Problem: Cascading Cylinders
What is the maximum stroke if the blind end of each cylinder is connected to the rod of the previous cylinder?
How many different discrete positions are there?
See the Solution
When working with a pneumatic cylinder and no feedback of any kind, it is hard to get any precise position except completely retracted or completely extended. Our first position is with all cylinders retracted. The next is extending cylinder 1 only, then 2 only. See the following truth table:
000000 = all cylinders retracted.
Cylinder number one is the right digit and cylinder six is the left digit.
000001 = cylinder 1 only is extended
1 = extended, 0 = retracted
000010 = cylinder 2 only is extended
000011 = cylinder 1 & 2 are extended
000100 = cylinder 3 is extended only
000101 = cylinder 3 & 1 are extended
000110 = cylinder 3 & 2 are extended
000111 = cylinder 3, 2. & 1 are extended
001000 = 4th cylinder
100000 = Position 32 and continue with another 31 positions for a total of 63 + all retracted
Math solution 2 yx 6 = 64 position counting all retracted. Two positions for each cylinder is the base number, six is the exponent. Because we started with 1-inch stroke and double that stroke each time, the total stroke is 63 inches. Remember position one is zero inches. The same math applies if you are using 6 on/off switches. Use the same binary math for the number of combinations that you will have to test to make sure there aren’t any problems with your circuit.
Note: A fan with four dip switches only has 16 combinations (2 yx 4) and by using binary math, the maximum number of tries to match the transmitter with the receiver is 16. Easier than taking a fan down to check on the code.
Deadline past. Not available for submissions.
By Ernie Parker, AI, AJPP, AJPPCC, S, MT, MM, MIH, MIP, MMH
This teaser is printed in the Fluid Power Journal. Those who submit the correct answer before the deadline will have their names printed in the Society Page newsletter and in Fluid Power Journal. The winners will also be entered into a drawing for a special gift.
Tagged air teaser, cylinders, q and a