We want to accurately position a table for a machine as shown in Figure CDP2.1. A traction-drive motor with a capstan roller possesses several desirable characteristics compared to the more popular ball screw.

The traction drive exhibits low friction and no backlash.

However, it is susceptible to disturbances. Develop a model of the traction drive shown in Figure CDP2.1(a)

for the parameters given in Table CDP2.1. The drive uses a DC armature-controlled motor with a capstan roller attached to the shaft. The drive bar moves the linear slide-table. The slide uses an air bearing, so its friction is negligible. We are considering the open-loop model, Figure CDP2.1(b), and its transfer function in this problem. Feedback will be introduced later.

X Linear slide Drive bar Traction drive motor and capstan roller (a) Va(s) G(s) X(s) (b) FIGURE CDP2.1 (a) Traction drive, capstan roller, and linear slide. (b) The block diagram model.