Minimally invasive surgical methods employ an offset drive shaft to actuate an end effector. A minimally invasive surgical method includes introducing an end effector to an internal surgical site. The end effector includes an end effector base that is coupled to the instrument shaft via a wrist. An end effector articulation mechanism is operated to reorient the end effector base relative to the instrument shaft. A surgical task is performed by operating a motor to rotate an offset drive shaft relative to the instrument shaft to actuate the end effector.