The invention discloses a BS speed reducer, comprising an input shaft, an input shaft cover, a gap adjusting screw, a machine body, a fixing plate, a driving plate, a rolling bead, an output shaft and an output shaft cover. The BS speed reducer is characterized in that the machine body is internally provided with the input shaft, the fixing plate, the driving plate and the output shaft; S-shaped cycloid grooves are arranged on the two side faces of the fixing plate, and the driving plate is matched with S-shaped cycloid grooves which are arranged at one side of each of the input shaft cover and the output shaft; the input shaft cover is connected with the fixing plate; rolling beads are placed into the S-shaped cycloid grooves between the input shaft cover and the fixing plate, between the fixing plate and the driving plate, as well as between the driving plate and the output shaft cover; and the gap adjusting screw is arranged on the input shaft cover. The speed reducer has the advantages of compact structure, small volume, light weight, zero gap, low noises, large transmission power and stable and reliable transmission; and the transmission efficiency can reach to 88-93%. The speed reducer adopts two groups of S-shaped cycloid differential motions to realize the speed reduction and can completely change the speed reducing principle of the traditional speed change which utilizes a gear or a worm wheel tooth number to change the speed.