Subject:
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SSClagorpion - The Sequencer (long)
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Newsgroups:
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lugnet.technic
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Date:
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Sat, 3 Jul 2004 23:43:31 GMT
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Viewed:
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24214 times
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Airline flights offer long stretches of nothing to do. I use these times to
brainstorm into my my LEGO idea logbook.
On a flight to Boston, I figured out how to graphically design pneumatic
sequencers. This led to creations such as inchworm, quad242, and hex363.
On my recent flight from California I was pondering the sequencer used by
quad242 and hex363..... because I was planning on using this sequencer for
SSClagorpion.
The quad242/363 sequencer uses a 10 step sequence to achieve walking. Four of
the ten steps do not involve leg movement, but instead involve movement of
timing only pistons.
By staring at the sequencer and overlapping piston movements, I've eliminated
all four of the dead cycles and now have a six step sequencer with no dead
cycles. Below is a graph I used to develop this new circuit. Horiztonal lines in
the graph represent unchanging pistons. Backslashes represent contracting
pistons, and forward slashes represent expanding pistons.
| | | |_|_|_| Leg group 1 vertical timing piston
A |\|_|/| | | |
|_| | | |_|_| Leg group 1 vertical muscle pistons
B | |\|_|/| | |
|_|_|_| | | | Leg group 2 vertical timing piston
C | | | |\|_|/|
| |_|_|_| | | Leg group 2 vertical muscle pistons
D |/| | | |\|_|
| | | |_|_| |
E |_|_|/| | |\| All leg's horizontal muscle pistons.
1 2 3 4 5 6 <--- Step Number
Below is a graph showing the two leg groups horizontal and vertical movements.
We are looking in from the side at a leg from each leg group. Each horizontal
and vertical arrow (pardon the ascii art), represents a step in the timing
diagram above. Each arrow is tagged with the step number associated with the
graph above.
6 3
<-----A <-----A
1| LG1 |5 4| LG2 |2
V-----> V----->
3 6
The above graph leads to the following six step image sequence.
After step 1
....... .......
. . . . Piston D expands
X...... ......X
After step 2
....... ......X
. . . . Piston B contracts
X...... .......
After step 3
....... X......
. . . . Pistons E expand/contract
......X .......
After step 4
....... .......
. . . . Piston B expands
......X X......
After step 5
......X .......
. . . . Piston D contracts
....... X......
After step 6
X...... .......
. . . . Pistons E expand/contract
....... ......X
For those of you familiar with my method for describing pneumatic circuits I end
up with these equations.
Ac = BC~E
Ax = ~B
Bc = ~AD
Bx = A
Cc = ADE
Cx = ~D
Dc = B~C
Dx = C
Ec = ~D
Ex = ~B
The idea behind this design technique is to use a piston combined with one
switch to get an AND gate (credit to Mark Terrabain for this simple and elegant
concept). By combining piston's expanded/contracted states using AND gates, we
can implement the above formulas. These AND functions let us synchronize the
transitions from step to step, no matter how fast or slow pistons expand.
The purpose for pistons A and C are to make the vertical leg pistons B and D
always have pressure applied (so we don't have to use Steve Hassenplug's
mechanical leg lock). My initial circuits for quad242 sometimes have the
vertical leg muscle pistons pressurized all the time, and it would collapse
under its own weight. By adding pistons A and C (which are not always
pressured, but also are never weight bearing), we can control pistons B and D
and always have them be pressurized.
Quad242's and hex363's original circuit's were completely synchronized. This led
to the four dead cycles where pistons A and C were transitioning.
The new six step sequencer breaks the complete synchronization at two points in
the circuit to eliminate all dead cycles.
At the end of step 3, we expect pistons A and E to be expanded. These cause
piston B to expand and C to contract in step 4. This leads us to this formula
for piston C
Cc = AE
If we try to use this same formula for piston B's contract port, piston B will
not always be pressurized allowing it to collapse because it is weight bearing.
So for piston B we have to use this formula:
Bx = A
This now allows for a race in the pneumatic circuit. Piston C cannot contract
until both pistons A and E expand completly, but Piston B will expand whenever
piston A is expanded. If piston A expands more slowly or at the same rate as
pison E, pistons B and C will get change stimulus at the same time. But if
piston A expands more rapidly than piston E, Piston B will will start to expand
before piston C starts to contract. So piston B can race ahead of of piston C.
This means that piston B could start to put the foot down before the horizontal
sweep of piston E completes. I don't think this will be a huge issue unless
horizontal leg sweeps are twice as slow as leg drops. A small amount of overlap
between leg drop and horizontal sweep will be a non-issue.
Anyway... for anyone still reading this long diatribe, I think the new circuit
will work 40% faster than its predecessor.
I'm going to study to see if I can eliminate pistons A and C using Steve's
mechanical leg lock.
Kevin
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Message has 2 Replies:
 | | Re: SSClagorpion - The Sequencer (long)
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| (...) Sounds good. I think the whole thing will go faster, if there are less pistons to move, because less air is required. So, how many pistons are there? It looks like just the five. Can we put sensors on pistons A & C to determine which state (...) (20 years ago, 4-Jul-04, to lugnet.technic)
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