hello good morning and welcome to this beautiful session we are going to talk about one short series the aim basic aim of this series is to help first of all those students who are not you know comfortable with Hindi part so we are going to cover this entire series in total English number one thing and this series as we have mentioned here this is one short series it means whatever topic we are going to pick in one session in that session doesn't matter what is going to be the length of this video in that entire in that video itself entire topic will be covered better you know so today we are going to look at the very first chapter of theory of machine which is simple mechanism and in this very short crisp video I am going to cover all important topics of simple mechanism chapter which are going to be asked in Gate 2023 acha whenever I am going to teach you uh theory of machine car this particular chapter in paid batches so this is going to take at least at least uh 22-25 hours not less than that but again again exams are very very close and our focus should be only on Those portions from where chances of getting questions is very very high so what are those topics which I am going to cover let's have a look uh uh in this session I am going to cover first of all majorly I will be covering degree of freedom of mechanism what is the degree of freedom of mechanism crash of slow questions are asked here but Inverness of mechanism then we will have a look at mechanical advantage a very uh you know very small topic but sometimes questions are also asked here and then we have a transmission angle rarely asked but again a very important portion so these These are the crisp the crisp content of this chapter which I am going to deliver here before directly jumping into degree of freedom of the mechanism let's understand what is the mechanism whenever we see around us we are surrounded by so many mechanisms so many machines and in fact three idiot movies if you have seen three dead movie so ranchodas has also given example of machine that anything which makes your life simple is called as machine meta Hannah so I think feeling everybody has what is machine well if you are looking just looking up at your fan this is also a mechanism meta if you are looking at the folding table of your house that is also a mechanism if you are looking at uh you know IC engine this is also a mechanism and in fact this is the mechanism which is most widely used in this entire world now mechanism is made up of certain small small parts which we are going to call it as kinematic link what is the meaning of kinematic language very very careful there is a very important part of mechanism which is known as kinematic link by definition it is defined as every small part of the machine or mechanism which is going to have relative motion with respect to some other part look here at this IC engine in this IC engine how many parts you can see so I'm not going to uh I'm not asking you to uh to count these nuts and screws also I am going to I am asking you to count all those parts which are having some relative motion with respect to some other part in this particular mechanism let's have a look let's have a look for a moment very easily you can see here sir there is one thing disco we can call it as cylinder this is my cylinder head cylinder body and this inside this cylinder body I am going to have one crank this is the crank and this crank can have rotation inside the cylinder you know about this axis so with respect to this cylinder this is one link another link which is crank this crank can have rotation relative motion is there so crank will be considered as another link crank is connected to connecting rod between them we are again having a pin joint so between then there will be some relative motion again connecting rod I will consider as a separate link and with respect to this connecting rod I have connected a piston here again with the help of pin joint and this piston and connecting rod can have relative motion so piston could be I will consider as a separate link so how many different different links you can see here but uh you can see there are total four links this very first one which you are calling at the as your cylinder this is your first link then we have this crank Azure second link then we have this connecting rod as your third link then we have this slider or piston as your fourth link these are going to be total four kinematic link which this IC engine is going to have now in reality this body is having this shape beautiful shape but in Practical we can represent this diagram as a line diagram a schematic diagram how I'm not going to make this entire 3D Beautiful diagram as always I will simply show I am having one link which I am calling as uh my cylinder or body of this engine which I am going to fix with my frame or chases of the vehicle now this once this Frame is fixed I have just represented this by a fixed symbol that's it this is the symbol of fixed link with respect to this link we are having a crank which can have rotation this is the crank which can have rotation pin joint is up with this crank I have again another link which I am calling it as connecting rod again we are having a pin joint here but and with this connecting rod I am having a slider which is connected here again with the help of pin joint okay and this slider is inside this piston is inside the cylinder so let me make the diagram this is my the slider or piston can move inside the cylinder this is again fixed link button this fixed this fixed it is not different different things these are same thing same thing this is also fixed this is also fixed so this is the entire one thing but uh actually you can see that this is in reality this is one thing but in my line diagram I have shown some part of the fix link here some part of the Finish link here but don't make this mistake that many people will count it yeah this is link number one earring number two has the ceiling number three and Gamera link number four here answer is link number five this is not link number five J link one has also link number one getting my point if you have got a clear idea he what is mechanism how we are going to represent that and how we are going