A cylindrical configuration robot has three joints TRL The c

A cylindrical configuration robot has three joints TRL. The control system for the robot has a 12 bits storage capacity for each joint. The telescoping joint (L) obtains its vertical motion by the rotational joint (R) about a horizontal axis. The total range of rotation is 180degrees. When fully extended, the robot\'s telescoping link measures 75 inches from the pivot point. When fully retracted robot\'s telescoping link measures 30 inches from the pivot point. Determine the following: a. The control resolution for both the L and R axes, b. The combined control resolution of the R and L axes in linear scale when the telescoping arm is folly extended and folly retracted. c. If the mechanical inaccuracy of the L axis can be characterized by a normal distribution with standard deviation equals 0.0008 inches. Determine the spatial resolution and the repeatability for this axis.

Solution

Control memory = 12 bit

From the equation above, number of increments = 2^12 = 4096

(a) Total range for rotational joints = 180

Control resolution for each rotational joint = 180/4096

= 0.0439

Total range for linear joint = 75 - 30 = 45 inch= 3.75ft.

Control resolution for linear joint = 3.75/4096 = 0.0009155ft.

(b) combined resolution= 180*75/(12*4096^2)

= 0.000067 ft.