In this paper we consider a representative a priori unstable Hamiltoniansystem with 2 + 1/2 degrees of freedom and we applythe geometric mechanism for diffusion introduced in [A. Delshams,R. de la Llave, T.M. Seara, A geometric mechanism for diffusion inHamiltonian systems overcoming the large gap problem: heuristicsand rigorous verification on a model, Mem. Amer. Math. Soc.179 (844) (2006), viii + 141 pp.], and generalized in [A. Delshams,G. Huguet, Geography of resonances and Arnold diffusion in a prioriunstable Hamiltonian systems, Nonlinearity 22 (8) (2009) 1997–2077]. We provide explicit, concrete and easily verifiable conditionsfor the existence of diffusing orbits.The simplification of the hypotheses allows us to perform thestraightforward computations along the proof and present the geometricmechanism of diffusion in an easily understandable way.In particular, we fully describe the construction of the scatteringmap and the combination of two types of dynamics on a normallyhyperbolic invariant manifold.