The isotropy of the generalized inertia ellipsoid is an evaluation index that can measure dynamic performance of a robot. This has significance in motion planning and design of a jumping robot. The generalized inertia of a jumping robot is analyzed. The generalized inertia tensor and the generalized inertia ellipsoid (GIE) are derived from the kinetic energy of the robot mechanism. From the viewpoint of geometrical shape change of the GIE, nonlinear characteristics of a jumping robot are analyzed. With the goal of minimizing nonlinear effects during its movement, the mechanism parameters of a jumping robot are optimized by adopting isotropy of the generalized inertia ellipsoid as its objective function. Example results demonstrate the efficiency and validity of the proposed optimization method.