Nowadays, 3D printers based on Cartesian kinematics are becoming extremely popular due to their reliability and inexpensiveness. In the early stages of the 3D printer design, once it is chosen to use the Cartesian kinematics, it is always necessary to select relative positions of axes and linear drives (prismatic joints), which would be optimal for the particular specification. Within the class of Cartesian mechanics, many designs are possible. Using the Euler–Lagrange formalism, this paper introduces a method for estimating the natural frequencies of Cartesian 3D printers based on the kinematic scheme. Comparison with the finite element method and experimental validation of the proposed method are given. The method can help to develop preliminary designs of Cartesian 3D printers and is especially useful for emerging 3D-printing technologies.