to make numbering of the links on that many people may think kisser always always links are going to be some solid body or some rested body these are this cylinder is a result body inside that we have already crank solid connecting rod and this riveted piston it is not always the truth better it is not necessary that your kinematic link need to be reset body it is if even if it is not result body I can use it to transfer power or motion from one link to another link for example here luckily luckily whatever kinematic links I have shown here luckily all these links are resident in nature resid means they are solid the deformation Whenever there is motion relative motion here so deformation in the links is very very less they seem to be rigid whatever you have seen this cylinder this kind of crank connecting rod piston everything is example of result link here you may have result link but sometimes even flexible bodies can also be used to transfer motion or power power from one link to another link for example we have this belt and pulley Drive now try to consider how many links you can see here but now we have this smaller pulley which is rotating about some fixed link obviously this is rotating about some fix link so this is your pulley is going to have rotation fix follow link always we are going to call it as link number one sir this is link number one link one get respect me this pulley is going to have rotation this is my link number two and now again we have another pulley here again we have another pulley here this is also rotating with effects link fixed score you have called as link number one so a b this is also going to be building number one also but uh you know respect my police rotating link number two respect another pulley which I am calling it as link number three link two car motion is getting transferred into link three motion why with the help of this belt and this belt because it is capable of transferring motion of Link number two to link number three I will treat this belt as my link but by Nature this is flexible this is not rigid so this is called as flexible link button so everybody knows that links may be result in nature sometimes link may be flexible in nature or even sometimes fluids Kobe we can also use as links you know whenever fluid is being used to transfer motion or power from one part of the mechanism to the another part of the mechanism from one link to another link now here look here but closely closely closely the example which I have shown here what I am trying to show we are having a cylinder this is a cylinder better and inside that we have filled some liquid yeah but I have filled some liquid this is the liquid metal this is the liquid from one part from where this is the plunger this is a plunger single link if you are going to apply certain small amount of force here at this end at this Ram you can lift a very heavy weight now how many links you can see here but uh how many links you can see here the very first link is this one cylinder I will call it as link number one this is something which I am going to call it as link number one this is my link number one this is fixed link number one link one get respect me this this plunger or this Ram can have certain motion this is something which I am saying as link number two this is my link number two email link number two here a link to go you are going to apply some link to go you are going to give some power that means some Force some velocity you have given some power you have given some motion and motion is getting transferred from this place to another link this is link number two this is something which I am calling as link number three length 3 is going to have motion link 2Go you have given input length 3 by you are going to get some motion by which part has a transferred motion of Link number two to link number three sir we have used fluid this is fluid inside me you can see there is some fluid which is part of this mechanism and it is transferring motion from link number two to three so the fluid which is being used here whatever fluid you are using that fluid I will call it as include link getting a point so I think everybody has got a clear idea these are links can be of three types three types it may be a result link but not necessarily that it has always to be result now it may be rigid body it may be flexible body or it may be even fluid getting a point now ah you are going to connect links in certain order to get some kind of motions so uh cutting all these parts and directly coming to that particular portion from where questions are going to be asked questions May the very first thing examination my simple mechanism chapter say the very first thing which is going to be asked is degree of freedom of the mechanism they will give you certain type of mechanism and they will ask try to find out try to calculate what is the degree of freedom I'm not um you know doing derivation part here but let me give you a very important formula degree of Freedom first of all what is the meaning of degree of Freedom degree this is something uh if I tell you the raw definition of degree of Freedom degree of bottom is the number of independent variable which is required to Define motion or position of certain body which is having some motion anybody which is having motion and if I want to Define its position or motion completely so how many parameters I have to tell you and from the point of view of mechanism if you are talking Q what is the meaning of degree of freedom in the field of mechanisms it is defined as number of inputs which is required to get constrained output you know I will show you with one example better in the field of degree of Freedom one mathematician sir kuzback has done a you know beautiful job he has given a formula but this formula which I am writing here this is only for planar mechanism degree of freedom for planar mechanism if we talk why we are talking about planar mechanism because in our syllabus only planar mechanism is there but only planar mechanism planar mechanism May degree of Freedom Kelly we have a beautiful formula which is 3 l minus 1 minus 2 J minus h from where we have derived this formula this we will see when we will talk about ah theory of machine