15. Suppose the mechanical inaccuracies in the open-loop positioning system of Example 7.1 are described by a normal distribution with standard deviation = 0.006 mm. The range of the worktable axis is 1600 mm, and there are 16 bits in the binary register used by the digital controller to store the programmed position. Other relevant parameters from Example 7.1 are the following: pitch = 6.0 mm gear ratio between motor shaft and screw = 8.0, and number of step angles in the stepper motor = 28. Determine the (a) control resolution, (b) accuracy, and (c) repeatability of the positioning system.