Cable-Extension Transducer; sometimes also known as a string pot; draw wire sensor; string encoder or VO-vo sensor, is a device used to detect and measure linear position and velocity using a flexible cable and spring-loaded spool. Simply mount the transducer's body to a fixed surface and attach the stainless steel cable to the movable object. As the object moves, the digital encoder produces pulses proportional to the cable's linear extension. The diameter of the spool is R = 5 cm and the maximum displacement the transducer can detect is 150 cm. The maximum tension on the cable is 20 N when the cable is fully extended and 5 N when the cable is in the initial condition. The moment of inertia of the spool is J = 10 kgm^2 and the viscous friction of the shaft is B = 2.1 * 10^-2 Ns.
Next, draw the necessary circuit after the encoder to read the position. Assume that the encoder has 1000 pulses/rev. What would be the resolution of the transducer measuring displacement (X direction)? Find the spring constant (K) of the power spring in terms of N/rads. (Notice that tension is maximum when the cable is fully extended and there is pretension when the cable is in the zero position). Find the maximum speed that can be measured by this transducer. (Hint: Write down the differential equation and try to find the maximum speed of the cable under minimum spring torque).