course in detail that's a different thing but you have to understand what is the meaning of each and every term in this formula in this formula this L is denoting number of lengths how many number of links you have so you have to carefully calculate all the links which are present in the mechanism number one thing second thing this is J what is this this is number of actually I have written a number of those pairs which are having degree of item one number of number of pairs having degree of Freedom one or also known as lower payers beta generally lower pairs are having you know surface contact and they are going to show generally generally mark my word generally generally they are going to show one degree of freedom on the other hand this h is something which is number of pairs between the links having degree of Freedom 2 and generally higher pairs are going to show this kind of nature better if you if you can calculate you know carefully how many number of links are there how many lower pairs are there how many higher pairs are there just put down all these value and if this formula is going to give you what is the degree of product value let me let me give you one example so that you get so that you will get more clarity how this formula is being used suppose suppose suppose for example I have a mechanism something like this mechanism something like this there are few links which are connected with the help of pin joints something like this one link is fixed this one is fixed try to count and question me they are asking you here for this mechanism try to find out what is the degree of freedom whichever is a fixed link I will call it as link number one this is link number one this is link number two and yearly number three here this is number four this is link number five so how many links total links are there but uh five links are there how many lower pairs or binary joints are there they're lower pairs one lower pair is this one lower pair is this turning pair number now one lower pair is this one over pair is this one lower pair is this you know one degree of federal pair one degree of normal appear one degree of federal appear one degree of fremal appear here so how many pairs are there one two three four five five lower pairs put on the value lower pairs five lower pairs there is a no higher pair higher those pairs where you are going to have Point contact or line contact and there is no higher pair higher pair is zero carefully calculated these values and put down them put down these values in Formula 3 l minus 1 minus 2 J minus H and now put down put down these values what you will get 3 times L minus 1 which is 5 minus 1 minus 2 into J J is how much better 5 minus H H is how much zero this is 4 4 3 the 12 12 minus 10 this is coming out to be two degree of Freedom comes out to be do for this mechanism degree of Freedom comes out to be two it means in this mechanism if you are go if you are willing to get constrained output so you have to give input at two different different links if you can give input one input here input number one another input somewhere here this is input number two then only you can get constrained unique output from here unique output getting my point so what is the meaning of degree of freedom and how do we calculate it everybody has got a clear idea another example another example suppose suppose suppose for example if you are having a cabin follower device you know this is a cam El this is going to have rotation and there is a follower beta Skipper you are having a follower follower looks something like knife edge follower is there as a kuch this is something like this and with respect to fix link it is also having contact how many links you can see here this is another question how many links you can see here sir always link number one link one respect my cam can I have rotation this is my link number two uh link to get respect by this link number this follower is also having certain type of motion this is my link number three and again this fixed value link is or fixed link is your link number one how many total links are there total number of links I can see there are total number of links are three how many lower pairs are there sir 1 and 2K which may we are having turning pair here we are having turning pair lower pair surface contact three and one between three and one we are going to have sliding pair and sliding pair is again example of lower pair surface contact is there now we are having two lower pairs two lower pairs where between 1 and 2 and 3 and 1 1 2 and between three and one we are going to have lower pairs surface contacts we are going to have one two k which we are having turning pair and three one k which we are having sliding pair do you have any higher pair here yes definitely we have one Higher pair link number two one number link number three you can see that we are having very less contact Point contact this is your higher repair how many higher pairs are there sir there is only one Higher pair put down these values in the formula degree of Freedom f is equal to 3 l minus 1 minus 2 J minus h put this value Alka value 3 here J car value is 2 and higher value is 1. try to calculate what is going to be the answer 3 minus 1 2 2 3 6 minus two rules of 4 minus one answer is coming out to be 6 minus 4 minus 1 this is coming out to be one degree of product value you have got as 1 beta getting my point so example examination may they are going to ask questions first question simple mechanism chapter say the very first question if if question is Being Framed so the very first question will be from degree of freedomala part they will give you certain type of mechanism and they are going to ask what is going to be degree of freedom of this particular mechanism here now uh how do we calculate degree of Freedom everybody is comfortable no the equation which we have seen here this equation let me write down the name this equation was given by I have already mentioned given by Sir kuzback and that's why this equation is called as putback equation very important equation this is used to calculate degree of freedom of any mechanism now there was another mathematician whose name was grubler keep this name in your mind examinations where