A method for stiffness analysis of overconstrained parallel robotic mechanisms with Scara motion

Cao, Wen-ao; Yang, Donghao; Ding, Huafeng

doi:10.1016/j.rcim.2017.08.014

Cited by 30 publications

(10 citation statements)

References 26 publications

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“…Cao et al derived the stiffness model of the PM based on the strain energy and the static equilibrium equation, the result obtained from the proposed method was very close to the counterpart obtained from FEM. 16 In addition, Raoofian et al obtained the Cartesian stiffness matrix of the PM based on the matrix structure analysis methodology, and four stiffness indices were extracted from Cartesian stiffness matrix by applying linear algebra to evaluate the stiffness of the mechanism in the design embodiment stage. 17 Wu et al derived an accurate stiffness model of a 5-DOF hybrid machine tool with actuation redundancy by using the assembly method.…”

Section: Introductionmentioning

confidence: 99%

Stiffness analysis and optimization of an asymmetric 3T1R parallel mechanism

Zhu,

Ma,

et al. 2023

Proceedings of the Institution of Mechanical Engineers, Part C:

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In this paper, an asymmetric 3T1R parallel mechanism is proposed that has higher stiffness in specific directions. The stiffness model is established by using virtual spring theory, and the Cartesian stiffness matrix is obtained. The stiffness performance evaluation indices are deduced by the dimensionless parameterization method. Under the condition of satisfying the high-speed performance and dexterity, the optimal size parameters of the mechanism are got by using the DE (differential evolution) algorithm with stiffness performance as the index. By comparing the stiffness performance atlases before and after the optimization, it is showed that the stiffness performance has been improved and the reachable workspace has been increased. The results verify the feasibility of the proposed performance indices and optimization algorithm.

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Section: Introductionmentioning

confidence: 99%

Stiffness analysis and optimization of an asymmetric 3T1R parallel mechanism

Zhu,

Ma,

et al. 2023

Proceedings of the Institution of Mechanical Engineers, Part C:

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show abstract

“…Due to the advent of modern computers, the high accuracy of FEA approaches is more accessible and has made them an appropriate method for examining the results of the other methods at the final stage. 4,[12][13][14][15][16][17][18][19] MSA relies on the same concept of FEA which each element in FEA is replaced with large compliant elements of the manipulators. Indeed, MSA is a reasonable compromise between the accuracy and computational time.…”

Section: Introductionmentioning

confidence: 99%

“…Screw theory and strain energy method have been used in solving the statically indeterminate system of over-constrained PMs. 4,15,16 Also, geometric algebra can be naturally integrated with screw theory. 32 In this paper, the statically indeterminate problem has been solved based on the defined stiffness coefficient in appropriate directions.…”

Section: Introductionmentioning

confidence: 99%

An analytical approach to the stiffness calculation of statically indeterminate 3-DOF delta parallelogram-type parallel robot

Dastjerdi,

Sheikhi,

Tale Masouleh

2023

Proceedings of the Institution of Mechanical Engineers, Part C:

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This paper introduces an analytical approach entailing a clear physical meaning for calculating the stiffness of the 3-DOF Delta parallel robot. By defining suitable linear and torsion springs, the stiffness of the robot components in different postures and the stiffness coefficients of the indeterminate parallelogram under conceivable wrenches are comprehensively obtained. Moreover, the stiffness coefficients for each limb chain are assigned, and then by considering the assigned stiffness coefficients and static equilibriums the indeterminate problem of 3-RUU DPRs is solved. By reformulating the forward kinematics which takes into account the deflected components and based on the elastic properties, the deflection in each manipulator component is calculated and the amount of moving platform twist is obtained. The proposed approach is validated by the FEA method and results reveal that the maximum error of the proposed method is 0.1489° in the orientation and 0.1420 mm in translation compared to the FEA. Then to avoid the problem of different units of translation and orientation in indexing, the virtual work concept is used for assigning an index number.

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“…Hu and Lu 11 proposed a new stiffness analysis approach considering the internal restraint force in 3-RPS PM. Cao et al 12 proposed a general method to solve the stiffness of the overconstrained PM with Scara motion and carried out stiffness optimization based on the proposed stiffness performance evaluation index. Considering the active force and restraint force, Zhang 13 analyzed the influence of position parameters and structural parameters on the stiffness of the 2SPR + RPS PM with 3-RDOF.…”

Section: Introductionmentioning

confidence: 99%

Stiffness performance analysis of a 3-PRPS kinematically redundant parallel mechanism

Xue

et al. 2022

Proceedings of the Institution of Mechanical Engineers, Part C:

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The stiffness performance of a spatial kinematically redundant parallel mechanism (KRPM) with three relative degree-of-freedom (RDOF) is analyzed. Firstly, the composition principle of the KRPM is introduced, the RDOF is analyzed, the kinematics model is established, and the overall Jacobian matrix is established based on the screw theory. Secondly, the workspace of the KRPM is drawn, and the theoretical stiffness model is established considering the internal restraint force and the external load. The stiffness variation in the workspace is drawn, and the effectiveness of the theoretical stiffness model is verified through finite element analysis. Finally, according to the theoretical stiffness model, four task-based stiffness performance evaluation indexes are obtained, and they are optimized based on the NSGA-II multi-objective genetic algorithm. The results show that adding and adjusting redundant actuators in a parallel mechanism can effectively improve the stiffness performance of the mechanism. In the meantime, different stiffness optimization schemes can be proposed for different task paths based on the NSGA-II genetic algorithm.

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A method for stiffness analysis of overconstrained parallel robotic mechanisms with Scara motion

Cited by 30 publications

References 26 publications

Stiffness analysis and optimization of an asymmetric 3T1R parallel mechanism

Stiffness analysis and optimization of an asymmetric 3T1R parallel mechanism

An analytical approach to the stiffness calculation of statically indeterminate 3-DOF delta parallelogram-type parallel robot

Stiffness performance analysis of a 3-PRPS kinematically redundant parallel mechanism

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