A method for optimizing a mobile platform to form a wheeled manipulator is presented. For a given manipulator, this mobile platform is optimized to have maximum tip-over stability against the reaction forces and moments caused by the movement of the manipulator. This optimization is formulated as a max–min problem, i.e., to maximize a stable region ratio (SRR) over the manipulator's workspace while minimizing a tip-over moment (TOM). For a practical solution, this max–min problem is converted to two subproblems. The first one is the worst-case analysis to determine the maximum positive value of TOM through searching over the manipulator's workspace. A positive value of TOM indicates tip-over instability. The three parameters used for this search are pertaining to the mobile platform itself, i.e., the number of support wheels, the size, and mass of the mobile platform. The second subproblem is to optimize the placement of the manipulator and accessory on the mobile platform against the identified worst case so that the entire manipulator's workspace is stable. The effectiveness of the proposed method is demonstrated by applying it to optimize a mobile drilling and riveting robot.