The leg mechanism of the novel jumping robot, Salto, is designed to achieve multiple functions during the sub-200 ms time span that the leg interacts with the ground, including minimizing impulse loading, balancing angular momentum, and manipulating power output of the robot's series-elastic actuator. This is all accomplished passively with a single degree-of-freedom linkage that has a coupled, unintuitive design which was synthesized using the technique described in this paper. Power delivered through the mechanism is increased beyond the motor's limit by using variable mechanical advantage to modulate energy storage and release in a series-elastic actuator. This power modulating behavior may enable high amplitude, high frequency jumps. We aim to achieve all required behaviors with a linkage composed only of revolute joints, simplifying the robot's hardware but necessitating a complex design procedure since there are no pre-existing solutions. The synthesis procedure has two phases: (1) design exploration to initially compile linkage candidates, and (2) kinematic tuning to incorporate power modulating characteristics and ensure an impulse-limited, rotation-free jump motion. The final design is an eight-bar linkage with a stroke greater than half the robot's total height that produces a simulated maximum jump power 3.6 times greater than its motor's limit. A 0.27 m tall prototype is shown to exhibit minimal pitch rotations during meter high test jumps.