This paper presents a design method of a two-hop wireless power transfer (WPT) system for installing on a robot arm. The class-E inverter and the class-D rectifier are used on the transmission and receiving sides, respectively, in the proposed WPT system. Analytical equations for the proposed WPT system are derived as functions of the geometrical and physical parameters of the coils, such as the outer diameter and height of the coils, winding-wire diameter, and number of turns. Using the analytical equations, we can optimize the WPT system to obtain the design values with the theoretically highest power-delivery efficiency under the size limitation of the robot arm. The circuit experiments are in quantitative agreement with the theoretical predictions obtained from the analysis, indicating the validity of the analysis and design method. The experimental prototype achieved 83.6% power-delivery efficiency at 6.78MHz operating frequency and 39.3W output power.