## 1 Introduction  
Roundness measurement is an important operation to assure the quality of cylinders [1]. Various sizes of small cylinders are employed in mechanical components; for example, a needle roller in a mechanical bearing [2]. Since the roundness of a needle roller affects the performance of the mechanical bearing in which the needle roller is integrated [3], it is necessary to evaluate the roundness of such a small cylinder with high precision [4].  
In machine shops, a method with a dial gauge and a V-block is often employed in roundness measurement of a cylinder [5; 6; 7]. Meanwhile, the accuracy of roundness measurement in this method strongly depends on the skill of an operator, and it becomes much more difficult to carry out measurement with the decrease of the size of a workpiece. On the other hand, a roundness measuring instrument based on the rotary-scan method, in which a precision spindle and a displacement gauge are used, can carry out precise roundness measurement of a cylinder [8]. Compared with the V-block method described above, a roundness measuring instrument can reduce a deviation in roundness measurement induced by the operator. Meanwhile, even with a roundness measuring instrument, it becomes much more difficult to carry out measurement with the decrease of the size of a workpiece. Especially, the centering alignment of a small cylinder is a challenging task, and the influence of the eccentricity of a workpiece becomes much more significant with the decrease of the length and the diameter of a workpiece. Therefore, it has been difficult to carry out precision roundness measurement of a small cylinder having a diameter of less than a few millimeters [9].  
In responding to the background described above, an alternative method referred to as the stitching linear-scan method has been proposed [10]. In the method, a series of arc-profiles around the circumference of a small cylinder is obtained by using a linear-scan surface form stylus profiler [11], which is often employed for measurement of a surface form/roughness [12], and the roundness profile is reconstructed by stitching the obtained arc-profiles. It has been revealed that the proposed method can carry out roundness measurement of a small cylinder having a diameter and a length of 1.5 mm and 5 mm, respectively, which has been a challenging task using the conventional methods. Also, a good agreement can be found between the obtained roundness of a small cylinder with a diameter of 3 mm by the stitching linear-scan method and a conventional roundness measuring instrument. These results have demonstrated the feasibility of the proposed stitching linear-scan method. Meanwhile, in the proposed method, the angular misalignments of a small cylinder could affect the measurement uncertainty. Furthermore, an intensive analysis of the measurement uncertainty of the stitching linear-scan method has remained to be addressed.  
To address the aforementioned issues, a new technique for the compensation of angular misalignments of a small cylinder in the stitching linear-scan method is proposed in this paper. The proposed technique is designed in such a way that a linear-scan surface form stylus profilometer for roundness measurement is utilized to detect angular misalignments of a small cylinder in a simple manner. An experimental setup capable of compensating for the angular misalignments is also developed, and the feasibility of the proposed technique is verified in experiments. Furthermore, numerical calculations are carried out based on a Monte Carlo method [7; 13] to estimate the measurement uncertainty of the stitching linear-scan method.  
Detection and Compensation of Angular Misalignments of a Small Cylinder in the Stitching Linear-Scan Method