Currently, the bike frame quality check (QC) mostly relies on human operation in industry. However, some drawbacks such as it being time-consuming, having low accuracy and involving non-computerized processes are still unavoidable. Apart from these problems, measured data are difficult to systematically analyze for tracking sources of product defects in the production process. For this reason, this paper aims to develop a 3D geometry mathematical model suitable for bicycle frames QC using robotic arm-based measurement. Unlike the traditional way to find coefficients of a space sphere, the proposed model requires only three check point coordinates to achieve the sphere axis coordinate and its radius. In the practical work, the contact sensor combined with the robotic arm is used to realize the compliance items measurement in shaft length, internal diameter, verticality, parallelism, etc. The proposed model is validated based on both mathematic verification and actual bike frame check.Appl. Sci. 2019, 9, 5355 2 of 17 material handling, welding, thermal spraying, assembly, palletizing, drilling, and painting, etc. [18][19][20][21]. For instance, a platform based on a robotic arm using three degrees of freedom (DoF) principle was proposed to estimate the calibration parameters of microelectromechanical systems (MEMS) [22]. It can be placed indifferent positions for collecting a dataset of points evenly distributed. This case implies that the measurement technique using robotic arms may provide a good solution for the bike frame QC process. System Description System StructureThe proposed system structure of bike frame quality check is shown in Figure 1a, consisting of subsystems such as robotic arm, graphical user interface (GUI), programmable logic controller (PLC), contact sensor, mathematical model, database, and workbench. Each subsystem is responsible to carry out a specific task, described as follows. (1) Robotic arm can carry the contact sensor and move it to the check points. Therefore, the coordinates of check points can be found based on the robotic arm coordinate system. (2) The contact sensor can feedback a digital signal to the robotic arm immediately once it touches the surface of the check points. (3) PLC is to control the rotating disk to rotate the bike frame 90 • for the robotic arm to reach every check point. (4) Graphical user interface (GUI) provides a friendly user interface for users to input data and display a real-time measurement outcome.(5) Mathematical model presents a geometry algorithm that can effectively integrate 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 center coordinate of check point and its diameter can be calculated accurately and simply. (6) A database using MySQL is used to store the measured data and export measurement data report. (7) The workbench shown in Figure 1b is designed to sustain all hardware devices. It contains: (1) a fixing frame, (2) A rotating disk, ...

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.