Repeat Problem 1-13 assuming that the 8-bit encoder is located on the motor shaft that is connected to the link through a 50:1 gear reduction. Assume perfect gears. Problem 1-13 Referring to Figure 1.24, suppose that the tip of a single link travels a distance d between two points. A linear axis would travel the distanced while a rotational link would travel through an arc length le as shown. Using the law of cosines, show that the distance d is given by d = l/2(1 cos 0) which is of course less than fe. With 10-bit accuracy, =1 meter, and e = 90, what is the resolution of the linear link? of the rotational link? Figure 1.24: Diagram for Problem 1-12, 1-13, and 1-14.