 Now, welcome to the lecture 28, which is on logic circuits. This is also under the module fluidics and fluid logic. In last lecture, we have already given a hints about the logic circuits along with the little discussion on the devices. In this lecture, we shall consider one or two circuits to understand the logic circuits in better way. Now, in last lecture, what we have seen that many functions can be simplified. For instance, if a logic output is given by y is equal to a c plus a b c that means, a and c plus or a and b and c that can be simplified to simply y is equal to a and c. Similarly, another expression what we took that such a big function that also can be simplified as not a and not of c or not of b. Also, the third example was on that x and y plus that is or a and b and c the whole into again x and y or not a or not b or not c can be represented by simply x and y. The circuit look at this circuit here I shall I can discuss a little bit about the circuit. Say remember this function x and y. So, input x and input y we put first allow to pass through and and device output is x and y or x y. Similarly, we have put a b c these three inputs in another AND gate. Remember this gate may have 1, 2, 3, 4, 5 inputs in that case the same AND gate, but here three input here two inputs. Also, I would like to mention the same this gate also can be used here only the say any one of them there is no input it is not connected to input. Remember this thing the same device also can be used here, but we have separate devices for two input three inputs etcetera. Now, here in this case output is a b c. Now, again it is possible that this we can directly connected to three not function not devices. Because if you remember this is the equations then what we are doing again this we are connecting through this or this this function this output we are getting here. Now, we are getting this output here and this output here. So, again we pass through and another OR gate to get the total function as an output and what we have done here this output we have allowed through an OR gates and this output we have allowed through the same OR gate as a second input and we have got this output. Now, what we need to do this AND this. So, we have used another AND device to get this function that means now what is done actually we have to say these are five inputs. Now, then these are describing their different conditions sometimes this AND this, sometimes this AND this AND this is coming and then this OR this and sometimes not of that that means not of that means signal 1 and 0 none of them is there that is connected through OR and then finally we get this output. So, these were our basic functions. Now, definitely here we are going through different conditions to get this function. It might be say this is a large machine system where these functions are performed to get this output, but it might be these functions are being used for some other performance only when we would like to get this output we can simplify this. How these circuits already five inputs I have told and nine logic elements how nine 1 2 3 4 5 6 7 8 9 to get this output to get an output is equal to x y output is only this much. Then this can be replaced by input is equal to x y and output and it is through AND AND gate and we are getting this output or in other words say suppose say these are being used from some other functions, but to get this output simply we take this output directly here. Because what we have seen through simplifications we can simplify to this, but this is an arbitrary function we have taken and we have taken this output. So, it is like that this is one part of the machines it is performing something and one part of this machine is performing something. Then finally what we do when this total function is required we simply take this output with two inputs and one logic elements only we can solve this. Now this another example which I have also shown you this is u is equal to a or b and a or c this can be simplified u is equal to a plus b plus a that this simplification is shown here. While we are simplifying you can see this first steps are normally the general algebra like things then we take a common still it is a general algebra, but after that we will find a plus b plus c is equal to 1 it has to be or in other words whatever the value of a this will be there. If a is equal to 0 say for example a plus b plus c 3 are 0 in that case this will be 0 if let us consider a is equal to 1 in that case if you just write a this will be 1. Suppose a is equal to 0, but b is equal to 1 and c is equal to 0 in that case still this will be 0. So, whatever the value of a always this will be equal with this one. So, for this part it is the Boolean algebra you have to take care of that. Now in device if we had to make a circuit following all these steps here then first of all what we will do we will take an or device with a and b input and then another or device where a and c are the inputs and then finally, we pass it through and gate and this must be equivalent to that here b and c through and gate and a is through or gate simply this function the output will be same. This method of simplification is a great help in building large logic circuits logic circuits operating with fluids and using binary or yes and no principles can be suitably contrived to answer such situations. Sensors are needed to collect from various stations information of the yes no time. This means that I would say that whether a function is no or yes we should how we can know that usually these are collected through sensors which are passed on the fluid control switches