An anti-backlash nut designed to translate along a lead screw in two longitudinal directions is disclosed. The nut has one or more longitudinal flexure members each having one end fixed to the nut and the other one free floating. Internal threads are formed at the free floating ends of the flexure members complementary to the threads of the screw. Incline ramps are located on the exterior of the free floating ends. A flexible compression member in the form of an O-ring surrounds the ramps for continuously urging the threads at the free floating end into forceful engagement with the threads of the screw. There is an adjustable sleeve for urging the O-ring against the ramps with variable force to increase and decrease the force with which the threads of the flexure members engage the threads of the screw.