Forward Kinematics and Workspace Determination of a Novel Redundantly Actuated Parallel Manipulator

Abstract

This paper presents a novel redundantly actuated 2RPU-2SPR parallel manipulator that can be employed to form a five-axis hybrid kinematic machine tool for large heterogeneous complex structural component machining in aerospace field. On the contrary to series manipulators, the parallel manipulator has the potential merits of high stiffness, high speed, excellent dynamic performance, and complicated surface processing capability. First, by resorting to the screw theory, the degree of freedom of the proposed parallel manipulator is briefly addressed with general configuration and verified by Grübler-Kutzbach (G-K) criteria as well. Next, the inverse kinematics solution for such manipulator is deduced in detail; however, the forward kinematics is mathematically intractable. To deal with such problem, the forward kinematics is solved by means of three back propagation (BP) neural network optimization strategies. The remarkable simulation results of the parallel manipulator demonstrate that the BP neural network with position compensation is an appropriate method for solving the forward kinematics because of its various advantages, such as high efficiency and high convergence ratios. Simultaneously, workspaces, including joint space and workspace of the proposed parallel manipulator, are graphically depicted based on the previous research, which illustrate that the proposed manipulator is a good candidate for engineering practical application.

Adaptive Fuzzy Sliding Mode Control for a 3-DOF Parallel Manipulator with Parameters Uncertainties

“…Let the parameters 푧, 훼, 훽 be as the three independent variables to describe the translation and rotations of the upper platform, i.e., the three independent degrees of freedom. e mobility analysis of the parallel manipulator including initial configuration and general configuration has been addressed in detail in our previous work [30] by resorting to the screw theory and modified Grubler-Kutzbach (G-K) criterion. To avoid repetition, herein, the mobility regarding the parallel manipulator is not described in this paper.…”

Trajectory Tracking Control Study of a New Parallel Mechanism with Redundant Actuation

“…One is forward kinematics with the black line depicted in Figure 4. In the forward kinematics, the position of the actuated joints is known, then the position and orientations of the moving platform can be obtained by adopting the back propagation (BP) neural network optimization method or Newton-Raphson iteration, which converges rather quickly when the initial values are close to the desired solution [42,43]. However, the solving…”

Non-singular terminal sliding mode control for redundantly actuated parallel mechanism

“…The architecture of the 2RPU-2SPR redundantly actuated parallel mechanism (R, P, U, and S indicate rotational, prismatic, universal, and spherical kinematic joints, respectively) is shown in Figure 1. 41 It mainly consists of a fixed platform, a moving platform, and four limbs with two of the same identical kinematic configuration. The prismatic joints described by the linear joint variables d i connects the fixed platform to the moving platform via a rotational joint followed by a universal joint or a spherical joint followed by a rotational joint.…”