1. Industrial Automation
Lucas Method

2. Re-look at Cascade A+, B+, B-, C+, C-, A-
Can we get a better circuit than that obtained by Cascade, i.e. with fewer components?
Consider the example:
A+, B+, B-, C+, C-, A-
I II III
The Groupings
In Cascade, 2 Group valves are needed to switch the group manifolds from I, to II to III, and back to I in sequence after the B+, C+ and A- motions respectively.
Can the b+, c+ and a- limit valves do this without using additional valves?

3. Lucas Method A+, B+, B-, C+, C-, A- I II III Basic approach
Uses the limit valve of the last motions(b+, c+, a-) to supply pressure to the next Group manifold and turn this off only at the end of the Group.
Example: Use a 3/2 air-reset valve for b+ to supply air pressure to Group II. Reset b+ at the beginning of Group III.

4. The Lucas Method - Procedure
Divide the sequence into groups so that:
1. No letter appears more than once in any group.
2. The last letter in a group must appear again somewhere in the next group.
3. The last letter in all groups, except for the last group, must be plus. The last letter in the last group can be either plus or minus.
Examples No. 1:
Step 1
A+, B+, C+, B-, D+, D-, E+, E-, C-, A-
I II III IV

5. The Lucas Method - Procedure
Divide the sequence into groups so that:
1. No letter appears more than once in any group.
2. The last letter in a group must appear again somewhere in the next group.
3. The last letter in all groups, except for the last group, must be plus. The last letter in the last group can be either plus or minus.
Examples No. 2:
Step 1
A+, B+, B-, C+, A-, D+, E+, C-, D-, E-
I II I

6. The Lucas Method - Procedure
Divide the sequence into groups so that:
1. No letter appears more than once in any group.
2. The last letter in a group must appear again somewhere in the next group.
3. The last letter in all groups, except for the last group, must be plus. The last letter in the last group can be either plus or minus.
Examples No. 3:
Step 1
A+, B+, C+, D+, B-, D-, E+, E-, C-, A-
I II III

7. The Lucas Method - Procedure
Divide the sequence into groups so that:
1. No letter appears more than once in any group.
2. The last letter in a group must appear again somewhere in the next group.
3. The last letter in all groups, except for the last group, must be plus. The last letter in the last group can be either plus or minus.
Examples No. 4: (one that cannot be divided)
Step 1
A+, B+, A-, A+, B-, A-

8. Step 1: Divide the sequence into groups
Consider the example
I II III
Step 1: Divide the sequence into groups
START A+, B+, B-, C+, C-, A-
Allocate 4/2 control valves and 3/2 limit valves

9. After dividing the sequence properly Two Approaches
Approach I: Design according to sequence of operations keeping in mind how the Group Manifolds should be switched.
Approach II: Following design rules.

10. Approach 1 Design by Sequence
Draw in the Group manifold lines
Draw in the START pushbutton. Its input should come directly from Group I manifold since START is the first action in Group I.
The output from START should initiate the next action, i.e. cause the A+ motion, i.e. connected to + side of Control Valve for Cylinder A.
START A+, B+, B-, C+, C-, A-
I II III
Example

11. Approach 1 Design by Sequence
At the end of the A+ motion, limit valve a+ would be actuated.
Take input of a+ from its own Group I manifold, and its output to initiated the next action, i.e. connect to + side of Control Valve for Cylinder B.
Limit valve a+ should be spring-returned since it has done its job when the signal goes to Control Valve B.
START A+, B+, B-, C+, C-, A-
I II III
Example

12. Approach 1 Design by Sequence
At the end of the B+ motion, limit valve b+ would be actuated. When this happens, we need to switch to Group II manifold and reset Group I manifold.
Take input of b+ from air supply and connect output to supply Group II manifold. Since we need to maintain air supply to Group II manifold until Group III comes on, use an air-reset limit valve for b+ and connect its reset to Group III manifold.
START A+, B+, B-, C+, C-, A-
I II III
Example

13. Approach 1 Design by Sequence
We’re now in Group II with Group II powered up.
Initiate first action in Group II by connecting Group II to - side of Control Valve for B to initiate B- motion.
At the end of the stroke, b- limit valve is actuated.
Connect Group II manifold to input of b- limit valve and pass signal to + side of Control Valve for C to initiate C+ motion.
START A+, B+, B-, C+, C-, A-
I II III
Example

