A study of teeth generation for arbitrary-shaped sprockets

ABSTRACT In the noncircular sprocket designing process, drawing the teeth cannot be automatically performed using any function in the drawing software, and it needs complicated manual operations and adjustments. The accuracy and time waste are big problems here. This paper proposes a procedure to automatically generate a complete 3D sprocket design from a set of sprocket pitch coordinates. Japanese standard tooth profile (JIS B 1801) is used as an example model in the procedure development. First, the tooth profile equation is derived using the theory of gearing in a particular coordinate system. Subsequently, the coordinate transformation matrix is built to attach the tooth profile on every sprocket pitch coordinate in the correct direction, remove some coordinates surpassing the outer diameter limit, and build the complete 3D sprocket profile. The proposed procedure can be implemented into programming languages with the sprocket pitch coordinate file as the input and the set of sprocket teeth coordinate as the output. With the proposed procedure, a 3D design of any shape sprocket can be generated quickly and accurately.