This paper analyses the dynamics of an antagonistically ac-tuated tensegrity mechanism. The mechanism is subject to gravity effects , which produce both stable and unstable equilibrium configurations. The workspace is shown to be not necessarily connected and its size depends on both the geometric, spring and actuator parameters of the mechanism. The antagonistic actuation forces, which are bounded, enable controlling both the stiffness and the position within certain limits. A computed torque control law is applied and simulations show interesting behaviors of the mechanism when the desired motion makes the mechanism jump between two connected components of the workspace.