Measuring and reconstructing the shape of workpieces have been considered as a fundamental step in both reverse engineering and product quality control. Owing to increasing structural complexity of recent products, measurements from multiple directions are typically required in current scanning techniques. Specifically, the plane structured light can be applied to measure one area of a part at a time, with an additional algorithm required to merge the collected data of each area. Alternatively, the line structured light sensor integrated on CNC machines or CMMs could also realize multi-view measurement. However, the system needs to be repeatedly calibrated at each new direction. This paper presents a flexible scanning method by integrating laser line sensors with articulated arm coordinate measuring machines (AACMM). Since the output of the laser line sensor is 2D raw data in the laser plane, our system model introduces an explicit transformation from the 2D sensor coordinate frame to the 3D base coordinate frame of the AACMM (i.e., the translation and rotation the of the 2D sensor coordinate in the sixth coordinate system of AACMM). To solve the model, the “conjugate pairs” are proposed and identified by measuring a fixed point (e.g., a sphere center). Moreover, a search algorithm is adopted to find the optimal solution, which noticeably boosts the model accuracy. The experimental results show that the error of the system is about 0.2 mm, which is caused by the error of the AACMM, the sensor error and the calibration error. By measuring a complicated part, the proposed system is proved to be flexible and facilitate, with the ability to measure a part expediently from any necessary direction. Furthermore, the proposed calibration method can also be used for robot hand-eye relationship calibration.