Cooperative position and orientation modeling for dual-robot mirror milling under multi-source constraints

摘要

The mirror milling method applied in the machining of thin-walled workpieces can effectively reduce machining deformation and improve machining quality. However, it is challenging to model the collaborative relationship between the positions and orientations of dual-robot end effectors due to the coupled effects of multiple constraints. To address this issue, we propose a streamlined and adaptable system dynamics modeling technique based on the Udwadia-Kalaba (U-K) method that innovates and optimizes in terms of constraint extraction, transformation, and introduction. Firstly, based on the principle of similarity, we establish the unconstrained dynamic model of the system using the Denavit-Hartenberg (D-H) convention, Jacobian matrix, and Lagrangian equation. Simultaneously, in conjunction with the geometric constraints of the workpiece, the orientation and position cooperation constraints of the dual-robot end effectors are extracted and transformed based on the constraint-following theory. This transformation is applicable to general cases of varying curvature and thickness, resulting in an easily manageable form concerning four-point trajectory constraints. By integrating the unconstrained dynamic equation with the standardized constraint equation via the U-K method, we can construct the dynamic equation of the system under multiple-source constraints. Lastly, by employing SolidWorks and MATLAB for a joint simulation, we create a visual dynamic model of the system. The feasibility of the modeling method, in terms of cooperation, is demonstrated by processing a cylindrical thin-walled shell as the workpiece.

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