The complexity of today's embedded and cyberphysical systems is rapidly increasing and makes the consideration of higher levels of abstraction during the design process inevitable. In this context, the impact of modeling languages such as UML and its profiles such as MARTE is growing. Here, CCSL provides a formal description of timing constraints which have to be enforced on the considered system. This builds the basis for many further design steps and can be used e. g. for checking the consistency of the specification, for code generation, or for proving whether the time constraints have correctly been implemented at lower abstraction levels. However, most of the approaches available thus far usually focus on sole design tasks only -often even without an explicit consideration of the system's functional behavior. In this work, we are aiming for overcoming this drawback by providing a method to automatically generate a generic representation of a set of clock constraints in terms of a transition relation. Afterwards, the resulting transition relation can easily be utilized for the above mentioned design tasks. A discussion on the applicability of the generic description as well as an exemplary evaluation shows the promise of the proposed generic representation.