Bird wings generally contain a 4-bar pantograph mechanism in the forearm that enables the wrist joint to be actuated from the elbow joint thus reducing the number of wing muscles and hence reducing the wing inertia and inertial drag. In this paper we develop a theoretical model of inertial power for flapping flight to estimate the advantage of the 4-bar pantograph mechanism by comparing the inertial power required for the case where wrist muscles are present in the forearm with the case where wrist muscles are not present in the forearm. It is difficult to predict how wrist muscles would look when there is no pantograph mechanism. Therefore a lower bound and upper bound case are defined. The lower bound case involves redistributing the elbow muscles with no increase in wing mass. The upper bound case involves replicating the biceps-triceps muscles near the wrist joint. At minimum power speed the model estimates that the 4-bar pantograph mechanism reduces the inertial power for the gull from between 6.1%-12.3% and reduces the overall power by 0.6%-1.2%. When account is taken of the tight margins involved in the design of a flying vehicle, the energy savings produced by the pantograph mechanism are significant. A ring-billed gull was chosen for the case study and an adult specimen was obtained to gather morphometric data. Lessons for the design of flapping micro air vehicles are discussed.