A transmission device for transmitting a force and a torque between a handling device and a tool of a medical instrument includes transmission members interconnected in a hinged manner. A convex coupling portion of a first transmission member is in each case held interlockingly in a concave coupling portion of an adjacent second transmission member in such a way that a rotation of the first transmission member about its longitudinal axis causes a rotation of the second transmission member about its longitudinal axis. A convex coupling portion of a first transmission member is in each case held interlockingly in a concave coupling portion of an adjacent second transmission member in such a way that a tensile force can be transmitted between the first transmission member and the second transmission member.