A geometric approach for the outer-rotor profile as a conjugate to the inner-rotor in a hypotrochoidal rotor pump (hypogerotor pump) is proposed by means of the principle of the instantaneous center and the homogeneous coordinate transformation. The inner-rotor profile is defined by the combination of two circular arcs. Next, the radius of curvature of the outer-rotor is derived with the relationships of the trochoid ratio and the inner-rotor tooth size ratio. Then by examining the minimum radius of curvature of the extended hypotrochoidal outer-rotor profile on the convex section, an explicit formula to avoid undercutting in the hypogerotor pump is proposed. It is found that undercut or self-intersection does not occur so long as the minimum value of the radius of curvature on the convex section is not less than zero. Design examples are presented to simulate the operation and to demonstrate the feasibility of the approaches using a computer-aided design program developed on C++ language.