Modular Calculation of the Jacobian Matrix and Its Application to the Performance Analyses of a Forging Robot

Abstract

This paper presents a modular approach for the calculation of the Jacobian matrix based on the composite modeling method. By decomposing the complicated mechanisms into simpler modules, the system Jacobian matrices can be obtained from the separated modules' local ones, which can be derived much easier. Additionally, the kinematics and dynamics models of newly designed mechanisms can be constructed fast by reusing the predefined modules, as well as the system Jacobian matrices. Therefore, the Jacobian matrix based performance indices can be obtained with this modular approach easily to characterize kinematic and dynamic manipulability, and the force capability. In order to verify the proposed method, a forging robot, which can be simplified as a complex planar 2-d.o.f. mechanism with a multiple closed-loop structure, is studied as an example. The manipulability ellipse, dynamic manipulability ellipse and inertia matching ellipse are analyzed using this approach, and the performance measures with respect to the joint space are illustrated to describe the kinematic and dynamic capability of the manipulator intuitively. The research work in this paper can serve as the basis for designing and optimizing forging robots, and motion planning for the forging process.

Keywords:

• COMPOSITE MODELING METHOD
• JACOBIAN MATRIX
• PERFORMANCE ANALYSIS
• FORGING ROBOT
• MODULAR APPROACH