Question

5. A precision table-leveling scheme shown in figure relies on thermal expansion of actuators wnder two comers to level the table by raising or lowering their respective comers. The parameters are as follows: Tact = actuator temperature Tamb = ambient air temperature heat-flow coefficient between the actuator and the air C = thermal capacity of the actuator R = resistance of the heater Assume that (1) the actuator acts as a pure electric resistance, (2) the heat flow into the actuator is proportional to the electric power input, and (3) the motion d is proportional to the difference between Tact and Tamb, due to thermal expansion. Find the differential equations relating the height of the actuator d versus the applied voltage v (2 points) (al (a) Precision table kept level by actuators; (b) side view of one actuator

Answer 1

2 6 dr

vid eit t voltage v v)