Jacobian-based natural frequency analysis of parallel manipulators

Hoevenaars, A.G.L.; Krut, Sébastien; Herder, Just L.

doi:10.1016/j.mechmachtheory.2019.103775

Cited by 15 publications

(7 citation statements)

References 39 publications

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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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Section: Discussionmentioning

confidence: 99%

Linearised loop kinematics to study pathways between conformations

Hoevenaars

André²

2021

Preprint

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“…In the control of the parallel manipulator mechanism, the speed of the parallel manipulator needs to be analysed so that the speed of the central reference point of the end picking device can be obtained. On this basis, the speed Jacobi matrix of the parallel manipulator is obtained, and the speed Jacobi matrix is the linear transformation between the generalized output speed and the generalized input speed of the robot mechanism, usually denoted as JT(q) (Dai et al, 2016;Hoevenaars et al, 2020).…”

Section: Speed Analysismentioning

confidence: 99%

Design and Experiment of a Safflower Picking Robot Based on a Parallel Manipulator

et al. 2022

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To mitigate the large demand for safflower picking labour and the low efficiency of manual picking, a safflower picking robot that is based on a parallel manipulator is designed. The whole robot mainly consists of a walking device, parallel manipulator device, vision device, picking device, filament collection device, control system, and motor drive system. The forward and inverse kinematics analysis of the parallel manipulator is analysed via a geometric method, the kinematics model is established, and the computational analysis of the parallel manipulator working speed is based on the Jacobi matrix. For driving angle errors of 0.001~0.005°, the moving platform's motion accuracy is 0.2174-0.9387 mm, which meets the position accuracy requirements of the test stage. Based on MATLAB software, the Monte Carlo method is employed to solve the working space of the parallel manipulator, which is approximately an equilateral triangle with a side length of 0.35 m, which satisfies the safflower growth space picking conditions. The prototype is constructed, and safflower picking experiments are carried out under laboratory conditions. The average picking period of each flower bulb was 16 s, and the average net picking rate of the filaments was 87.91%. The experimental results verified the applicability of the safflower picking robot.

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“…Besides, Abo-Shanab (Abo-Shanab, 2020) showcased the application of the Jacobian matrix for the dynamic modeling of a 3-RRR planar parallel manipulator. Similarly, Hoevenaars et al (Hoevenaars et al, 2020) explained the natural frequency analysis of parallel manipulators taking the example of the Heli4 robot. Therefore, the Jacobian matrix is necessary for several studies, especially in closed-chain mechanisms.…”

Section: Introductionmentioning

confidence: 99%

Dimensional Synthesis, Dexterity Analysis and Experimental Validation of a Six Degree of Freedom Parallel Manipulator

Thomas

Sudheer

Joy

2023

Preprint

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This paper presents a design approach based on the dimensionless Jacobian matrix to determine the maximum dextrous workspace for a Six Degree of Freedom (DoF) 3-PPSS (P-Prismatic, S-Spherical) parallel manipulator. As the end-effector of the 3-PPSS manipulator can exhibit both translational and rotational motions, the Jacobian matrix mapping the end-effector velocities and the joint velocities will be dimensionally inhomogeneous. These dimensional inconsistencies within its elements make calculating the associated condition number impossible. Hence, a unit vector approach is introduced in this paper to derive a Jacobian matrix with dimensionless terms to study the dexterity characteristics of the 3-PPSS manipulator. The design procedure follows a systematic approach of choosing the manipulator dimensions corresponding to the maximum dextrous workspace. The manipulator dexterity is characterized by the Global Conditioning Index (GCI). This paper also illustrates the Local Conditioning Index (LCI) distribution within the workspace corresponding to the optimal manipulator dimensions. Finally, the performance of the 3-PPSS manipulator is evaluated experimentally by implementing an intelligent control based on the Inter-Integrated Circuit (I2C) protocol.

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Jacobian-based natural frequency analysis of parallel manipulators

Cited by 15 publications

References 39 publications

Linearised loop kinematics to study pathways between conformations

Linearised loop kinematics to study pathways between conformations

Design and Experiment of a Safflower Picking Robot Based on a Parallel Manipulator

Dimensional Synthesis, Dexterity Analysis and Experimental Validation of a Six Degree of Freedom Parallel Manipulator

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