sometimes they may ask he write down the grumblers criteria Governor's equation we are going to discuss what is this criteria actually he has done nothing I have what they have done he has takenberg equation which was F is equal to 3 l minus 1 minus 2 J minus H which we have just seen a baby he said Grandma said he if there have to be any mechanism if there is any planar mechanism in this world which is having degree of product one without any higher pair with only lower pairs keep in mind again I'm repeating if there have to exist any mechanism or any mechanism with one degree of freedom and no higher pair so that mechanism have to follow my criteria and for that criteria what he has done is he has put these values simply in this coursework equation and the this equation turned out to be how much degree of freedom but you feel put 1 is equal to 3 l minus one open career but three L minus three minus so what you will get 3 l minus 2 J this one coming this side minus 4 is equal to zero this is the equation which we are going to call it as this is equation criteria keep in mind this is something which is called as goodwag equation and from back equation Graveler has derived some another you know not so useful criteria but still this criteria is in the books sometimes examination they may ask which of the following is the cosmic equation option A B C D they will give and you have to select the correct option number one thing second thing sometimes they may ask which of the following represents groblers option A B C D some some few things they will give and few confusing things they will give again when I was in my uh childhood graduation days I used to be very very confused options are so close very very close looking you know they will give you options option a option b option C 3 l minus 2 J plus 4 is equal to 0 3 l minus four J plus two is equal to these kind of equations are they are going to give getting a wine so much close to each other so you have to very very carefully remember these things what are these equations you know to satisfy this equation this grubler's criteria equation minimum minimum minimum four links are required with the four links whatever mechanism you are going to make with the four links and no higher pair Yankee with four links four level four links with four links and four lower pair whichever mechanism you can get those would be called as the simplest mechanism because this is a minimum number of mechanism minimum number of links which you have used here if more than four links if you are going to use maybe maybe somebody has used sir I have used six links and I'm also getting without higher pair I have six link some lower pairs no higher pair and so my mechanism is also giving me degree of number one what do we call it you will call it as complex mechanism or compound mechanism not simple that will be termed as compound mechanism or some people also call it as complex mechanism simple mechanism is this which is having only four links and four lower pair and only this thing is in in your syllabus you know in any examination if you really want to crack that examination you have to understand what are the dimensions of that syllabus you have to understand the syllabus thoroughly so that at least you must know the boundaries where you have to stop just because sir I am enjoying this subject uh can you please teach me the complex mechanism you have to have to control your emotions getting my point so only simple mechanism is in your syllabus and we will talk about only that thing with the four links with the four links and for lower pair whichever mechanism which you are going to get those are called as a simple mechanism which I have already written here four lower pairs four links and four lower pair that mechanism is called as a simple mechanism there are three kind of possibilities number one you may have four links and all these links you may connect with the help of turning pair this is something which is known as a four bar mechanism on the other hand somebody is saying sir I will be having four links but this time one turning pair I'm going to replace with the help of sliding pair any pair one sliding pair all these pairs are lower pairs all these pairs are lower pairs four links three trending pair one sliding pair this is called as a single slider crank mechanism and if somebody is saying kidneys are again one one more turning pair go I am going to replace with the help of sliding pair so this time you are going to have two turning pair and two siding pair this is something which is known as double slider mechanism these are three examples these are only three examples of simple mechanism only three kind of situations are possible but either you may have four bar mechanism or you may have single slider crank mechanism or you may have double slider crank mechanism nothing nothing else nothing else everything we have covered no rasa and then not much in the detail a little bit let's have a look about what is a four bar mechanism and how does it look Betty four bar mechanism let me write four bar mechanism and whatever I am discussing now believe me whatever points key points I am discussing here examination make questions from only these topics they can they can ask four bar mechanism very very careful very very careful suppose suppose four wire mechanism means you are going to have four links sir these are my four lengths and all these four links go I have connected with the help of turning Bell so yay this is the PIN joint this is also pin joint pin jointer this is also pin joint you know how many links you have this is the link number one earring number two has the ceiling number three and the ceiling number four there are total four links four links one two three four four running pair four bar mechanism now in this four bar mechanism you can fix one link suppose somebody said somebody said I am going to fix this link your your wish somebody's saying sir I will fix this link your wish you can fix this link somebody is saying ladies or I will fix this link your wish Buddha you can fix any of these links there are total four links you can choose you are free to choose which link you want to fix and whichever link you have fixed suppose somebody