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

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. INDEX TERMS Parallel robots, artificial neural networks, complex numbers, kinematics, Newton-Raphson. I. 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]. These features are essential in industrial applications, such as simulators, machine tools, and CNCs, among others [2]. Due to their special characteristics, parallel robots are currently studied by various authors [3]-[8]. Parallel robots are used in several applications where high levels of accuracy and precision are required: for example, in spray paint operations [9] and machining operations [10]. To gain control of robots, the kinematic models that govern their movements are needed. These models are classified into inverse kinematics and direct kinematics. Various mathematical tools have been used to model the kinematics of parallel robots, such as homogeneous matrices [11], complex The associate editor coordinating the review of this manuscript and approving it for publication was Yongming Li .