The acceleration radius is defined as a global index for quantifying the dynamic capabilities of manipulator-positioning systems over a continuous operation region. It is generalization of previously proposed manipulability indices that are local measures of the acceleration capability. The problem of computing the acceleration radius is formulated as an optimization problem. A numerical algorithm for solving the resulting generalized semi-infinite program is presented, and the application of the acceleration radius concept to examples of manipulator design and workspace specification is illustrated. Several directions for future research are discussed.>