14. START A+, B+, B-, C+, C-, A- Approach 1 Example I II III
At the end of the C+ motion, limit valve c+ would be actuated. When this happens, we need to switch to Group III. Group II manifold will be reset.
Take input of c+ from air supply and connect output to supply Group III manifold. Since we need to maintain air supply to Group III manifold until Group I comes on, use an air-reset limit valve for c+ and connect its reset to Group I manifold.
START A+, B+, B-, C+, C-, A-
I II III
Example

15. Approach 1 Design by Sequence
We’re now in Group III with Group III powered up.
Initiate first action in Group III by connecting Group III to - side of Control Valve for C to initiate C- motion.
At the end of the stroke, c- limit valve is actuated.
Connect Group III manifold to input of c- limit valve and pass signal to - side of Control Valve for A to initiate A- motion.
START A+, B+, B-, C+, C-, A-
I II III
Example

16. Approach 1 Design by Sequence
At the end of the A- motion, limit valve a- would be actuated. When this happens, we need to switch to Group I. Group III manifold will be reset.
Take input of a- from air supply and connect output to supply Group I manifold. Since we need to maintain air supply to Group I manifold until Group II comes on, use an air-reset limit valve for a- and connect its reset to Group II manifold. Circuit/sequence is now complete.
START A+, B+, B-, C+, C-, A-
I II III
Example

17. Approach 2
Designing based on design rules.
If rules are followed, a working circuit will result.
This approach does not require thinking. Not so good for an engineer.

18. Step 2 START A+, B+, B-, C+, C-, A- Example
Allocate a 3/2 mechanical-operated, air-reset limit valve to each cylinder stroke extremity which is last in a group.
Join the inlet to air supply.
Join the outlet to the manifold of the next group in the sequence.
Join the reset input to the manifold of the next-but-one group in the sequence.
START A+, B+, B-, C+, C-, A-
I II III
Example
Allocate 4/2 control valves and 3/2 limit valves

19. Step 2 START A+, B+, B-, C+, C-, A- Example I II III
Allocate a 3/2 mechanical-operated, air-reset limit valve to each cylinder stroke extremity which is last in a group.
Join the inlet to air supply.
Join the outlet to the manifold of the next group in the sequence.
Join the reset input to the manifold of the next-but-one group in the sequence.
START A+, B+, B-, C+, C-, A-
I II III
Example

20. Step 2 START A+, B+, B-, C+, C-, A- Example I II III
Allocate a 3/2 mechanical-operated, air-reset limit valve to each cylinder stroke extremity which is last in a group.
Join the inlet to air supply.
Join the outlet to the manifold of the next group in the sequence.
Join the reset input to the manifold of the next-but-one group in the sequence.
START A+, B+, B-, C+, C-, A-
I II III
Example

21. Step 3 START A+, B+, B-, C+, C-, A-
For each cylinder, assign a 4/2 air-pilot-operated control valve.
Join the end of the cylinder control valve applicable to the first letters in each group to its own Group manifold.
START A+, B+, B-, C+, C-, A-
Example
I II III

22. Step 3 START A+, B+, B-, C+, C-, A-
For each cylinder, assign a 4/2 air-pilot-operated control valve.
Join the end of the cylinder control valve applicable to the first letters in each group to its own Group manifold.
START A+, B+, B-, C+, C-, A-
Example
I II III

23. Step 3 START A+, B+, B-, C+, C-, A-
For each cylinder, assign a 4/2 air-pilot-operated control valve.
Join the end of the cylinder control valve applicable to the first letters in each group to its own Group manifold.
START A+, B+, B-, C+, C-, A-
Example
I II III

24. Step 4 START A+, B+, B-, C+, C-, A- Example
To all other cylinder stroke extremities, allocate a 3/2 spring-returned limit valve.
Join the inlets to their own Group manifolds.
Join the outlets to the appropriate end of the cylinder control valve applicable to the next letter in the sequence.
START A+, B+, B-, C+, C-, A-
Example
I II III

25. Step 4 START A+, B+, B-, C+, C-, A- Example
To all other cylinder stroke extremities, allocate a 3/2 spring-returned limit valve.
Join the inlets to their own Group manifolds.
Join the outlets to the appropriate end of the cylinder control valve applicable to the next letter in the sequence.
START A+, B+, B-, C+, C-, A-
Example
I II III

26. Step 4 START A+, B+, B-, C+, C-, A- Example
To all other cylinder stroke extremities, allocate a 3/2 spring-returned limit valve.
Join the inlets to their own Group manifolds.
Join the outlets to the appropriate end of the cylinder control valve applicable to the next letter in the sequence.
START A+, B+, B-, C+, C-, A-
Example
I II III

