A cuspidal manipulator is one which can change posture without meeting a singularity. The non-singular posture changing ability is an important feature which should be considered when designing new manipulators. The aim of this work is to provide aids for the designer in order that, in the synthesis process, he/she has the possibility to adjust the kinematic parameters according to whether a cuspidal manipulator design is desired or not. This study applies for non-redundant 3R positioning manipulators or 6R spatial manipulators with spherical wrist.