A kinematic digital twin approach to study the chaotic mixing of a liquid food system by using a delta robot with 4-DOF

Chaotic mixing offers a route to intensify liquid food processing while limiting damage to shear-sensitive structures. This study develops a kinematic digital twin of a 4-DOF delta-robot for mixing operations and uses it to evaluate chaotic trajectories for liquids. The mixing tank is discretized into a 3D voxel grid, and the Overall Distribution Ratio (ODR) is introduced as a dimensionless volumetric coverage metric that quantifies how effectively a moving tool sweeps the working volume. ODR is interpreted as a comparative surrogate of the mixing potential rather than as a direct measure of homogeneity, and it is complemented by a spatial uniformity index that quantifies how evenly the coverage is distributed inside the tank. In this study, 13 chaotic attractors and a conventional 2-DOF planetary trajectory are compared across 2 mixing tools (standard propeller, dispersive disk), motor speeds (400, 800, 1200, 1600 RPM), feed rates (3000, 6000, 9000, 12000, 15000, 18000 mm/min) and, the scale-up strategy evaluates by increasing the tank scales from 180 mm to 360 mm. As a result, the best performing chaotic trajectories retained or increased their coverage on scale-up, whereas the 2-DOF baseline lost about 35% of its coverage. Chaotic trajectories with spatially distributed basins (Aizawa, Sprott A, Guckenheimer-Holmes, Rössler) systematically outperform the 2-DOF baseline, achieving ODR values up to about 72%, whereas the 2-DOF motion rarely exceeds 20-25%. Further, the dispersive disk provides an advantage of about 6 percentage points over a standard propeller. The volumetric coverage was found to depend on the total distance traveled by the tool rather than on the feed rate and the mixing time separately. Since the plateau distance was reached within the first minutes of operation in all the tested conditions, the feed rate had a negligible effect on the final coverage. The multivariable optimization reveals the top trajectories and the conditions that can be selected for the industrial applications. Overall, the Aizawa trajectory had the highest ODR value (∼72%), followed by Sprott A and Guckenheimer-Holmes. The best chaotic configurations produce dense, spatially distributed sweeping volumes that extend into the near-wall and mid-height regions of the mixing tank. This is different from the center-toroidal patterns common in planetary mixers. Therefore, this chaotic delta-robot mixing study, characterized through a kinematic digital twin, provides a geometrically scale-resilient way to pre-screen trajectories, tooling and operating conditions computationally before performing the experiment.