The error analysis of the NC machined free form surfaces in reverse engineering

In this paper a feasible methodology that deals with the issues in reverse engineering is reported. It starts by introducing the cubic polynomial to construct the CAD model in accordance with the points measured from the original object by using the optical non-contact scanning system. The needed control points for reconstruction are sifted from the tight squeezed scanned point cloud. Next, based on the control point, the interference-free algorithm connected with the developed CAM system is used to generate the fine-cutting tool paths for NC machining to avoid over-cut. When carrying out the error analysis, points scanned from the machined replica are compared to the reconstructed CAD model to investigate the error distribution. The test-point is sampled statistically from the scanned points due to analyzing the large number of points. The suitable sample size can stand for the entire population with sufficient confidence and accuracy. Meanwhile, a datum is needed to unify both the coordinate systems of the test-point and the reconstructed CAD model to make sense of the aftermath of error detection. For fulfilling the tasks of coordinate alignment and error detection, the test-point is transformed iteratively by means of the rigid-body transformation matrix, so as to minimize the sum of squares distance. The Nelder–Meade simplex method is used in resolving the parameters of the rigid-body transformation matrix in an optimal fashion, where the trouble that arises from resolving the derivates of non-linear equation can be prevented. Once the sum of squares distance in the normal direction converges to a preset value, the coordinate system of the reconstructed CAD model and that of the test-point are treated as consistent. As a result, the margin of error and the error distribution are evaluated. An example for system implementation was also demonstrated to show the validity of the proposed methodology .