performing gear coordinate measurement on-board multi-axis CNC machines is not just feasible but potentially offers several benefits. For the operation to yield valid results, two critical issues must be addressed: 1) how to convert the machine coordinates resulted from touch-trigger probes to gear tooth deviations, and 2) how to minimize the impact of system errors on measurement accuracy. Serving as measurement references is a grid-net of points on the gear tooth numerically determined from the tooth surface equations. A touch-trigger probe with spherical stylus is considered as having directionally variable effective radius. The multi-axis CNC machine is modeled as a two-branched linkage. The probing system comprised of the probe, the gear, the CNC machine and a referencing sphere forms two closed kinematic chains, Equations of closure are derived which define the mapping between machine coordinates and Cartesian coordinates. Forward and inverse kinematic solutions are obtained for determining the probe stylus effective radius, measuring the gear and evaluating gear tooth deviations. Measurement accuracy is maximized to approach the repeatability of the probing system by means of minimizing the number of moving machine axes for probing and dynamic determination of the effective Stylus radius. The methods are presented with the example of measuring face gears on a 6-axis CNC machine.
