The drum-worm transmission device was designed as a robot reducer applied to the robot joint, which benefits the domestic localization of robot reducer. Surfaces of the beveloid internal gear tooth were used as the tool surfaces. By analyzing the internal meshing motion of the drum-worm pair, 6 frames were established. Relationships between the worm-wheel's rotation angle, the worm's rotation angle and working angle were determined by the auxiliary frame and the working frame on the internal gear. According to meshing principles, equations of the drum-worm pair's meshing, second limit curve and first limit curve were established and then drawn by MATLAB R2013b. According to parameters of the U10PLUS KV170 motor, design parameters of the drum-worm transmission device were determined. Spirals of the worm-tooth's surfaces were drawn by MATLAB to output ibl files, and then 3D-models of the drum-worm transmission device were drawn by Creo 2.0. The assemble of the internal gear and the worm in the Creo simulation environment without interference-fit was realized by adjusting the relative axial position of the beveloid internal gear with symmetrical wedge teeth. Comparing with the 220 mm-center-distance toroidal worm pair with same design parameters, the center distance of the drum-worm pair was reduced to 100 mm, which indicated that the drum-worm pair was more compact. According to distributions of the drum-worm pair's contact lines on both surfaces of a tooth, the internal gear's width was reduced from the 110 mm design-width to the 75 mm working width. Analyzing relative positions between the worm pair's first limit curve and tooth-root lines, the non-undercutting was determined by the first curve distributed inside the worm's tooth-root. Combined with traditional design methods, the beveloid internal gear plane enveloping external-rotor drum-worm transmission device with an integrated structure of drive, transmission and support was designed. In terms of driving, the motor was installed inside the worm to realize the integration of the worm and the motor. In terms of transmission, the relative axial position of the internal gear was adjusted to realize the worm pair's backlash adjustment and wear compensation. In terms of support, the support shaft was used for positioning and installation to simplify the device structure without cabinet installation. Symmetrical wedge teeth of the internal gear benefited installation and adjustment of the worm pair to realize the backlash adjustment and the wear compensation as well as the improvement of utilization ratio of the worm pair. Designing internal gear according to working width benefited the reduction of manufacture cost of the internal gear. Rationalities of the meshing transmission were verified by analyzing spacial positions of the worm pair's contact lines, second limit curve and first limit curve as well as the worm's tooth-root lines. The design scheme of an integrated structure of drive, transmission and support applied to the robot joint was proposed, and the design of the beveloid internal gear plane enveloping external-rotor drum-worm transmission device was realized.
