International audienceAssembly/disassembly (A/D) simulations are important to improve designs and efficiency of product development processes. In order to get efficient simulation processes it is important to simulate all the possible relative movements between the components in a mechanical system (assembly). This is important both in the context of interactive simulation and in the context of immersive/real time simulations. If some categories of movements are missing, simulations can loose key configurations, hence they may be no longer meaningful. This paper deals with a theoretical framework for developing of a kinematical model able to represent all the valid relative movements of a reference component with respect to its surrounding ones, which form a family of trajectories. It is based on the analysis of the three basic movements: translation, rotation and helical movements. In order to determine the compatibility between different families of trajectories, a bi-quaternion is associated to each contact area between the different components. All possible trajectories for each component are analyzed, for the three basic type of movements, in order to find the compatible ones, which leads to the specification of an operator. Thus, the results of all the possible associations are determined and a general combination operator is proposed and its properties are demonstrated. This operator can form, in a real time simulation environment, the basis for determining at each moment, the valid movements between components, thus reducing the complexity of collision detection algorithms