Rotary power head is a key component of the cutting drill. After researching the current situation of the rotary power head, this paper proposed a new device called higher-order elliptic profile movable tooth transmission, and applied this device to the cutting drill, then designed a new rotary power head based on this device. The moving parts in a higher-order elliptic profile movable tooth transmission are self-balancing, such as the input shaft and the output one. The transmission can achieve the random difference of the teeth. A rotary power head of a drill with this transmission has many advantages, such as convenient disassembly or loading, large transmission torque, small radial size and the suitability for heavy loads. Finally, 3D model based on Solidworks2010 was established in this paper.