General method of determination of rotational conicoid profile error

A general method of determination of rotational conicoid profile error is provided. Firstly the general equation of a conicoid is acquired from all measurement points by using least squares method (LSM). And then a certain eigenvalue with its eigenvector of the quadratic terms matrix of the equation, which is the pivot of the rotational conicoid, are obtained by means of a highly accurate method. Moreover, the transformational matrix can be obtained and used to all measurement points. Finally the profile error formula of each rotational conicoid is presented along with its characteristics. In order to verify the effectiveness, an example was given. This algorithm has no model error, no special demands for the positions of work piece in the measurement space. This method has a wide usage in the field of coordinate instruments.