The obturators have their origins on either sides of the obturator foramen.

http://en.wikipedia.org/wiki/Pelvis

The obturators have their origins on either sides of the obturator foramen and are inserted into the trochanteric fossa on the femur. Quadratus arises on the ischial tuberosity and is inserted into the intertrochanteric crest. The superior and inferior gemelli, arising from the ischial spine and ischial tuberosity respectively, can be thought of as marginal heads of the obturator internus, and their main function is to assist this muscle.