Eventos Anais de eventos
COBEM 2023
27th International Congress of Mechanical Engineering
Optimal dimensional synthesis of a six-link steering linkage using natural coordinates as design variables
Submission Author:
Carlos Pinzon , SC , Brazil
Co-Authors:
neider nadid romero nuñez, Carlos Pinzon, Rodrigo de Souza Vieira, Daniel Martins
Presenter: Carlos Pinzon
doi://10.26678/ABCM.COBEM2023.COB2023-0689
Abstract
Traditionally, in the dimensional synthesis of mechanisms, angles, lengths, and directed segments are mainly used as design variables and have seldom been questioned in the literature. This article uses natural coordinates as design variables in the optimal synthesis of a six-link steering linkage, showing a particular advantage over traditional design variables. The design variables correspond to the Cartesian coordinates of the kinematic pairs to the left of the line of symmetry in the neutral position of the mechanism. This way, the mechanism assembly mode is defined, and the Ackermann condition in the neutral position is guaranteed. During the optimization process, the assemblage of the mechanism may be physically impossible. To overcome this drawback, we added the residual of the constraints to the objective function multiplied by a penalty constant, ensuring that when minimizing the objective function, the constraints in the range of motion are satisfied. In addition, using the above penalty solves the problem of singular positions. The optimization problem is formulated as a multi-objective optimization problem. The primary objective function is the sum of the squared differences between the outer wheel steering angle and the ideal angle given by the Ackerman condition. The secondary objective function is the sum of the squared differences in the transmission angles and the right angle, equivalent to the sum squared of the pressure angles. The optimization problem was implemented in Matlab, considering three different weights of the objective functions. The steering angles are close to the Ackermann condition in the optimized mechanisms. In the cases where the transmission angles were included, these angles were guaranteed to be within the established limits. Moreover, the procedure proposed in this work can be extended to more complicated mechanisms, such as the double butterfly mechanism, and the procedure could even be implemented in spatial mechanisms. The ideas presented here are not confined to steering mechanisms and can be extended to other applications.
Keywords
Optimal dimensional synthesis, steering linkage, natural coordinates, design variables
