# Selection of Optimal Path Control Algorithms for Probe Heads Used on Five-Axis Measuring Systems
## 1 Introduction
### Five-Axis Coordinate Measuring System  
Articulating probing systems have been utilized in CMM measurements for many years. They allow the ability to change the orientation of the stylus using two rotations around mutually perpendicular axes. Two configurations are used in their construction. In the first approach, the axis running through the stylus coincides with the probing system's vertical axis of rotation (axial adjustment); whereas in the second solution, the axis running through the stylus is parallel to the vertical axis of rotation of the probing system, and offset from it at a specified distance (side adjustment). The first solution is regarded as more accurate; however, on the contrary to the second approach, it has a limited range for rotation about the horizontal axis of a probe. Another possible classification of articulating probing systems can be found in [9], dividing them depending on the qualification process. For some probing systems the experimental qualification is needed for all orientations used during measurement; however, in the second option qualification is done only in several positions and then interpolated for any orientation. Despite the used solution, articulating probing systems working with classic CMMs have a fixed orientation during coordinate measurements, which is kept by a locking mechanism, or by the servo control system. The stylus orientation can be changed before or after point probing, but actual measurements are done only using translational moves of machine elements. Additionally, it should be noted that usually the producers specify the step of the angular increment for possible rotations, for example \(2.5^{\circ}\), \(7.5^{\circ}\), or \(15^{\circ}\). The reason for the requirement of the proper operation of the articulating probing systems is the high repeatability of angular positioning. Otherwise, any change in orientation would entail the requalification of the probe head. In five-axis measuring systems the articulating probing system becomes a crucial element of the whole device. Such a probe can remain fixed in a chosen orientation, but its rotary motions can also be utilized during measurements. In that case, the data set needed for point coordinate determination is expanded by information about the angular position of the probe head, which is given by angular encoders. The probe heads utilize axial adjustment, with two orthogonal axes of rotation. The range of possible rotations for the vertical axis of revolution, which will be called B axis in the rest of the paper, is \(-180^{\circ}\) to \(180^{\circ}\), and for the horizontal axis, which will be called A axis in the rest of the paper, the range from \(-115^{\circ}\) to \(115^{\circ}\). The probing system is oriented vertically (along the machine quill) when A and B angles are set to \(0^{\circ}\). Both measuring and touch trigger probes can work as a part of the five-axis measuring system, and both kinds use the same kinematics. One of the main differences between articulated probe heads used in three-axis CMMs and those utilized in five-axis measurements is the continuous indexation of the head. As the articulated probes use rotary moves for measurements, it must be possible to set the probe orientation freely within the working range of the probe. This is realizable thanks to the qualification process designed especially for such probing systems. It is divided into two steps: Firstly, the geometrical calibration of the head (as it is named by producers of such devices) is performed, then the probe is qualified. Both procedures are similar and based on calibration sphere measurements. However, the first procedure is done with short styli, to minimize bending and gravitational effects and, in turn, to accurately assess the geometrical errors of the head mechanism, whereas the second procedure is done for stylus and stylus tip configuration, which are chosen for measurements.