The direct kinematic problem in parallel manipulators has multiple solutions that are traditionally called assembly modes. Non-singular transitions between some of these solutions have been detected and shown in the past. Cusp points have been defined as special points on the projection of the singularity curve onto the joint space that have the property of allowing such a non-singular transitions when encircling them. In this paper the authors will show that the condition for such a transition is more general. Authors also argue about the need for a differentiation between the concept of assembly mode and solution of the direct kinematic problem.