which may be valves or fluidic elements. They in turn allows to off that is control the pressurized working fluid into the actuators to perform the required work. These combinations of logic elements into suitable circuits need naturally the knowledge of individual elements. For example, the basic logic operations like not or and etcetera can be accomplished in practice by fluid elements like fluidic jet interactive devices as conventional valves. Check valves, subtle valves and directional control valves can be combined suitable to perform a wide variety of logic functions and this leads to a more economical use of valves. Now here I would like to mention that while we are describing fluidic devices we told clearly that fluidic devices has no moving components and from that definition we told that direction control valve, the check valve etcetera which we use in fluid drives are not logic devices are not fluid devices. However, using those valves you can develop logic circuits also. So, do not be confused this when these are being used to make a logic functions a logic circuits but these are not fluidic devices. The conventional valve can thus be used for information transfer as well as the power transfer. The using these valves in logic circuits the one advantage is that these powers can directly be used not much amplification is required. Of course, many valves especially the hydraulic ones are often too large and expensive to allow their use in any but the simplest logic circuits. Suppose if we would like to use we can use this hydraulic valves to make a logic circuits but normally it will be expensive and may become bulky. So, maybe you may find that where the fluidics fluid logics are being used for the hydraulic circuit also you may find that circuit this logic circuit part may be with fluidic devices and then that is connected to hydraulic parts. But you can make with hydraulic parts as well. Of course, nowadays attempts of miniaturizations of are going on that means many hydraulic valves many hydraulic components are made very miniature form to make circuits but many cases I would say those are expensive and not much beneficial and that can be plugged into the main manifold for the performance for the output. However, fluid logic circuits can be much better fabricated in the area of pneumatics using fluidic devices. A few examples are shown in the following slides to illustrate how some single type of logic element can be arranged in circuits to produce all the other logic functions here is a interesting thing. Now, multi-implute NOR element is such a universal type NOR element has a very special role in fluid logic or so to say in logic circuits. Now, in this figure A B C D I will show you now that will illustrate how the NOR element can be used to make other logic devices. Say we here we will see we will go through that ES, NOR or AND these four function or these four gate can be built only by using NOR element, NOR element not element not this is NOR element remember this thing. Now, first take there is an ES element we have already learned this is an ES element amplification element. Now, this can be made by NOR elements. We have put A you see this NOR device is like that this is a this this looks like say D and then a vertical bar and then output that means if A input is there then output will be A bar that we know and here we have seen that this is multiple input this devices usually you will find that if you think of the electronic devices this is very simple small element you will find so many input only one output in case of fluidic device also you may find there are 3 4 5 input and then one output. So, we have taken such a device we do not have this device, but we had this NOR device. Now, you simply connect another NOR device in front of it and you will get this output. So, these two combining is giving this ES gate this means that this ES gate can be made by two NOR elements. Let us take another this is a NOT gate. Now, this also can be made by NOR simply that use this gate this is a NOR gate in a sense NOR OR. So, OR function must be there. So, there will be multiple input difference between this and this one is that this is a NOR device and this is only a NOR device. NOR device is having only one input and one output inverse of that NOR gate is having the input and input. Say multiple inputs and then the NOT gate of that. Now, using such a NOR gate and with only one input we can get the NOR gate this is very simple, but this can be done. Now, let us take this another case this is OR element in some OR element you can use you will find that this is extended up to this point it can be ended here or it can be taken up to this point. Maybe there are some standard international symbols are there which we are not using, but let us look at this how this can be built by NOR elements. In that case we have taken one NOR element say a plus b we are getting this output a plus b per then what we did this whole output we are taking through another NOR elements that means this whole output is put only into a single input of this device to get this one. So, again we have got this gate using two NOR elements now we will take an AND in that case what we have done first we have used a NOR device to get a NOT and then we have taken another device to have b NOT. Now, this two a NOT and b NOT we have taken to have, but here we should remember that this is a bar b bar please. Which is giving this a dot b dot. So, in this case you will find that some Boolean algebraic taken otherwise this will be a bar b bar no this is you can say this is three NOR elements so a bar b bar and then