathway along a transition using molecular dynamics, which is often performed with a reduced set of degrees of freedom. This study has thereby provided the first examples of how linearisation of inverse kinematics can be applied to the analysis of proteins.

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“…It is assumed that K L is the general stiffness matrix of the leg of the wall-climbing hexapod robot. According to equation (11), the stiffness matrix K L can be given by…”

Section: General Stiffness Model Of Serial Mechanismmentioning

confidence: 99%

“…For a linear deformation, the relationship between force and deformation is described by a stiffness matrix. [11][12][13] In general, considering the flexibilities of each compliant element, the stiffness model of robot which has six legs can be established directly. 14 Some works contain the results of the manipulator under external loading, the influence of the passive joint, 15 and internal constraints.…”

Section: Introductionmentioning

confidence: 99%

A novel stiffness model for a wall-climbing hexapod robot based on nonlinear variable stiffness

Wang

2018

Advances in Mechanical Engineering

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In this article, the most contribution is to propose a novel general stiffness model to analyze the stiffness of a wallclimbing hexapod robot. First, we propose a new general stiffness model of serial mechanism, which includes the linear and nonlinear stiffness models. By comparison, the nonlinear stiffness model is a variable stiffness model which introduces the external load force as a variable, obtaining that the nonlinear stiffness model can greatly improve the accuracy of stiffness model than linear stiffness model. Then, the stiffness model of one leg of the robot and the overall stiffness model of the robot are derived based on the general stiffness model. Next, to improve the stiffness of the robot, a new minimum and maximum stiffness are introduced, which provide with effective reference for the selection and optimization of the structural parameters of the robot. Finally, we develop a new wall-climbing hexapod robot based on selection and optimization of the structural parameters, then the experiments are used to show that the selection of structure parameters of the robot effectively improve the stiffness of the robot.

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Experimental Validation of Jacobian-Based Stiffness Analysis Method for Parallel Manipulators With Nonredundant Legs

Cited by 12 publications

References 27 publications

Consistent modeling resolves asymmetry in stiffness matrices

Consistent modeling resolves asymmetry in stiffness matrices

Linearised loop kinematics to study pathways between conformations

A novel stiffness model for a wall-climbing hexapod robot based on nonlinear variable stiffness

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