The concept of the tangent and cotangent bundles plays a central role in describing the dynamics of mechanical systems with singular configuration space. There is no any unified approach to the description of these objects at the present time. The reason for considering a particular construction is that the constructed model gives these bundles in the classical case. One example of such a generalization is the algebra of cosymbols of differential operators of the smooth functions algebra on a singular manifold in the category of geometric modules. This algebra has the natural structure of the Hopf algebra and the algebra dual to it in the classical case coincides with the cotangent bundle of a smooth manifold. Generalizing this example, we introduce the notion of a universal graded algebra for which we can define the structure of the Hopf algebra and the Poisson bracket is defined in a natural way on the dual algebra. This allows us to determine the evolution equation of the system.