has fixed this link if you have fixed this particular link I will say that this is my link number one which is fixed link and fixed link adjacent either this or this any of the link go you can give input and from other you are going to collect output suppose somebody has given input here this will be called as your input link press link okay another side may you can have your output link okay fix any of the link any one link whichever you want once you have fixed certain link to fix link okay adjacent me either this side or this side any one sideway you can give input from other side you have to take output here whichever link which is connecting input to Output this particular link is called as your coupler link don't call it as connecting dot many people many many innocent children they are calling it as connecting rod navigate that is not connecting rod coupler coupler or you can call it as coupling Rod connecting rod this word we will use when you know when it is part of your single slider can get IC in general apart you know I see in general we can use this connecting nodular term but till that time coupling Rod or coupler only this thing you have to use acha sir can you feel this input link this is fixed about this point this is this is this can have rotation about this point input link input link has no other option it can have rotation about this point output link similarly output link can have rotation is capacity there is no choice it can also have rotation only both these links can have rotation only now depending upon whether input valid link it is having capable of having complete rotation or not or output on a link it is having complete rotation or partial rotation to go rotation only rotation is a choice for input and output link only rotation is possible only rotation is possible now this rotation may be complete or incomplete means it may be complete rotation or partial rotation only rotation it may be complete rotation or it may be partial rotation or partial rotation or you can say incomplete rotation or also known as oscillation button getting a point partial rotation complete rotation if any particular link with respect with respect to some Center if it can have 360 degree rotation something like this complete rotation foreign with respect to some fixed point it can go up to this level and up to this level that's it sir this it is having motion something like this rotation hey but this is not complete at some point it have to stop it cannot go beyond this again it have to come back it really stops from at some point again it will go back so between these two positions it is going to have motion this angle you know between two extreme portion is called as swing angle this is swing angle and these two extreme positions are known as toggle positions at toggle position this length angular velocity is going to be zero common sense these two end positions extreme positions are known as to toggle positions keep this thing in your mind and please note it down somewhere that toggle positions pay link velocity is going to be zero that's it that's it now sir how it will be decided that which link is going to have complete rotation or when any link can have complete rotation how can we decide for this crash off has given a uh experimental law which is known as gresham's law it will help you to find out it will help you to find out let me write crash of law foreign gives you a condition that for any forward mechanism this is only for bar mechanel do not try to apply this law in singles networking mechanism or double cylinder current mechanism this has limitation this is only for four bar mechanism and in four bar mechanism depending upon which link you have fixed and what are the dimensions of other links so these dimensions and your choice of which link you want to fix this collectively will decide whether you can get crank or not rank any link which can have rotation you will call it as crank any link out of input and output any link which is not having complete rotation incomplete rotation partial rotation oscillation that is something which you are going to call it as either rocker or some people will also call it as liver now when you can get crank this side or even this side maybe some situations are there that input output both links are having complete Evolution so sir can I call it as this is also my crank this is also my crank yes but if both these links are having complete rotation so both these links you will call if this is also my crank complete version this link is also my crank why because this is also having complete rotation both these links you will call it as crank okay if any of the link is not having complete rotation for example so only this one is having complete rotation so this is crank this is lever or rocker none of the link is having complete rotation this is also having oscillation this is also having oscillation in complete rotation sorry incoming rotation this is rocker from here something like this it is having a rocker Roller Motion this link is also not having complete rotation getting my point by fixing sometimes by fixing this link you may get both as Crank by fixing some other link suppose you have fixed this link now you are getting one link guys crying another link as rocker suppose by fixing another link you are getting input output both as a rocker so these by fixing different different links of any kinematic chain you may get a different different type of motions and all these different different type of motions mechanisms are known as inversion examinations May sometimes they may ask another word there is a term which is known as inverse and meta just for inform information means by fixing different different links by fixing different different links Common Sense either you can fix link number one or you can fix link number two or link number three or link number four one at a time link one go fixed score and then try to see which kind of motion is there length of try to see which kind of motion playing three Go Fixer would try to see which kind of motion getting a point so by fixing different different links we may get different mechanisms mechanisms different kind of motions getting opened these mechanisms these are different