reverse of that will give us a dot b bar. This is a theorem is there you see this is not a plus b by bar it is a bar plus b bar look at this suppose a is equal to 1 then a bar is equal to 0 b is equal to say 1 then b bar is equal to 0 then a bar by b bar is equal to a bar plus b bar. So, a bar plus b bar is equal to 0 output is 0 now that also you can get a dot b now let us consider a is equal to 0 so this is 1 b is equal to 1 so this is 0. So, a bar plus b bar is equal to 1 now a dot b will give the same result so you have to get just go through this exercise to get, but this is mind it this is a NOR element at this stage apparently it is output is a bar plus b bar which again equal to a dot b dot. Let us take a practical case of using valves in logic control in that case what we have supposing that a simple application has the recruitment of maintaining the level of water unaltered in a reservoir by sensing the water level and adjusting the inflow. Now what we have done in this case let us see say this is an valve what is there this is the input and it is directly going through if the disturbance is not there once the disturbance is there then this will be opposite to that and then there will be actuation of this one. So, what we do when there is some disturbance that means this is moved. Then it is a naught and this valve is being actuated. So, it is like that the water is when the water is being filled and it is touching this one then valve is being closed. Now so to say you can see this functions you can read it later, but one thing you should remember in such cases you need some delay because if you think that when the water is filled then this is valve it stopped then when the valve should start again if the water level comes down and immediately it starts operating then again it will go up and sometimes it is not desired. So, it is like that when the water is coming down it has to go up to certain low level only then this valve will start. So, it needs a another delay switch which is not shown here it is only as if shown that when it is filled then this valve is stopped. Here again the same valve we have we have now described here the logic function which I have told you. If the new new valve has a and output a the small a and the hydraulic valve has got the input a and the output v then the action of the system can be summarized in a tabular form which I am showing here in the in the in the slides. Now a is the this device a is the input and a this small a is the output and then v is the input signal for the main valve. Now high level a is equal to 1 then a is equal to 0 that is a bar then valve is also 0 the 0 means here this is not functioning when only this low level this is 0 then a is equal to 1 then valve is equal to 1. So, this means that a is equal to capital A is equal to a bar and a is equal to v these two functions. So, if you had to make a logic circuits you can make the logic circuits accordingly, but using these devices it is shown how this water level is maintained, but here again I would like to say that delay switch is not shown. A suitable logic circuits and system layout is to be designed for sorting a series of objects which are given certain codes attached to them so that they can sorted in three separate groups automatically according to these codes. So, here so let us consider this is a design problem the problem is like that we have a sorting machine or sorting conveyor say to say a object will come then depending on the what object it is we have to send it three separate conveyor. For the system layout it is presumed that the coded objects will be coming one after another on a belt conveyor. A certain location each of them will be stopped for a while the codes will be read and then they will be switched to three sort in three separate groups. A schematic may be as in the this figure figure number five in the next slide. Now, look at this, now this is a real system in that case what we find there is a conveyor. This conveyor is moving right to left. Now, on that conveyor the objects are coming from another source. Sometimes it might be manually we are putting there or may be from another conveyor it is coming together. Say let us consider in a factory where the productions they are coming the finished product are coming into the main conveyor here and then they need to be sorted out say three different products are there. They need to be sorted out and they to be sent to the three conveyors. Now, it might be say two are the product acceptable product and third might be the rejected one. It might be in that way also or depending on the size they are being sent to different conveyor. Whatever may be it need to be recognized whether this whether these objects is say identical to the first one and or it is a different one. And again they should be recognized as if this is the first one then it should go to the first conveyor. If this is the second type then it should go to the second conveyor and if it is third type then it is the third conveyor like this. So, what is done basically when the object is coming first of all what we should do we must stop it and then we should recognize it that what it is type recognition. So, definitely there should have a sensor which will recognize what object it is. Now, while it is being recognized. So, it should be held here it cannot simply pass there. After it is being recognized here then it should be sensed that what or this information should send to the system which is diverting these items to different conveyor. Now, you see these are the switching conveyors these are this is a single one, two three what we have