Abstract
In order to efficiently solve a forward kinematics of parallel manipulators for real-time applications, a Jacobian free monotonic descent algorithm is proposed in this article. The system of nonlinear equations of a specified 6-degree-of-freedom parallel manipulator is established using a geometric analysis method. The proposed Jacobian free monotonic descent algorithm is modified using a traditional Newton–Raphson method by employing a first-order Taylor series expansion to numerically approximate a Jacobian matrix. A monotonic descent factor is employed for preventing the iteration from divergence even with poor initial conditions. The proposed algorithm inherits the merits of the Newton–Raphson algorithm and overcomes its drawbacks. The Jacobian free monotonic descent algorithm is programmed in MATLAB/Simulink and then is compiled to a real-time PC system with xPC target technology for implementation. The experimental results demonstrate that the proposed Jacobian free monotonic descent algorithm is ef...
Highlights
A 6-degree-of-freedom (DOF) parallel manipulator, sometimes called hexapod or parallel kinematic machine (PKM), is a closed-loop mechanism presenting very good performance in terms of accuracy, rigidity, and ability to manipulate large loads.[1,2,3] It has been extensively studied by virtue of its superior performance and widely utilized in motion simulators, isolation platforms, radio telescope, machine-tool industry, and so on.[4]
As one of the key research issues in the parallel manipulator, the kinematics problem is closely related to the relations between the mechanism’s position, velocity, acceleration, and mechanism parameters such as link lengths and angles, which are divided into two categories: an inverse kinematics problem (IKP) and forward kinematics problem (FKP).[5]
Since the FKP is widely applied in the closed-loop control system to real-time estimate the pose of the end-effectors, many efforts have been made in solving FKP either in general cases or special cases
Summary
A 6-degree-of-freedom (DOF) parallel manipulator, sometimes called hexapod or parallel kinematic machine (PKM), is a closed-loop mechanism presenting very good performance in terms of accuracy, rigidity, and ability to manipulate large loads.[1,2,3] It has been extensively studied by virtue of its superior performance and widely utilized in motion simulators, isolation platforms, radio telescope, machine-tool industry, and so on.[4]. Yang et al.[25] adopted a monotonic descent operator in the traditional NR algorithm and updated operator by descent rules according to the computing results of each iteration to conquer the disadvantages of possible diverging with inappropriate initial solutions In their researches, they mainly concentrated on the sensitivity of the initial conditions, computation efficiency and generality of the Jacobian matrix, which usually require detailed analytical analysis and vary from one configuration of parallel manipulator to another type, were not covered. Before implementing the NR algorithm in a real-time system, a detailed analytical analysis is needed to get the Jacobian matrix and the analysis varies from one configuration of parallel manipulator to another type, which is cumbersome and timeconsuming To solve this problem, the proposed JFMD algorithm forms the Jacobian matrix in a numerical way using a first-order Taylor series expansion approximation. Turn to Step 2 and continue the iterative loop
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