A new algorithm to assess revolute surfaces through theory of surface contiunous symmetry

This paper presents a new approach to the evaluation of revolute surfaces based on surface invariance with regard to the rigid motions. The approach transforms the measurement data through an opportune homogeneous transformation matrix in order to minimize the distance between the cloud of measured points and the reference element of the class of revolution surfaces from which the sampling comes. The best transformation parameters are searched minimizing the distance between the cloud of measured points and a geometric element having the same geometric nature of the reference element of the class of the revolution surface. Afterwards the individuation of the best-fit set of transformation parameters, the form tolerance of the inspected feature can be assessed following the tolerance definition supplied by the GD&T Y 14.5 standard. Numerical simulations were performed in order to validate the effectiveness and the robustness of the approach. The great advantage of this new algorithm is that its formulation may be applied to assess any kind of surfaces without any adaptation effort.