shown this is a single one and this actually being pulled or pulled by this cylinder. So, when it is coming to this there might have another conveyor or maybe a hopper to collect this it might be another conveyor or hopper whatever it might be this is another hopper. So, this single component the single part of the conveyor is being diverted to put into three different paths. Now, also what we should observe is that here if we look into this cylinder this is a double acting cylinder because this can move this way and that way, but this actuation only in single directions and this is only stopping the item. Whereas, if you look into this cylinder this is a special cylinder in this cylinder middle portion at the middle portion is closed. That means, as if there are two cylinders this can be constructed by simply see taking these two cylinders and they are coupled in the reverse direction two three different paths. Now, also what we should observe that here if we look into this cylinder this is a double acting cylinder because this can move this way and that way, but this actuation only in single directions and this is only stopping the item stopping the item. Whereas, if you look into this cylinder this is a special cylinder in this cylinder middle portion at the middle portion is closed. That means, as if there are two cylinders this can be constructed by simply see taking these two cylinders and they are coupled in the reverse direction. Now, this end of course is having a joint one end is fixed to the reference frame it can swing over there say you can imagine a ball joint is there while this is being extended then this is also rotating absolutely this way or that way because this is a another fixed point. So, when it is being contracted it is coming like this and when it is being extended then again it is going in this direction. So, we need some ball joints and then these two pistons are separate and that also in each chamber these are double acting. Now, we have named this is cylinder A this is cylinder D and this is cylinder C A D C remember. Now, these are these valves are you can say actually the logic devices are there, but it might be as I told that ordinary hydraulic valve basically these are pneumatic valve and the circuit are made using this ordinary pneumatic valve. Now, next we consider the switching conveyor is controlled and operated by the tandem cylinder C D this cylinder is called tandem and its swiveling position is determined according to the code read out just a short while ago. That means, a code is read here this code is A and B we have to with the sensor we have to read this code then with this code we can find out what is the object. So, that will be first recognized and then it will be said this information will be sent to the next section. Then the shorting of one object is completed this stopping cylinder A retracts that means, this will retract and will allow the next object to go through the shorting process. That means, this basically it is stopping here. Now, here actually the shorting process is there. So, objects are coming one object here then this is stopping the other object. So, it is being recognized once the recognition process is over then this will be this will this will operate and it will go its directions and then this will be retracted and this will go here. That means, this conveyor is basically running and stopping run and stop run and stop at stop conditions it is one object is being held another object is being recognized and once it is recognized again the conveyor start this is diverted and then another object comes it is like that. It is obvious that a number of sensors are necessary to send back information to the logic circuits as their inputs. For example, 3 sensors C D E are shown at the ends of 3 shorting conveyors indicating end of travel that means, we have the sensor here A B sorry C D E these 3 sensors are there. This is the showing the sensor positions nothing else, but actually sensors are named as C D and E. Now, when the object is passing through this then it is being sense that object has passed. So, that information is going into the main logic circuits any one of them reporting back means that one shorting is over that means once this is passing this is already passed then another short is covered over. So, immediately this will go to the another conveyor say for example, the items 2 consecutive items has same identity that identity is A B bar and this is perhaps A bar B it is not coming. So, we have to check it that means here the shorting is like that one is A B one is A B bar one is A bar B these 3 shortings are there. Now, let us consider 2 items consecutive items is having A B bar identity then it is like that when this is passing through there this conveyor only then A bar B is passing this will allow to enter here and this means this is allowing to enter here means this is running. So, the object which was stopped here it has now come here and suppose first item was here and second item was A B. So, it will go there, but by that time another will come over here 2 other sensors A B are needed to read the code on the object and send the information to the relevant logic circuit as inputs. All these sensors need only to report yes or no that is 1 or 0 the codes formed by A B and therefore, A is equal to 1 B is equal to 1 A is equal to 1 B is equal to 0 or A is equal to 0 B is equal to 1. So, these 3 codes are there. The fourth combinations namely A is equal to 0 B is equal to 0 gives ambiguous information because it may also indicate that the sensor are not working at all. So, whether A is equal to 0 and B is equal