different kind of mechanisms are known as in vardhan we call them as inversion keep in mind I have written we may get there is no guarantee that by fixing different different link you will get there is no guarantee no no no no by fixing different different links you will definitely get different different type of mechanisms I am not saying that there are chances that by fixing this link you will get some different type of motions some different type of mechanisms by fixing another link whatever type of mechanisms you are going to get this is exactly same which you have got earlier so you will not count these as a different inversions but now for if you want to say something as different inversion it have to have different motions different mechanisms getting a point this is the basic thing Mata over mechanism if we are talking so forward mechanism we may have we may have these three inverdance let me write inversion in of 4 bar mechanism I will show with the help of Animation also sir you may have one possibility is a input output both out of some some link you have fixed and input output both are be having as crank both are having complete rotation so this is called as crank crank mechanism you may also call it as double crank mechanism sometimes by fixing some some type of Link only one link can have rotation other link is not having rotation so one is cranked another is a rocker crank rocker mechanism this is called as crank rocker mechanism sometimes rocker rocker mechanism both links are not having rotation partial rotation rocker rocker mechanism this is called as rocker rocker mechanism getting a point now if you want to have continuous rotation if you want to have continuous relative motion if you want to connect motor at least one crank is needed can I write here for continuous relative motion at least one crank is needed at least one crank both are crying I'm happy but at least one crank is needed why for continuous relative motion rocker basic Behavior as I had that rocker if it is going to have motion so rocker at some point of time it is going to stop again it will come back and when it is stops it breaks the motion again it will come back at some position it will again stop break the motion again it will start moving and add extreme pushing it will stop getting opened so rocker motion it will stop at extreme position zero velocity again zero velocity rank will have continuous rotation motor these are the three possible inversions which four bar mechanisms can have now how do we decide how do we decide that when you are going to get crank rocker when you are going to get rocker rocker when you are going to get crank rocker examinations make questions law first of all this is only for forward mechanism as I have already mentioned what this law indicates it indicates for continuous relative motion for for continuous relative motion means for at least one crying for at least one crank length should be in such a way that summation of shortest plus longest link should not be larger than summation of other two links it means if it should not be more than other tooling Square summation to what are the conditions which may arise sir less it may be less or equal than the summation but greater getting a point so shortest plus longest link transformation should be less than or equal to P plus Q getting a point getting my point this is the necessary condition not the sufficient condition Matlab if this condition is satisfied you also have to check which link you have fixed then you will decide if grashof's law is satisfied if summations are in this manner so where you may get one crank or you may get two cranks but at least one crank you may get you may get again it depends upon which link you have fixed if some drastic link you have fixed even this may be the situation if I grasshop's law is satisfied and still you have whatever chain you have that is Crash of chain but still you have fixed some such a bad link that neither input nor output anything nothing is going to have complete rotation now uh let me give you one example suppose suppose suppose if shortest Plus longest length summation is less than p plus Q both okay uh suppose I will just tell you the results and then I will show you some animation so that you can get a better feeling also here suppose uh this is the shortest link this is the forward mechanism this is the shortest link this seems to be the longest link and this is p this is q you can careful couples if grashof's law is satisfied and if you have fixed shortest and both of these links this one will have complete rotation a b complete rotation you are going to get crank crank mechanism you will get crank crank mechanism let me write shortest rank crank you are going to get on the other hand shortest distance if you are going to fix this will have complete rotation but this link will not have this one is going to be input this is going to be your output input link can have complete rotation output link cannot have complete rotation but this is going to be have as rocker adjacent to shortest you will get triangle rocker mechanism and last this one shortest score you have made as coupler opposite to shortness is fixed you will get rocker rocker mechanism sir please please tell me that what if shortest K adjacent is same thing here adjacent to the shortest is fixed doesn't matter this side or this side either you can fix this or you can fix this result is going to be crank rocker shortest link complete rotation other link will not have complete rotation getting a point acha whichever mechanisms are there which satisfy this law Gresham those are known as chain maybe there may be one situation when shortest cook you have made as coupler you are going to get rocker rocker mechanism I will I will show the animation just wait for few more minutes another situation may arise sir what if shortest plus longest equal to P plus Q foreign law is not satisfied doesn't matter which link you have fixed you can never get crank one special situation one special case sir Test Plus longest conservation P plus q k equals so already you have discussed equality was you have already told that equality whenever equality is there you will have exactly same results nothing is going