Kinematic performance of planar 5R symmetrical parallel mechanism subjected to clearances and uncertainties

Lara-Molina, Fabian Andres; Koroishi, Edson Hideki; Steffen, Valder; Martins, Leandro Augusto

doi:10.1007/s40430-018-1118-4

Cited by 16 publications

(19 citation statements)

References 36 publications

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“…• The use of two configurations in mechanism modeling makes it possible to clarify and systematize the relationships that exist between the reference position and the deformed position. This clarification is not found in the traditional modeling studies of the 5R planar parallel mechanism [36,37]. The systems of equations generated during the analysis were eight equations and eight nonlinear unknowns of the polynomial type for the inverse kinematic problem case in both configurations.…”

Section: Discussionmentioning

confidence: 92%

“…The new features presented in this work in the modeling part are summarized below: Two-configuration modeling allows a clear and correct analysis of the transition of movements and relationships between local and mobile bases. This modeling process is traditionally carried out in a single configuration presented in [33,34,35,36,37,38,49] which prevents us from observing the physics of the movement and in particular the relationships between mobile systems or bases. The mathematical modeling of the 5R planar parallel mechanism generated by the systematization of complex numbers presented in [47] developed a nonlinear equation system.…”

Section: A Modeling In the Final Configurationmentioning

confidence: 99%

“…On the other hand, the 5R planar parallel mechanism has been studied by various authors [33,34,35,36,37,38,39,40,41] as this mechanism has some advantages such as: 1) it has a simple structure, 2) it has a large workspace, 3) it has good flexibility and lack of singularities in the accessible workspace, and 4) it is easy to control [33]. This robot has been studied in various applications of Artificial Intelligence.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Modeling in Two Configurations of a 5R 2-DoF Planar Parallel Mechanism and Solution to the Inverse Kinematic Modeling Using Artificial Neural Network

López

Mora-Pulido

et al. 2021

IEEE Access

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This article introduces a new kinematic modeling method used to analyze coupled rigid multibody movements. The method was applied to the study of a 5R planar parallel mechanism's kinematics and consists of analyzing two fixed configurations of the mechanism to systematize the rotational relationships between the two structures. Mathematical models were developed using complex numbers. The inverse kinematic problem was modeled as a system of eight nonlinear equations and eight unknowns, which was solved with Newton-Raphson's method. Subsequently, with the inverse problem model, a numerical database related to the mechanism configurations, including singular positions, was generated to train a multilayer neural network. The Levenberg-Marquardt algorithm was used for network training. Finally, an interpolated linear path was used to understand the efficiency of the trained network.

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Section: Discussionmentioning

confidence: 92%

Section: A Modeling In the Final Configurationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Modeling in Two Configurations of a 5R 2-DoF Planar Parallel Mechanism and Solution to the Inverse Kinematic Modeling Using Artificial Neural Network

López

Mora-Pulido

et al. 2021

IEEE Access

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“…The effects of small variations (link lengths and joint positions) on the kinematic performance can be assessed in early stages of the mechanism design process, which corresponds to the need for improving the tolerance analysis. Lara-Molina et al [8] present a study on planar 5R symmetrical mechanisms in which Monte Carlo simulation was used to determine the effects of small deviations of link lengths and joint clearances in several design atlases (Maximum Inscribed Workspace, Global Conditioning Index, and Minimum Conditioning Index). Jawale et al [9] revise the use of a Partial Derivative Formulation (PDA) to estimate the output (angular) error in four-bar mechanisms (FBM) subjected to link tolerances.…”

Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

Tolerance Analysis of Planar Mechanisms Based on a Residual Approach: A Complementary Method to DLM

Tinoco

Durango

2019

Mathematical Problems in Engineering

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The kinematic performance of mechanisms is affected by different uncertainty sources involved in the manufacturing and assembling cycle; among these are the geometric variations. It is known that the effects of these variations produce position errors which are not usually included in the design process. With this objective, a complementary method for the tolerance analysis of planar mechanisms that incorporate geometric variations is presented in this paper. The approach is based on Direct Linearization Method (DLM) that does not consider all the kinematically admissible solutions. DLM naturally minimizes a residual functional ; however it is possible to maximize the residual by means of a proposed complementary method called H-Based Residual Method (RMH). From the proposed methodology, local and global error domains can be defined to predict the maximum and minimum position errors caused by the input variations. DLM and RMH were applied in a four-bar mechanism with dimensional and angular variations to estimate positioning errors. The results show intervals where output positions were invariant with respect to angular variations of the crank. These computations were performed through a distance ratio established with the output deviations determined with nominal angular variations. Furthermore, domain errors were predicted for a set of positions generated by a multivariate normal random algorithm with 1000 combinations of input variations (links lengths). These domains delimited all solutions created in each position stage. It means that by applying the proposed methodology it is possible to estimate the geometric errors of any combination of variations.

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“…The clearances in the axisymmetrical joints were previously modeled by [6]. Moreover, the uncertainty effect of joint clearance has widely been studied by using probabilistic approaches [7][8][9]. Additionally, several approaches have been developed to assess the influence of joint clearances on the kinematic accuracy of mechanisms.…”

Section: Introductionmentioning

confidence: 99%

A Fuzzy Approach for the Kinematic Reliability Assessment of Robotic Manipulators

Lara-Molina

Dumur

2021

Robotica

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SUMMARY This paper aims at developing a novel method to assess the kinematic reliability of robotic manipulators based on the fuzzy theory. The kinematic reliability quantifies the probability of obtaining positioning errors within acceptable limits. For this purpose, the fuzzy reliability evaluates the effect of the joint clearances on the end-effector position to compute a failure possibility index. As an alternative to the conventional methods reported in the literature, this failure possibility index conveys a novel assessment of the kinematic performance. The numerical results are compared with the well-known probabilistic approach based on the Monte Carlo simulation.

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Kinematic performance of planar 5R symmetrical parallel mechanism subjected to clearances and uncertainties

Cited by 16 publications

References 36 publications

Modeling in Two Configurations of a 5R 2-DoF Planar Parallel Mechanism and Solution to the Inverse Kinematic Modeling Using Artificial Neural Network

Modeling in Two Configurations of a 5R 2-DoF Planar Parallel Mechanism and Solution to the Inverse Kinematic Modeling Using Artificial Neural Network

Tolerance Analysis of Planar Mechanisms Based on a Residual Approach: A Complementary Method to DLM

A Fuzzy Approach for the Kinematic Reliability Assessment of Robotic Manipulators

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