RBE 1001 HW 10 Mechanisms (Multi-Stage Elevator) Name: Problem statement: As in the video shown in class, your robot is required to lift a large 20. lb ball and apparatus 5.0 ft high in 2.5 seconds. You decide to use a 2-stage telescopic elevator crane to do this. The upper stage weighs 10. lb; the middle stage weighs 5.0 lb. You use a controlled sequencing cable arrangement as shown. You use ball-bearing sliders throughout the mechanism and decide to ignore friction and design a 2.0 inch dia winch drum to power it. 20.16 Cable 2 Stage 2 Stage 1 Cable2' Cable 1 ~2.0 in Winch - Thorsmission Motor + 1) How much mechanical output power is required to accomplish this task? (Hint: in 2.5 secs, how much vertical dist does the ball, the upper stage, and the middle stage travel respectively?) (ANS: ~ 80W) 1 2) Using FBD's of stage 2 and stage 1, what are the cable tension loads (F3, F2, F1)? (ANS: 15, 45, 100 lbs) 3) You choose the motor that has the attached performance. You wish to operate it at fewer than 30 amps. With an overall gearbox system efficiency of 85%, what is the minimum gear reduction ("e") you must have? (ANS: ~ 1/30) 4) If you do not provide an anti-backdrive mechanism, how much heating power (ie: P=FR) would need to be dissipated by the motor when holding the frictionless loaded mechanism stationary? (Recall that motor torque is proportional to current regardless of voltage applied and that the base resistance of the motor windings can be determined through Ohm's Law at motor stall.) (ANS: ~ 75W) 2 Voltage: 12V Speed (rpm) Torque (N m) Torque (in lbs) Current (A) Power Heat (wt) Efficiency (wt) 0 2.426 21.463 133.0 0.0 0% 1596 354 2.264 20.032 124.3 83.9 6% 1408 708 2.102 18.601 115.6 155.8 11% 1232 1062 1.941 17.170 106.9 215.7 17% 1068 1416 1.779 15.739 98.3 263.7 22% 915 1770 1.617 14.308 89.6 299.6 28% 775 2124 1.456 12.878 80.9 323.6 33% 647 2478 1.294 11.447 72.2 335.6 39% 531 2832 1.132 10.016 63.5 335.6 44% 427 3186 0.970 8.585 54.8 323.6 49% 334 3540 0.809 7.154 46.1 299.6 54% 254 3894 0.647 5.723 37.4 263.7 59% 186 4248 0.485 4.293 28.8 215.7 63% 129 4602 0.323 2.862 20.1 155.8 65% 85 4956 0.162 1.431 11.4 83.9 61% 53 5310 0.000 0.000 2.7 0.0 0% 32 3