Meshing principle of conical surface enveloping spiroid drive

•A novel type of the spiroid drive is put forward, which may be called the conical surface enveloping spiroid drive.•The meshing theory of the drive is established fully and systematically.•The reference-point-based meshing theory is developed to research the transmission.•An approach to compute the conjugate zone and the contact line for the gearing is put forth.•A technique is proposed to detect the solution existence and to provide the reasonable initial value for iteratively solving a system of nonlinear equations.•The meshing characteristics of the gearing are investigated numerically.