The invention discloses an under-actuated transmission device based on flange transmission. The under-actuated transmission device based on flange transmission comprises a flange plate, a rolling mechanism, a transmission mechanism, and a driving mechanism for driving the flange plate to move; a flange guide rail is arranged on the flange plate; and the rolling mechanism is mounted on the flange guide rail in a repeated moving manner through the driving mechanism, and drives the transmission mechanism to move. As the transmission mechanism is connected with the rolling mechanism, and the rolling mechanism is mounted on the flange guide rail, when the driving mechanism drives the flange plate to move, the rolling mechanism moves along the flange guide rail to drive the transmission mechanism to move so as to realize conversion from single drive to multi-direction movement; and the under-actuated transmission device based on flange transmission is simple in structure, wider in application range and convenient for adjustment and operation, and can preferably realize under-actuated transmission.