27. Step 5 START A+, B+, B-, C+, C-, A- Example
If the rules indicated above are followed, a working circuit will result. Apart from the insertion of any auxiliary units, for example to control the speed of the cylinders, it only remains to insert a suitable start-stop manually-operated valve.
START A+, B+, B-, C+, C-, A-
Example
I II III

28. Step 5 START A+, B+, B-, C+, C-, A- Example
If the rules indicated above are followed, a working circuit will result. Apart from the insertion of any auxiliary units, for example to control the speed of the cylinders, it only remains to insert a suitable start-stop manually-operated valve.
START A+, B+, B-, C+, C-, A-
Example
I II III

29. Step 5 START A+, B+, B-, C+, C-, A- Example
If the rules indicated above are followed, a working circuit will result. Apart from the insertion of any auxiliary units, for example to control the speed of the cylinders, it only remains to insert a suitable start-stop manually-operated valve.
START A+, B+, B-, C+, C-, A-
Example
I II III

30. Rationale of Lucas Method
Rule 1: No letter appears more than once in any group.
This ensures that there are no conflicting actuation signals - same as for Cascade.
Since there are no repeating letters in any group, and because the limit valves inputs are from their respective group manifolds, there will not be any + and - motion for the same cylinder at the same time.
Rule 1

31. START A+, B+, B-, C+, C-, A- Example B- signal supplied by Group II
I II III
START A+, B+, B-, C+, C-, A-
Example
B- signal supplied by Group II
B+ signal supplied by Group I
Group I and Group II are not powered at the same time.

32. Rationale of Lucas Method
Rule 2: The last letter in all groups must appear again somewhere in the next group.
The limit valve, say x, associated with the last letter supplies air to the next Group(k) manifold
x needs to be reset when the Group (k+1) comes on to remove Group k.
This can only be done if the cylinder has moved away from x.
Rule 2 ensures that cylinder moves away from x somewhere during Group k motions.
Rule 2

33. Rule 2: The last letter in all groups must appear again somewhere in the next group.
….., X-, …, X+,… …..
K K K+1
To allow X- limit valve to be air-reset when Group K+1 is powered up.
X- limit valve actuated, supplying pressure to Group K
Cyl X must move away sometime during Group K.

34. Rationale of Lucas Method
Rule 3: The last letter in all groups, except for the last group, must be plus. The last letter in the last group can be either plus or minus.
The limit valves associated with the last letters in all groups take air supply as inputs and pass them on to the next Group’s manifolds.
A minus means that the associated limit valve is actuated initially when system is at rest, and the Group manifold it is supplying is powered.
Since not more than one Group should be ON at any one time, there cannot be more than one minus last letters.
Rule 3

35. START A+, B+, B-, C+, C-, A- Example
I II III
START A+, B+, B-, C+, C-, A-
Example
A minus last letter means that the Group manifold it supplies is powered when the system is at rest. Only one Group can be powered at any time.

36. Overlapped Functions I II III I
The signal to initiate motion is connected to all the control valves associated with the overlapping motions.
The limit valves associated with the overlapping motions, e.g. B-, C+, and X+, are all connected in series so that only upon completion of all three motions will the next motion in sequence be initiated. (Applicable for BOTH Cascade and Lucas methods.)

37. Overlapped Functions – for Lucas MethodB+ B- C+ X+ D+ A- C- D- X-
I II III I
If a group ends with a number of simultaneous motions, except for the last Group at least one letter of these overlapping motions must be plus. At least one of these letters (not necessarily plus) must appear again in the following Group.
For all overlapping cylinder stroke extremities that are last in any group, allocate one of the following limit valves:
if the letter appears again in the succeeding group, allocate a 3/2 air-reset limit valve and connect the air-reset input to the manifold of the next-but-one group in the sequence.
a 3/2 spring-returned limit valve if the identifying letter does not appear again in the subsequent group.

38. Overlapped Functions A+ B+ B- C+ X+ D+ A- C- D- X-
I II III I

39. Note a-, b+ and c+ are air-reset
Example A+ B+ B- C+ X+ D+ A- C- D- X-
I II III I
Note a-, b+ and c+ are air-reset

40. Step 2: LVs for Last letters
Example A+ B+ B- C+ X+ D+ A- C- D- X-
I II III I
Step 2: LVs for Last letters

41. Step 3: CVs for First letters
Example A+ B+ B- C+ X+ D+ A- C- D- X-
I II III I
Step 3: CVs for First letters

42. Step 3: CVs for First letters
Example A+ B+ B- C+ X+ D+ A- C- D- X-
I II III I
Step 3: CVs for First letters

43. Step 4: LVs for other letters
Example A+ B+ B- C+ X+ D+ A- C- D- X-
I II III I
Step 4: LVs for other letters

44. Step 4: LVs for other letters
Example A+ B+ B- C+ X+ D+ A- C- D- X-
I II III I
Step 4: LVs for other letters

45. Step 5: Adding Start PB I II III I A+ B+ B- C+ X+ D+ A- C- D- X-
Example
START A+ B+ B- C+ X+ D+ A- C- D- X-
I II III I
Step 5: Adding Start PB

