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A Linear Tape Motors sequentially bends flexures to precisely position a payload within a large, linear range. Movement is backlash free. Flexure bending is also used to drive large forces, using efficient mechanical advantage, anchor the Tape Motor against back-slipping and prevent sticking and jamming malfunctions. Existing permanent magnet motor drive technology can be easily adapted to energize and control the flexure bending motions. Combining flexures with rare earth permanent magnets, provides ultra compact Linear Tape Motors with very high power and force densities that hold position with power off. Their operating range can be is as long as required. Thus, Linear Tape Motors are attractive for space science instruments, where precision positioning in ultra cold operating conditions is required and where low mass and low power are premium. But, they will be attractive to many other applications as well, especially where long range, safe, precise movements of large force payloads are required, where simplicity and reliability are important, where speeds are moderate to low and where operating temperatures are not so extreme as to demagnetize the permanent magnets. The Linear Tape Motor concept is novel but, it is simple and is easily adapted to modern permanent magnet motor technology, both the hardware materials and construction methods and the electronics and computer technology that controls the hardware. Development should be short and inexpensive, with high prospects of success.