The aim of this paper is to describe a general and systematic methodology to make controllable transitions between different solutions of the direct kinematic problem (DKP) from the joint space. This work is focused on parallel manipulators and the goal is the usage of just the input variables domain. This way, such transitions can be made controlling all the inputs simultaneously at all times. To do so, it is necessary to analyze the locus of direct kinematics singularities, where different direct kinematic solutions coalesce. It is necessary to specify which portions of such a locus specifically affect each solution. This analysis requires obtaining the locus of triple coalescence singularities. Having done this, all the information can be processed in order to obtain several maps in the joint space. Finally, it will establish the strategy on how to use these maps to connect desired solutions, including the application to a representative example.