46. Step 5: Adding Start PB I II III I A+ B+ B- C+ X+ D+ A- C- D- X-
Example A+ B+ B- C+ X+ D+ A- C- D- X-
I II III I
Step 5: Adding Start PB

47. Repeated Motions – Lucas Method
May not be easily resolved
If the sequence cannot be grouped without violating any of the rules, try adding dummy cylinders. Dummy cylinders are used to resolve logic circuit difficulties, are actually implemented and moves during the sequence but does nothing for the operation.
A+ B+ B- C+ B+ C- B- A-
A+ B+ B- C+ B+ C- D+ D- B- A-
I II III IV
Example:
Cannot be divided
Dummy

48. Repeated Motions
Cylinders requiring repeated motions will need "OR" logic at the control valve. The shuttle valve can be used as shown:
Example:
A+ B+ A- A+ B- A-

49. Repeated Motions – Lucas Method
If a cylinder with repeated motions has a movement which is last in a group, replace the limit valve for that letter with a spring-returned type. Take the inlet from its own group manifold and its outlet to another auxiliary control valve. The connections for this auxiliary valve are as shown below:

50. Start A1+ B+ A1- D+ D- A2+ B- A2-
I II III IV
For motion A1+ and A2+, piston will hit both a1+ and a2+ LVs
Rule (c) will allow only Manifold II to be powered at end of A1+ motion since pressure from Group I manifold is used to shift the associated auxiliary valve through a1+ LV.
At end of A2+ motion, only LV a2+ will pass pressure from Group III to shift associate auxiliary valve, powering up Group IV Manifold.
Reason

51. Start A1+ B+ A1- D+ D- A2+ B- A2-
I II III IV
For motion A1+ and A2+, piston will hit both a1+ and a2+ LVs
Rule (c) will allow only Manifold II to be powered at end of A1+ motion since pressure from Group I manifold is used to shift the associated auxiliary valve through a1+ LV.
At end of A2+ motion, only LV a2+ will pass pressure from Group III to shift associate auxiliary valve, powering up Group IV Manifold.
Reason

52. Example: Lucas Method for Repeated motions
I II III IV
Start A+ B+ A- D+ D- A+ B- A-

53. Example: Lucas Method for Repeated motions
I II III IV
Start A+ B+ A- D+ D- A+ B- A-

54. Example: Lucas Method for Repeated motions
I II III IV
Start A+ B+ A- D+ D- A+ B- A-

55. Example: Lucas Method for Repeated motions
I II III IV
Start A+ B+ A- D+ D- A+ B- A-

56. Example: Lucas Method for Repeated motions
I II III IV
Start A+ B+ A- D+ D- A+ B- A-

57. Example: Lucas Method for Repeated motions
I II III IV
Start A+ B+ A- D+ D- A+ B- A-

58. Example: Lucas Method for Repeated motions
I II III IV
Start A+ B+ A- D+ D- A+ B- A-

59. Example: Lucas Method for Repeated motions
I II III IV
Start A+ B+ A- D+ D- A+ B- A-

60. Example: Lucas Method for Repeated motions
I II III IV
Start A+ B+ A- D+ D- A+ B- A-

61. Example: Lucas Method for Repeated motions
I II III IV
Start A+ B+ A- D+ D- A+ B- A-

62. Sequence with Overlapping and Repeating motions
START A+ B+ A- C+ B- C-
Cascade Method: the rules for design remain the same.
Lucas Method:
Rules for dividing the sequence and for overlapping motions remains the same.
For all cylinder stroke extremities that are last in any group, allocate one of the following limit valves:
Letter that is a non-repeating motion:
if the letter appears in the succeeding group, use a 3/2 air-reset limit valve and connect its air-reset input to the next-but-one group in the sequence.
a 3/2 spring-returned limit valve otherwise.
For a letter that is a repeating motion, allocated a spring-return limit valve with its auxiliary valve and do the following:
If the letter appears again in the succeeding group, use a 3/2 air-reset auxiliary valve and its air-reset input to the next-but-one Group in the sequence.
Otherwise, use a 3/2 spring-returned auxiliary valve.

63. End of Lucas Method