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Simulation of XYC trajectory in five-axis machine tool and the Jacobian-based error estimation

Error estimation methods attract more attention with the increasing demands of five-axis machining. The link and motion errors are an important source of the machine tool deviations. These errors can be identified by the Jacobian matrix, an interesting tool which is simply constructed from the machine tool topology and joint coordinates. In this paper, the volumetric errors are simulated using the homogenous transformation matrix through a circular interpolation of the X and Y axes synchronized with a C-axis rotation. The Jacobian matrix is formed and after a singular value decomposition, the redundant and confounded error parameters are removed and consequently the Jacobian matrix is reduced. The simulated volumetric errors are then used to find error parameters in the case of a horizontal five-axis machine tool. The comparison of simulated and estimated error parameters shows the efficiency of using the Jacobian matrix in error identification.