## 2 Challenges for Modeling of Five-Axis Coordinate Measuring Systems
### Determination and Modeling of Other Sources of Errors
#### 2.3.4 Other Error Sources  
Other possible error sources include influence of probe head calibration and algorithms used for controlling a probe head measuring path. Calibration in the case of articulating probe heads with continuous orientation differs from that used for typical CMMs. It is divided into two parts: head calibration and probe calibration. Both are based on measurements of calibration sphere, but additionally the optimal touch speed and probe head maximal acceleration are determined. Furthermore, the calibration sphere is measured with various orientations of probe head which can determine the map of probe head errors. Studies conducted at LCM shows that calibration has certain impact on the measurements results, especially on measurements of length, to a minor extent it also affects form error measurement.  
Additionally, the functioning of five-axis systems can be affected by the algorithms responsible for measuring path controlling. For example, the dedicated software offers number of possibilities for cylindrical feature controlling which include measurements done from a fixed position of head or measurement path along the centroid. Depending on the chosen option, the difference between coordinates obtained along the cylinder axis can vary even in tenth of mm which, of course, affects the measurement result.  
It is extremely important to properly consider the impact of individual factors on the uncertainty of measurement which is a result of the virtual machine operation. Influence of factors such as length of stylus can be included into kinematic or probe head errors models. The situation is more complicated in case of factors like probe hysteresis or influence of probe calibration. Impact of the last of mentioned factors will not be visible with simulation because each time the same radial correction will be applied for certain measured points. However, if the value of actual tip ball radius would be burdened with error it would be transferred into measurement results. Therefore, it may be necessary to estimate the uncertainty associated with each of the factors and then include all of them as well as uncertainty  
Figure 4: The difference between radial errors obtained for different standards during calibration and five-axis measurements. The radial errors are shown in dependence on changing angle of approach \(\alpha\).  
obtained through the simulation in overall measurement uncertainty (e.g., using the propagation of uncertainty rule).  
The next source that should be taken into account is the influence of ambient conditions, especially temperature variations. The aforementioned geometrical model of the kinematic structure assumes that the mechanism is functioning at the reference conditions, i.e., at a temperature of 20 \({}^{\circ}\)C. Deviations from this temperature causes changes in the values of geometric parameters, especially those expressing the length. Implementation of a model which does not accommodate changes of parameter values with the temperature variation would lead to discrepancies between the actual position of the stylus tip center, and the position calculated using the forward kinematics.  
The research presented in [14; 15] shows that the thermal influences have a strong impact on the geometric accuracy of different kinematic structures. The influence of the temperature is not only connected with the linear expansion of materials. The temperature gradients of mechanism parts and the gradients of ambient temperature should also be considered as influences disturbing the accuracy of manipulators. Some of the errors connected with the temperature may be minimized by using resistant materials or sophisticated construction of the manipulators, however the thermal effects cannot be fully compensated. This is why the temperature influences should be incorporated in the Denavit-Hartenberg parametric model and then verified experimentally.