Orbital angular momentum (OAM, Jo), systemic mass (M) and orbital period (P) distributions of chromospherically active binaries (CAB) and W Ursae Majoris (W UMa) systems were investigated. The diagrams of and logJo-logP, logM-logP and logJo-logM were formed from 119 CAB and 102 W UMa stars. The log Jo-logM diagram is found to be most meaningful in demonstrating dynamical evolution of binary star orbits. A slightly curved borderline (contact border) separating the detached and the contact systems was discovered on the logJo-logM diagram. Since the orbital size (a) and period (P) of binaries are determined by their current Jo, M and mass ratio, q, the rates of OAM loss (dlogJo/dt) and mass loss (dlogM/dt) are primary parameters to determine the direction and the speed of the dynamical evolution. A detached system becomes a contact system if its own dynamical evolution enables it to pass the contact border on the logJo-logM diagram. The evolution of q for a mass-losing detached system is unknown unless the mass-loss rate for each component is known. Assuming q is constant in the first approximation and using the mean decreasing rates of Jo and M from the kinematical ages of CAB stars, it has been predicted that 11, 23 and 39 per cent of current CAB stars would transform to W UMa systems if their nuclear evolution permits them to live 2, 4 and 6Gyr, respectively.