Inspired by the idea of the coordinate transformation of the robot arm, the tube structure is analogized to the robot arm structure, and the conversion method of the tube bend processing parameters LRA to the three-dimensional coordinate points is obtained. The method first regards the tube as a “mechanical arm”; then, using the similarity of the LRA processing parameters and D-H parameters, all the LRA parameters are converted into D-H parameters; finally, the D-H parameter method is applied to calculate the distance between each axis of the " mechanical arm ". If the first space coordinate point is defined as the origin of the base coordinate system , then the position of the origin of other coordinate systems in the base coordinate system can be obtained; It has been proved by experiments that this method fast and feasible.

Tubes are widely used in the aerospace field for such things as engines, fuel pipelines, cooling systems, etc. To improve manufacturing efficiency and accuracy, researchers develop multi-camera vision methods for measuring tube geometry parameters. However, these methods cannot measure the exact position of the endpoints of the tube because the projection points of the tube endpoints have no obvious texture features in the image. To solve the above problem, a precise measurement method for tube endpoints based on spatial geometry and perspective projection model is proposed in this paper. First, we establish a Plücker coordinate system, which treats the end of the tube as a cylinder. Then, several line equations parallel to the center line are calculated on the surface of the cylinder, and their intersections with the end face are obtained on these lines, which refer to the optical center of the camera, the radius of the tube, etc. These intersections are projected onto the centerline and optimized to get the endpoint. Finally, we build a multi-camera vision measurement system consisting of 10 industrial cameras to verify the effectiveness of the proposed method. Extensive experiments have shown that the average error of this method is within 0.1 mm and the standard deviation is within 0.08 mm, which proves the superiority of our proposed method.