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.

中文翻译：

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测量自行车车架时三维几何模型的实现

这项研究提出了一种用于自行车车架的测量方法，以解决通常依赖于人手操纵的数字卡尺或机械模具的问题，从而避免了长时间的处理和测量错误。在这种机制中，所测量的数据基于手写记录，因此在使用计算机进行进一步的数据分析时可能会出现困难。因此，本研究旨在建立三维几何数学模型，特别适用于基于机械臂的自行车车架测量。所提出的数学几何模型有效地将球体公式与法线向量的内积集成在一起，从而仅使用三个测量点即可在球体公式中找到四个参数。因此，可以精确且简单地计算出检查点的中心坐标及其直径。实际的模型性能还证明，可以在快速，稳健性和精确性方面实现所有关键的质量检查项目，例如自行车车架不同旋转轴的中心平面偏移，内径，轴线点和平行度。此外，提出了使用两个不同的自行车车架在估计的标准偏差和测量不确定度中的测量精度，以验证所提出模型的有效性。