Metrological feasibilities of CMM touch trigger probes. Part I: 3D theoretical model of probe pretravel

New 3D model of the inaccuracy of a touch trigger probe used to collect coordinates of a measured object by coordinate measuring machine (CMM) is proposed. The analysis is performed both for one and two stage types of probes. The influence of a stylus length and diameter, a spring force and direction of a contact point approach are taken into consideration. The effects of frictional interaction between the stylus ball and a measured surface are also taken into consideration. The theoretical analysis of a tough trigger probe hysteresis is presented. Finally a computer simulation of mathematical modeling in the XYZ space is shown.