to 0 you have to so should some devices then this is not an object either or may be sensor is not working something like that. In a similar way the 10 name cylinder must be able to work in 3 different way. Now you say what is there if you look into this logic we are not going into the little development of this logic here, but it is A plus B plus A B A plus B or A B then this is actuated you see how this will be operated. If you look into this A plus B A plus B is equal to A in that case this signal is there that means this is being retracted and for that one A B plus A bar B is equal to B in that case this is also retracted. So, that means we are getting this is a fully not fully extended this side extended and this side not extended. So, this is the middle position only and when this is retracted and this is also retracted then we are getting this position whereas if these 2 cylinders are fully extended only we are then getting this position these are operated by this functions A B DOS already it is decided once it is decided then this function are performed once this function are performed we get these operations that we will see this mathematical part is not being shown in this slides, but we will see this how the logic circuits looks like. If extension is indicated as 1 retraction as 0 the 3 positions would be for different combinations of C and D. Now it is like that C D is not shown that is we have named this cylinder A B C D C and D this is 0 the action is that position 1 being to leading to short conveyor. Now this is 0 1 or 1 0 position 2 leading to short conveyor another short conveyor and position 3 leading to short conveyor I mean this is position 1 position 2 and position 3 this for this combination position 3 we are getting this position 2 for this combinations you say you can see position 2 is having 2 alternative positions. So, this is retracted this is extended or this is retracted this is extended. So that is why for these 2 conditions position 2 will be available position 1 is available only when these 2 are collapsed position 3 will be available when these 2 are fully extended. Now this circuit look at this circuit it is I understand this is very difficult to draw this circuits, but if this circuit is shown to you you must be able to recognize what the function is being done and what is the possibilities. Now look at this these are the sensors say this is A then A B bar say it is like that in this sensor this input is A B bar. So, this will go through this and then this is the logic circuits in that logic circuits the one input is there and output is A then this is B. Now here in this what we are getting A is coming over here and we are getting A B A bar B through this output then A bar B is coming over here and here A bar B and here A is coming from there again it is going to B. Now this B is going there A is it is now coming it is being fed to here. So, we are we are getting A plus B and here we are getting C D E this is the stopping conditions here. Now from there we are getting C D E now this is the latching or memory outputs. Now here I would like to mention that there is we require a memory device memory device why we need it because as I have told that one when the one performance is not completed we should not have the another performance, but that is not on possible only by and or or gate bar or not gate we must need a memory device. So, that memory device is associated with and or etcetera gates. So, unless one performance is over the another performance will not be performed. So, here this memory device are put over here and then this is output amplifiers it is going to that C 1 and this is going to C 0. So, if this operates and then this will not operate that means, these are to operate the cylinder either retraction or full extension conditions similarly, for D 1 and D 0 and similarly, for A 1 and A 0. Now this is I would say this is a very complicated circuit in in that way. So, to understand what you should do you should take this picture and this picture together to understand what is being performed. Also you will find that we need to go through another exercise to understand the circuit in little way that might be in some other lectures, but out of this instruction what I expect that looking into this full figure and this figure we have to understand how the operation is being done one after another. With a memory device which I have mentioned the output will be X if the last input and this state will be maintained. So, long the other input remains inactive this is also true for the water level. If the last input is X is equal to 0 the output is A that state is sorry this is confusing A is the output here that state is maintained in both cases the last input signal memorized. In this example the logic circuit working with low pressure fluidic device the circuit which was shown the last circuit that was with logic fluidic devices. It is also possible to make it with the electronic devices. Hence the output signals from them have to be amplified before entering into the power system that is obvious as I have told if we would like to use the same source for actuating the cylinder we need to have some amplifier there which are not shown in this circuits. Now this is I suggest the book the fluid logic controls and industrial automations to follow this book but I do not think this book will be available in the market. But there is also some you may go through this book digital principle and applications this is published in India this book may be available yet whereas this book is to have the general idea about the fluid power devices. So, thank you.