Studies motion planning from one zero velocity state to another for a three-joint robot in a horizontal plane with a passive revolute third joint. Such a robot is small-Time locally controllable on an open subset of its zero velocity section, allowing it to follow any path in this subset arbitrarily closely. However some paths are "preferred" by the dynamics of the manipulator in that they can be followed at higher speeds. We describe an algorithm that plans collision-free paths in the robot's configuration space, where the motions correspond to dynamically preferred robot motions. Thus the problem of planning fast trajectories in the robot's six-dimensional state space is reduced to the computationally simpler problems of planning paths in the three-dimensional configuration space and time-scaling the paths according to the manipulator dynamics. Implementation on an underactuated manipulator is described.