Internal gear pump

1. An internal gear pump that accommodates: a ring-shaped internally toothed gear provided with internal teeth, and an externally toothed gear provided with external teeth which internally mesh with the internal teeth of the internally toothed gear, the externally toothed gear being eccentrically disposed inside the internally toothed gear, the number of internal teeth being one greater than the number of external teeth,

wherein, in any one of the external teeth and the internal teeth, a tooth tip section and a meshing section are formed by a curve having one continuous curvature, the curve being formed by Equations (1) to (5) below with which a maximum curvature is at an apex of a tooth tip, and the curvature gradually reduces towards a tooth bottom,

r=ro−dr ·cos θ,  Equation (1):

Px =( ro−dr )+¼ dr {1−cos(2θ)},  Equation (2):

Py =¼ dr {− 2θ+sin(2θ)},  Equation (3):

Qx=Px−r ·cos θ, and  Equation (4):

Qy=Py+r ·sin θ,  Equation (5):

where

r is a radius of a curve,

ro is a reference diameter,

dr is a variation,

θ is a parameter,

Px is an X coordinate of a trajectory center,

Py is a Y coordinate of the trajectory center,

Qx is an X coordinate of a point on a curve generated by the trajectory center (Px, Py), and

Qy is a Y coordinate of the point on the curve generated by the trajectory center (Px, Py).