We have found periodic life-like brachiating motions of a rigid-body ape model that use no muscle or gravitational energy to move steadily forward. The most complicated of these models has 5 links (a body and two arms, each with 2 links) and 7 degrees of freedom in flight. The defining feature of all our periodic solutions is that all collisions are at zero relative velocity. These motions are found using numerical integration and root-finding that is sufficiently precise so as to imply that the solutions found correspond to mathematical solutions with exactly zero energy cost. The only actuation and control in the model is for maintaining contact with and releasing handholds which requires no mechanical work. The similarity of these energy-free simulations to the motions of apes suggests that muscle-use minimization at least partially characterizes the coordination strategies they use.