Realisation of three-dimensional geometric model in case of bike frame measurement

This study presents a measurement method for a bike frame to solve a problem that usually relies on the digimatic callipers or mechanical molds handled by a human, therefore avoiding a long time process and measurement errors. In such a mechanism, the measured data is based on the handwritten record, and thus a difficulty may occur in further data analysis using the computer. For this reason, this study aims to develop a mathematical model of three-dimensional geometry especially applied for robotic arm-based bike frame measurement. The proposed mathematical geometric model effectively integrates the sphere formula with the inner product of normal vector to find four parameters in the sphere formula using only three measured points. Accordingly, the centre coordinate of the check point and its diameter can be calculated accurately and simply. The practical model performance also prooves that all crucial quality checking items such as centre plane offset, inside diameter, axis point and parallelism in different rotating shafts of bike frame can be achieved in term of rapid, robustness and precision. Moreover, the measurement accuracy in the estimated standard deviation and measurement uncertainty using two different bike frames is presented to verify the effectiveness of the proposed model.