In this work, we address the dual-arm manipulation of a two degrees-of-freedom articulated object that consists of two rigid links. This can include a linkage constrained along two motion directions, or two objects in contact, where the contact imposes motion constraints. We formulate the problem as a cooperative task, which allows the employment of coordinated task space frameworks, thus enabling redundancy exploitation by adjusting how the task is shared by the robot arms. In addition, we propose a method that can estimate the joint location and the direction of the degrees-of-freedom, based on the contact forces and the motion constraints imposed by the object. Experimental results demonstrate the performance of the system in its ability to estimate the two degrees of freedom independently or simultaneously.