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This paper presents the design approach for a microturbopump, which is the core component of a micro steam turbine power plant-on-a-chip that implements the Rankine thermodynamic cycle for micro power generation. The turbopump integrates components that are demonstrated for the first time at microscale, such as a four-stage radial planar type microturbine and a one-sided hydrostatic thrust bearing (TB) system, along with a spiral groove viscous pump, a partially grooved seal, and a hydrostatic journal bearing. This paper presents the analytical models developed for each component, including a flow resistance model for the TB and models based on lubrication theory for the pump and seal. They are integrated to enable the microsystem design by satisfying force and power balance conditions on the rotor. Considering our previous thermodynamic cycle analysis on the Rankine micro power generation system, which is aimed at generating a few watts of electric power for applications in portable electronics or waste energy harvesting, we have designed a centimeter-scale demo turbopump device delivering 4.7 W of turbine mechanical power and 71% of turbopump efficiency in order to demonstrate the effectiveness of the component design models and system design principles. Fabrication and testing of the microturbopump are presented in the second part of this two-part paper.