Computation of stiffness and stiffness bounds for parallel link manipulators

El‐Khasawneh, Bashar; Ferreira, Placid M.

doi:10.1016/s0890-6955(98)00039-x

Cited by 191 publications

(88 citation statements)

References 13 publications

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“…Several different expressions of stiffness have been used in the literature, including engineering stiffness, generalized stiffness matrix, and Cartesian stiffness matrix. The engineering stiffness is a one-dimensional stiffness expression obtained by evaluating the displacement in the same direction to the applied force [51]. The generalized stiffness matrix, according to Quennouelle and Gosselin [52], includes three contributions: stiffness of the unconstrained joints, stiffness due to dependent coordinated and internal wrench, and stiffness due to external wrench.…”

Section: Stiffnessmentioning

confidence: 99%

See 1 more Smart Citation

Kinematic Performance Measures and Optimization of Parallel Kinematics Manipulators: A Brief Review

Rosyid¹,

El‐Khasawneh²,

Alazzam³

2017

Kinematics

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This chapter covers a number of kinematic performance indices that are instrumental in designing parallel kinematics manipulators. These indices can be used selectively based on manipulator requirements and functionality. This would provide the very practical tool for designers to approach their needs in a very comprehensive fashion. Nevertheless, most applications require a more composite set of requirements that makes optimizing performance more challenging. The later part of this chapter will discuss single-objective and multi-objectives optimization that could handle certain performance indices or a combination of them. A brief description of most common techniques in the literature will be provided.

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Section: Stiffnessmentioning

confidence: 99%

“…• (Minimum, average, or maximum) eigenvalues (and eigenvectors) of the stiffness matrix [51]. For example, the evaluation of minimum and maximum eigenvalues across the workspace by Li and Xu [56].…”

Section: Stiffnessmentioning

confidence: 99%

Kinematic Performance Measures and Optimization of Parallel Kinematics Manipulators: A Brief Review

Rosyid¹,

El‐Khasawneh²,

Alazzam³

2017

Kinematics

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“…The stiffness maps of the workspace through Jacobian Matrix was established in (Gosselin, 1999), (Bi et al, 2007). The stiffness in X-, Y -and Z-directions were computed in (El-Khasawneh and Ferreira, 1999), where the minimum and maximum stiffness and directions in a given configuration were found through the eigenvectors analysis. An approach to get the stiffness model of a tripod-based PKM was presented in (Huang and Mei, 2001), where the machine structure is decomposed into two substructures: machine frame and parallel mechanism.…”

Section: Stiffnessmentioning

confidence: 99%

Kinematic and Elastostatic Design Optimisation of the 3-DOF Gantry-Tau Parallel Kinematic Manipulator

Tyapin

Hovland

2009

MIC

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One of the main advantages of the Gantry-Tau machine is a large accessible workspace/footprint ratio compared to many other parallel machines. The Gantry-Tau improves this ration further by allowing a change of assembly mode without internal link collisions or collisions between the links and end-effector. The reconfigurable Gantry-Tau kinematic design obtained by multi-objective optimisation according to this paper gives the following features: 3-D workspace/footprint ratio is more than 3.19, lowest Cartesian stiffness in the workspace is 5N/µm and no link collisions detected. The optimisation parameters are the support frame lengths, the actuator positions and the robot's arm lengths. The results comparison between the evolutionary complex search algorithm and gradient-based method used for the Gantry-Tau design in the past is also presented in this paper. The detailed statics model analysis of the Gantry-Tau based on a functionally dependency is presented in this paper for the first time. Both the statics model and complex search algorithm may be applied for other 3-DOF Hexapods without major changes. The existing lab prototype of the Gantry-Tau was assembled and completed at the University of Agder, Norway.

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“…C. Gosselin [10][11] considered the weak rigidity of the machine transmission parts, established the Jacobi matrix between the work piece coordinate system and the machine coordinates transmission parts, use the principle of virtual work to establish an integrated processing system stiffness model. Wan Min [12] considers the processing error due to the deformation of work piece and tool generated, contralateral milling process of the tool relative to the work piece at any sampling point deformation analyzed and calculated by finite element method, and the results are used for error compensation.…”

Section: Introductionmentioning

confidence: 99%

Modeling and Analysis of the Open Lmpeller Four Axis Machining System Composite Stiffness

Shi¹,

Lijian²,

Liu³

et al. 2016

IJCA

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Computation of stiffness and stiffness bounds for parallel link manipulators

Cited by 191 publications

References 13 publications

Kinematic Performance Measures and Optimization of Parallel Kinematics Manipulators: A Brief Review

Kinematic Performance Measures and Optimization of Parallel Kinematics Manipulators: A Brief Review

Kinematic and Elastostatic Design Optimisation of the 3-DOF Gantry-Tau Parallel Kinematic Manipulator

Modeling and Analysis of the Open Lmpeller Four Axis Machining System Composite Stiffness

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