Achieving robotic locomotion is in general a difficult task. When the system of concern is underactuated, i.e. it has more degrees of freedom than the number of control inputs available, dynamic constraints are imposed, further complicating the task. This is the case for the brachiation motion observed in the lesser apes, i.e. gibbons and siamangs, as the gait involves periods of time at which the ape is suspended by one arm with limited torques available to influence the rotation about the handhold. Earlier work has been concerned with modeling of a 24-degrees-of-freedom monkey robot and the design of a brachiation gait. In this thesis we develop a toolbox to facilitate the design of a controller based on transverse linearization for this brachiation gait. The main focus is to stabilize the single-support part of the gait, i.e. the part that is subjected to dynamic constraints due to the lack of torque about the handhold, as traditional control theory is unable to stabilize the desired motion in this case. The developed toolbox is used in designing a controller that orbitally stabilizes an inverted pendulum system. As an initial step in achieving orbital stabilization of the brachiating gait, asymptotic convergence to the virtual holonomic constraints is demonstrated for a simplified model of the 24 degrees-of-freedom monkey robot.