Page 121 - Robotics Designing the Mechanisms for Automated Machinery

110 Dynamic Analysis of Drives

Exercise 3E-3a)

The given mechanism (in Figure 3E-3a) consists of a DC electromotor with a char-
acteristic T= 4 - 0.1 CD Nm, a speed reducer carrying out a ratio 1:4, and a driven pinion
with a radius jR = 2 cm and moment of inertia together with the attached wheel of
2
/! = 0.01 kg m . The pinion of radius 2 cm is engaged with a rack of mass m l = 5 kg. The
rack lifts a mass ra 2 = 5 kg by means of a flexible cable. The rotor of the motor, its shaft,
2
and the wheel fastened to it have a moment of inertia I 0 = 0.001 kg m . Find the speed
of the mass m^ after the motor has been working for 0.1 second; find the distance the
mass m l travels in this time. At the beginning of the process the motor is at rest.
Answer the same questions for the case in which the drive is performed by an AC
electromotor. The characteristic of the latter is (see Expression (3.48)):

where

Exercise 3E-3b)

A screw jack driven by a DC electromotor is shown in Figure 3E-3b). The charac-
teristic of the motor is T = 4 - 0.1 a> Nm. The speed a> developed by the motor is reduced
by a transmission with a ratio 1:3. The "screw-nut" device lifts a mass m = 200 kg. The
2
moment of inertia of the rotor and the wheel attached to it IQ = 0.001 kg m ; the moment
2
of inertia of the screw and its driving wheel I 1 = 0.01 kg m ; and the pitch of the screw
is h = 10 mm. Find the height the mass will travel during time t= 0.5 sec. At the begin-
ning of the process the motor is at rest.

FIGURE 3E-3a)