Abstract: A rigid speed reducer with internal and external tooth profile tooth-enveloping. The rigid speed reducer includes first- and second-level speed-reducing mechanisms. The first-level speed-reducing mechanism includes: an eccentric gear; rotary arm bearing; externally-meshing curved gear; and gear pins fixed on a first supporting frame and externally meshed with the externally-meshing curved gear. The second-level speed-reducing mechanism includes: an eccentric transmission gear; rotary arm bearing; internally-meshing curved gear, which is internally meshed and fitted with the gear pin; and an output disk linked with an output shaft. The eccentric transmission gear is in transmission connection with the externally-meshing curved gear through a dowel pin. The internally-meshing curved gear is in transmission with the output disk through a transmission pin.