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.

This paper presents a methodological scheme to obtain the maximum benefit in occupational health by attending to psychosocial risk factors in a company. This scheme is based on selecting an optimal subset of psychosocial risk factors, considering the departments’ budget in a company as problem constraints. This methodology can be summarized in three steps: First, psychosocial risk factors in the company are identified and weighted, applying several instruments recommended by business regulations. Next, a mathematical model is built using the identified psychosocial risk factors information and the company budget for risk factors attention. This model represents the psychosocial risk optimization problem as a Multidimensional Knapsack Problem (MKP). Finally, since Multidimensional Knapsack Problem is NP-hard, one simulated annealing algorithm is applied to find a near-optimal subset of factors maximizing the psychosocial risk care level. This subset is according to the budgets assigned for each of the company’s departments. The proposed methodology is detailed using a case of study, and thirty instances of the Multidimensional Knapsack Problem are tested, and the results are interpreted under psychosocial risk problems to evaluate the simulated annealing algorithm’s performance (efficiency and efficacy) in solving these optimization problems. This evaluation shows that the proposed methodology can be used for the attention of psychosocial risk factors in real companies’ cases.

This study presents an interdisciplinary methodology for the Resource Allocation Problem (RAP) in a textile manufacturing environment, aligned with the principles of Industry 5.0, which emphasizes the convergence of advanced technologies and the human factor. The core of this research lies in the integration of an Artificial Neural Network (ANN) to predict worker performance, coupled with process automation, to optimize the allocation of workers to machines. A key ethical consideration addressed by this methodology is the focus on psychosocial factors and workplace well-being, recognizing their contribution to sustainability and organizational success. The benefits of this interdisciplinary approach to RAP are manifold. By considering psychosocial and productivity factors in the optimization model, the study moves beyond traditional methods that often prioritize efficiency at the expense of human considerations. This human-centered approach leads to a more sustainable and socially responsible production environment. The methodology contributes to the development of new tools for managing production in ways that are not only efficient but also significantly aligned with worker well-being. By embedding human-centered constraints directly into the optimization process, this study offers a pathway to mitigate potential issues such as worker overload and improve overall worker satisfaction. Ultimately, this research underscores the value of interdisciplinarity in operational research and production management by demonstrating a cohesive methodology that balances efficiency with ethical considerations for the workforce.

Quaternions are used in various applications, especially in those where it is necessary to model and represent rotational movements, both in the plane and in space, such as in the modeling of the movements of robots and mechanisms. In this article, a methodology to model the rigid rotations of coupled bodies by means of unit quaternions is presented. Two parallel robots were modeled: a planar RRR robot and a spatial motion PRRS robot using the proposed methodology. Inverse kinematic problems were formulated for both models. The planar RRR robot model generated a system of 21 nonlinear equations and 18 unknowns and a system of 36 nonlinear equations and 33 unknowns for the case of space robot PRRS; both systems of equations were of the polynomial algebraic type. The systems of equations were solved using the Broyden–Fletcher–Goldfarb–Shanno nonlinear programming algorithm and Mathematica V12 symbolic computation software. The modeling methodology and the algebra of unitary quaternions allowed the systematic study of the movements of both robots and the generation of mathematical models clearly and functionally.