A novel, low-cost technique for modelless calibration of a 3-axis parallel kinematic machine

Purpose The purpose of this paper is to propose a novel measurement technique and a modelless calibration method for improving the positioning accuracy of a three-axis parallel kinematic machine (PKM). The aim is to present a low-cost calibration alternative, for small and medium-sized enterprises, as well as educational and research teams, with no expensive measuring devices at their disposal. Design/methodology/approach Using a chessboard pattern on a ground-truth plane, a digital indicator, a two-dimensional eye-in-hand camera and a laser pointer, positioning errors are explored in the machine workspace. With the help of these measurements, interpolation functions are set up per direction, resulting in an interpolation vector function to compensate the volumetric errors in the workspace. Findings Based on the proof-of-concept system for the linear-delta PKM, it is shown that using the proposed measurement technique and modelless calibration method, positioning accuracy is significantly improved using simple setups. Originality/value In the proposed method, a combination of low-cost devices is applied to improve the three-dimensional positioning accuracy of a PKM. By using the presented tools, the parametric kinematic model is not required; furthermore, the calibration setup is simple, there is no need for hand–eye calibration and special fixturing in the machine workspace.

Structural dynamics of a 3 DOF parallel kinematic machine

Milling is an intrinsically interrupted cutting operation; therefore, vibrations occur. There are both self-excited (chatter) and forced vibration. Vibrations in milling appear due to the lack of dynamic stiffness of some components in the machine tool-tool-workpiece system. If the vibrations are excessive, the machine stability is negatively affected. In this paper a parallel kinematic machine is modelled and structurally analyzed, considering vibrational parameters (mass, inertia, stiffness, and damping). Theoretical results are used to verify the model. The proposed model provides an effective guide to design milling machines with the best structural arrangement (architecture) and enhancing performance. The value of this finding is in answering the research question: ""Should the machine tool-tool-workpiece system be kept decoupled to mitigate the vibration generated during a cutting operation?"". Two approaches were proposed to determine which option (coupled or decoupled bases) provides greater dynamic rigidity. The evidence shows that the decoupled base proposal maintains a cutting operation without displacement peaks due to greater operation times and better damping response.

A New Method for Error Modeling in the Kinematic Calibration of Redundantly Actuated Parallel Kinematic Machine

This paper presents a new method for error modeling and studies the kinematic calibration of redundantly actuated parallel kinematic machines (RA-PKM). First, a n-DOF RA-PKM is split into several n-DOF non-redundantly actuated sub-mechanisms by removing actuators in limbs in an ergodic manner without changing the DOF. The error model of the sub-mechanisms is established by differentiating the forward kinematics. Then, the complete error model of the RA-PKM is obtained by a weighted summation of errors for all sub-mechanisms. Finally, a kinematic calibration experiments are performed on a 3-DOF RA-PKM to verify the method of error modeling. The positioning and orientation error of the moving platform is replaced by the positioning error of the tool center point, which was reduced considerably from 3.427 mm to 0.177 mm through kinematic calibration. The experimental results demonstrate the improvement of the kinematic accuracy after kinematic calibration using the proposed error modeling method.