to change but one special case by looks it is different we are going to follow exactly the same thing but how will it look I'm just going to tell you that sir what is so special here Rabbi if you are going if you are having pair of equal length pair of equal length array what do I mean I mean that suppose suppose suppose if mechanism is there which is having links to two unit two unit six unit six unit getting a mind there are four links but links are in the form of pair two unit two unit six unit six unit you may have two different kind of configurations we will follow exactly these rules but two is special by looks to special configurations I am going to show you sir first one very first one which is known as Delta linkage deltoid linkage another is which is known as parallelogram linkage deltoid linkage how does it look sir to do the link another go to the link they are connected together shortest shortest and this is the longest this is longest shortest sources together longest longest together getting a point this is something which is known as Delta linkage on the other hand you may have kisser longest link longest link longest link is shortest link longest we are having shortest shortages again we are having longest and then again we are having shortest now how they are connected that's what I am showing shortest and my shortest longest in my longest one kind of configuration another configuration the longest side May shortest longest side my shortest that's it these two configurations are known as this is Del Droid linkage here this is also pen joint this is also pen joint this is also pen joint rules are exactly same sir any of the shortest if you are going to fix shortest either this or this any one sir whenever shortest is going to be fixed shortest if any of the longest this this one you have fixed so foreign a shot a shot both short link will have complete rotation on the other hand if any of the shortest screw you have fixed so sure shortest adjacent both links they are going to have complete rotation is coming up doesn't matter which link you have fixed here either short or long anything fix karoge you will always get double crank mechanism getting a point better now now what I want to say is this with the help of these animations you can easily check sir this is the grashof chain shortest while I link you have fixed the input link output link both are having complete rotations it is I'm not saying that angular velocity is of input out for that I have not made any comment input link will have a complete rotation output link will have complete rotation whether both these are going to have same velocities or not nothing I have said only complete notation that's it as you can see as you can see shortness input output both are having complete rotation number one thing second thing shortest distance rocker you can see here another situation sir shortest link foreign neither input nor output input output both are behaving as rocker beta getting a point acha if what if grashof's law is not satisfied grasshop's law satisfied so you will get a triple rocker mechanism what is the difference between triple rocker and double rocker but a feel the difference this is non-greash of chain non-gression of chain input is also rocker output is also rocker or even this shortest link is whereas whereas here here here here in this case input is rocker output is rocker but sir opposite my shortest link we cannot use it but this is shortest link the motion you can see this shortest link complete rotation you know it is having complete rotation this is rocker rocker this is rocker rocker and it this one is also rocker so that's why we call it as a triple rocker you're gonna similarly this is the example of parallelogram linkage but a parallelogram linkage shortest longest score if you have fixed so you are going to get crank crank mechanism very easily you are going to get crank crank mechanism Delta linkage example so this is Delta linkage either you are going to fix you know uh longest link or shortest link you are so one link is going to have complete rotation other link is going to have partial rotation as you can see here okay so that's enough that's enough uh Concepts pay we have done discussion I have shown you some animations also examinations this thing this page is going to be very very important for you everybody now if you are comfortable till this point now we can talk about single slider crank mechanism and single snap mechanism as I have already discussed that we are going to have again a simple mechanism example here we are going to have four links but this time one turning pair I will replace with the help of sliding pair and this time I am having only three sliding three turning pair only and one sliding pair will be introduced clear I have mentioned all the inversions all the possible inversions which are you know asked in examination inversion of single slider crank mechanism something it looks something like this this is the let me mention here you may have this is one link we have another link we have another link something like this this is the situation sir yes this is your link number one link one is with the help of pin joints this is number four again having pin joint and length four and one we are having sliding pair this is single slider crank mechanism kinematic chain now sometimes you are going to fix like number one you will get something sometimes you you are going to fix like number two you will get something which you are going to call it as a cylinder beta yeah number two this is something which you are going to call it as crank radius R say dimensions number three which is going to be your connecting rod which is going to be your connecting rod and this 4 is your slider or sometimes people will also call it as piston Mata bladder policy piston nothing but same if you will fix cylinder you will get something if you will fix crank you will get something it will fix connecting rod you will get some type of motion it will fix slattering will get some type of motion examination hey multiple times they have asked if you are going to fix which kind of you know mechanisms you are going to get if cylinder is fixed you may either get IC engine or reciprocating