Comparative Study of Cartesian and Polar 3D Printer Architectures by Mathematical Modelling

Objectives: To develop a unified math model for Cartesian and Polar printers that are driven by hybrid polar stepper motors. The aim is to perform a comparative analysis in terms of model complexity and motion behavior. Methods: This study highlights the area of research, focusing on the development of comprehensive mathematical models for Cartesian and polar 3D printers driven by a hybrid bipolar stepper motor. This approach develops axis-level modeling along with subsystems such as the stepper motor. This study takes the first steps toward developing a digital twin that enables real-time simulation and adaptive control for the next generation of 3D printers. Findings: The nonlinear differential equation ensures a high-fidelity representation of the real-world dynamics. In the case of a Cartesian printer, the model uses a simple linear kinematic equation for decoupled X-Y-Z motion. On the contrary, in the case of a polar printer, it introduces a nonlinear coupled inverse kinematic relation between radial (R) and angular axis (ϴ). Novelty: By developing a unified nonlinear electrotechnical model for Cartesian and polar printers, it enables high-fidelity dynamics without linearization. It forms the base of digital twin technology and extends towards next-generation additive manufacturing systems. Keywords: Cartesian 3D Printer, Polar 3D Printer, Unified Modelling, Digital twin, Comparative analysis