Robotic welding systems require stable, reliable supporting structures to maintain positioning accuracy, minimize deformation, and ensure safe operation during automated manufacturing processes. This study evaluates the structural performance of an automatic welding-jig conveyor frame made of aluminum extrusion profiles under loading uncertainty. A finite element analysis was conducted using Autodesk Fusion 360, supported by analytical beam-theory validation and mesh convergence assessment. Four aluminum profile configurations, namely 40×40, 40×40L 1N, 40×40L, and 40×40El, were investigated using Al6063-T5 material properties. Randomized parametric sampling was applied to generate variations in applied load, mesh size, and frame cross-sectional area, enabling assessment of displacement, von Mises stress, and safety factor under different structural conditions. The validation results showed acceptable agreement between analytical and numerical responses, with error ratios below 10%. The 40×40El profile, despite having the smallest cross-sectional area, remained structurally feasible, producing a maximum von Mises stress of 26.37 MPa, a maximum displacement of 356.27 μm, and a safety factor of 9.1 under the maximum loading condition. Parameter interaction analysis indicated that the applied load strongly influenced both displacement and stress, while the cross-sectional area mainly affected displacement. Mesh size showed a negligible influence within the converged range. The results demonstrate that the proposed finite element framework can support preliminary structural selection of modular aluminum frames for automated welding equipment.