Amir Rezaei

An interval-valued fuzzy controller for complex dynamical systems with application to a 3-PSP parallel robot

In this paper, we present a novel interval-valued fuzzy model-based controller for handling the effects of uncertainty in controlling a complex dynamical system. Theoretically, model-based controllers may be the ideal control mechanisms; however, they are highly sensitive to model uncertainties and lack robustness. These controllers are also computationally intensive, rendering them unusable for many real-world applications. In this work, we incorporate an interval fuzzy logic paradigm into a computed-torque controller for a 3-PSP parallel robot. This paradigm aims to handle the uncertainties in the robot model. The proposed approach benefits from algebraic operations on type-I fuzzy numbers to enhance its capability in dealing with uncertainty. The simulations prove the superiority of the proposed controller in the presence of uncertainty. Furthermore, comparisons with a competing type-I reduced controller as well as a PD controller show this superiority to be more pronounced especially when noise level is remarkably high. Moreover, the designed controller satisfies the computational complexity constraints for real-time implementation.

Position and stiffness analysis of a new asymmetric 2PRR–PPR parallel CNC machine

In this paper, structural stiffness analysis of a new 3-axis asymmetric planar parallel manipulator, a 2 P RR–P P R structural kinematic chain, is investigated. The manipulator is proposed as a tool holder for a 5-axis hybrid computer numerical control (CNC) machine. First, the structure of the robot is introduced and inverse kinematics solution is presented. Secondly, stiffness matrix of the robot is determined using a continuous method based on Castigliano’s theorem and calculation of strain energy of the robot components. This method removes the need for commonly used simplifying assumptions and, therefore, results in good accuracy. For this purpose, force and strain energy for each segment of the robot are analyzed. Finally, to verify the analytical results, commercial FEM software is used to simulate the physical structure of the manipulator. A numerical example is presented which confirms the correctness of the analytical formulations.

Stiffness Analysis of a Spatial Parallel Mechanism With Flexible Moving Platform

In this paper, stiffness analysis of a 3-DOF spatial, 3-PSP type, parallel manipulator is investigated. Most previous stiffness analysis studies of parallel manipulators are performed using lumped model as well as assuming a rigid moving platform. In this paper, unlike traditional stiffness analysis, the moving platform is assumed to be flexible. Additionally, a continuous method is used for obtaining mathematical model of the manipulator stiffness matrix. This method is based on strain energy and Castigliano’s theorem [1]. For this purpose, first we solve inverse kinematics problem then We must find relationship between the applied external torques on the moving platform and the resultant joints forces. Next, strain energy moving platform is calculated. Strain energy of this element is calculated using force analysis and inverse kinematics problem. Finally, a FEM model is generated and used to simulate the physical structure. Simulation results are compared with the analytical model.Copyright

Implementing the homotopy continuation method in a hybrid approach to solve the kinematics problem of spatial parallel robots

In this paper, first the application of homotopy continuation method (HCM) in numerically solving kinematics problem of spatial parallel manipulators is investigated. Using the HCM the forward kinematics problem (F-Kin) of a six degrees of freedom (DOFs) 6–3 Stewart platform and the inverse kinematics problem (I-Kin) of a 3-DOF 3-PSP robot are solved. The governing equations of the kinematics problems of the robots are developed and embedded in the homotopy continuation function. The HCM is utilized in order to solve the nonlinear system of equations derived from the kinematics analysis of the robots. Then, to represent the real case application an initial guess far from the correct answer is selected. It is shown that, comparing with the Newton–Raphson method (NRM), the F-Kin calculation time for the Stewart robot is decreased by 43%. Therefore, using the HCM a hybrid method is suggested to solve the F-Kin of the Stewart robot. Furthermore, the HCM, as an innovative method, relieves other downsides of the conventional numerical methods, including a proper initial guess requirement as well as the problems of convergence.