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

Eusebio Jimenez Lopez,Raul Servin De La Mora-Pulido,Mario Acosta Flores,Daniel Servin De La Mora-Pulido,Gabriel Luna-Sandoval,Francisco Javier Ochoa-Estrella

doi:10.1109/access.2021.3073402

Abstract

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.

Highlights

Parallel manipulators have been studied by several researchers over the past two decades, because they have competitive advantages over open-chain robots, for example, greater accuracy, increased load capacity, more rigidity, among others [1]
This nonlinearity does not affect the application of the modeling methodology presented in this work, as it can be applied to model mechanical systems that move in space, since Quaternions [50] are a formal extension of complex numbers
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

Summary

INTRODUCTION

Parallel manipulators have been studied by several researchers over the past two decades, because they have competitive advantages over open-chain robots, for example, greater accuracy, increased load capacity, more rigidity, among others [1]. The use of these tools and methods involves a high mathematical calculation This increased computational cost emphasizes the need to seek new alternative ways to solve a parallel robot’s direct and reverse kinematic problems. To provide data for the training of a neural network, it is necessary to model the movements of robots or mechanisms to generate mathematical models through which it is possible to formulate inverse and direct kinematic problems. These models are built using only one analysis configuration [27]–[31], limiting the motion relationships between the links that make up a robot. The reverse problem obtained with the Newton-Raphson method was compared to those generated by the neural network

COMPLEX NUMBERS

TRAINING A NEURAL NETWORK

GENERATION OF TRAINING DATA SET TO SOLVE KINEMATICS

DISCUSSION

CONCLUSION