Page 120 - Robotics Designing the Mechanisms for Automated Machinery

Exercises 109

Exercise 3E-2

A blade with mass m = 1 kg driven by a spring is shown in Figure 3E-2. In the begin-
ning, the spring is compressed by a distance L 0 = 0.2 m. When freed, the blade descends
for a distance L { = 0.1 m until it comes into contact with a wire having a thickness
h = 0.004 m. The required cutting force P = 800 N. The spring has a linear characteris-
tic shown in the figure with a constant c = 5000 N/m. Calculate the time needed by the
blade to complete cutting the wire or, in other words, to travel the distance L = L^ + h.
At initial time, t= 0, the blade is at rest.

Exercise 3E-3

The DC electromotor shown in Figure 3E-3, provided with a drum, lifts a mass
m = 10 kg by means of a rope wound on the drum with a radius r = 0.035 m. The rotat-
ing part of this system (rotor of the motor, shaft, and drum) has a moment of inertia
2
/ 0 = 0.005 kg m . The motor has a linear characteristic T= 5 - 0.05 <y Nm (where
T= torque, CD = angular speed). Calculate the time needed to obtain a rotational speed
0) =10 I/sec, and the height reached by mass m at this moment in time. At the begin-
ning of the process the motor is at rest.

FIGURE 3E-2

FIGURE 3E-3