Genetic and hybrid algorithms for optimization of non-singular 3PRR planar parallel kinematics mechanism for machining application

Abstract

SUMMARYThis paper proposes a special non-symmetric topology of a 3PRR planar parallel kinematics mechanism, which naturally avoids singularity within the workspace and can be utilized for hybrid kinematics machine tools. Subsequently, single-objective and multi-objective optimizations are conducted to improve the performance. The workspace area and minimum eigenvalue, as well as the condition number of the homogenized Cartesian stiffness matrix across the workspace, have been chosen as the objectives in the optimization based on their relevance to the machining application. The single-objective optimization is conducted by using a single-objective genetic algorithm and a hybrid algorithm, whereas the multi-objective optimization is conducted by using a multi-objective genetic algorithm, a weighted sum single-objective genetic algorithm, and a weighted sum hybrid algorithm. It is shown that the single-objective optimization gives superior value in the optimized objective, while sacrificing the other objectives, whereas the multi-objective optimization compromises the improvement of all objectives by providing non-dominated values. In terms of the algorithms, it is shown that a hybrid algorithm can either verify or refine the optimal value obtained by a genetic algorithm.

External Kinematic Calibration of Hybrid Kinematics Machine Utilizing Lower-DOF Planar Parallel Kinematics Mechanisms

“…As a result, x p2 = x p3 = x p . The optimization procedure is discussed in [17]. Figure 2 shows the hybrid scheme of the machine.…”

“…The complete forward kinematics of the mechanism at hand which includes the determination of the angle θ can be seen in [17]. In this paper, only the determination of x and y given the angle θ is presented for the kinematic calibration purpose.…”

Comparative Kinematic Analysis and Design Optimization of Redundant and Nonredundant Planar Parallel Manipulators Intended for Haptic Use

“…On the one hand, the optimization of geometric parameters of PMs is a well-studied problem. 5,[15][16][17][18][19] Generally speaking, the optimization goal is conducted to obtain a compact structure that covers a desired WS free from PS. The dexterity index is the most used performance index.…”

“…Saafi et al 5 optimized the geometric parameters of a new spherical PM in aim to eliminate PS from a prescribed WS. Rosyid et al 17 optimized a planar parallel robot for machining applications. Stocco et al proposed in ref.…”

Multibody Dynamics of Nonsymmetric Planar 3PRR Parallel Manipulator with Fully Flexible Links

“…While the previous works as summarized in Table 1 studied symmetric PMs, this work investigates a nonsymmetric planar 3PRR manipulator previously discussed in References [24,25]. In the previous works with symmetric topologies, only one branch, that is, one leg, can be used to evaluate the dynamics of the manipulator.…”