Kinematotropic linkage are fascinating as they can switch between motion mode with different DOF. Beside the mere curiosity, this phenomenon has also application potential. From this perspective it is crucial to consider the limitations that the actual motions impose on the operation of such linkages. Such a limiting factor is the smoothness of the transitory motion when switching between motion modes with different DOF. Given a particular kinematotropic mechanism, the feasible motions can be analyzed by means of a local higher-order analysis of the configuration space. This is addressed in this paper. The computational part of the method involves only Lie brackets of the instantaneous joint screws. Two examples are presented: a 7R linkage and the Wunderlich linkage. It is shown that the latter possesses a regular kinematotropy, i.e. it can smoothly move between its motion modes.