compressor but are depending upon input and from where output you are going to collect cylindrical fixed input you are giving add piston output you are kelping at crank this is known as IC engine reverse input you are giving at crank with help of motor piston pay you are collecting output you will get you will get a mechanism which is known as racy providing compressor button is somebody is going to fix crank you will get whatever motion mechanism or rotary cylinder engine somebody is going to fix connecting rod connecting you will get crank and slotted lever quick return motion mechanism or oscillating cylinder engine if slatter is fixed you will get hand pump as your mechanism out of all these mechanisms just you have to remember you know uh when we are going to get which type of mechanism but examination May examinations mechanism I will tell you how does it work and how questions can be asked here what is fixed here only one thing I am going to discuss where potions only that thing I am going to discuss crank and slaughtered motion mechanism in this short video I will talk only about those things which are very very important and again again I'm saying at the start I have mentioned but again I am saying otherwise this chapter is going to take at least 22 20 22 25 hours approximately to get feel of this chapter but I'm imagining I'm assuming you have already studied theory of machine and now you are looking for revision and this platform is going to be one stop solution for your revision only you know the very important things Rank and slotted lever quick return motion mechanism very very careful sir Catholics how does it look sir you are going to have this is your cylinder cylinder you are having this is your crank crank with the help of connecting rope with the help of pin joint you are having connecting rod and then you are having here you are having this is your slider what is fixed but uh you have fixed your connecting rod connecting rod code we have fixed this is my link number one link number one you are having link number two this is link number three and this is link number four which kind of motion you are going to get let me have let me show you that sir this is the idea in reality I may change shape you know length one so I am making here yelling number one this is my link number one which is my connecting rod link one code you have fixed is somewhere here you have connected link number two from at this point I have connected link number two so this is my link number two yelling number two camera this is smelling number two let me write yelling number one habitat this is my link number two K Elder per again with the help of pin joint I have link number three I will connect one link which I'm which I'll be saying as link number three okay one k other end pay um you have connected another Link Link number four so link one okay pin join say I am going to connect another link let me let me let me connect another link or that link I am giving some shape I am free to give it shape better I am free to give it some shape so slotted link I have given it shape or is link go I am connecting somewhere here with the help of pin joint I have connected this is another link which I have connected let me show it by green color so that you will have a beautiful Clarity better this length number four I have given some shape here again this is my link number four beta 4 and 3 where is link number three link number three is connected with link number two yeah this is my slider this is my link which I am saying as link number three beta now check one two turning pair had two three which we have running pair one fork which we have turning pair exactly same as I had Here length three and four I have sliding pair link three four give each way we have sliding pair but now if I give it some name this is point o this is point a this is your point B hello if you are going to connect motor here which is going to rotate link number two so link number two will have rotation where it will have rotation sir along this circle you know with Omega angular velocity it is rotating when this link to have where this link 2 will have complete rotation so link 3 is going to have this this link number four is going to have oscillation it is going to have oscillation and let me show you the extreme positions extreme positions one extreme position you are going to have will be somewhere here and initial Direction May another extreme pushing you are going to have somewhere here and these extreme position corresponding to this extreme position the location of crank will be sir crank will be sometimes here and it will be sometimes here careful careful careful when your crank is when you're crying is somewhere here this is slider point B will be somewhere here and this link it have to come to this point at this end this is a toggle position angular velocity is becoming zero here again crank is rotating with Omega angular velocity and it has moved somewhere here at this location this link it will come come traveling this entire distance it will come here and again stop again from this position when you're crank again will rotate add this position again this slotted lever will come back to this position block now everybody can see everybody can see sir motor if you have connected here so from this position which I am saying as B be one position from B1 position to this B two position this crank has traveled certain amount of angle which is I am saying as beat angle which is which seems to be larger as compared to when the same crank will travel from B2 to B1 position in this direction but this is something which I am saying as Alpha angle beta can you feel sir crank constant angular velocity so it will take larger amount of time to travel this larger amount of angle and this larger time when it has traveled from this position to this position this slotted link will travel here and again crank constant velocity say a small angle trouble from this position to this position plotted Liverpool again it will have to come back from this end to another end can you imagine okay sir this angle seems to be larger because this beta is more than Alpha that's why you can claim these are if you look at the motion of this particular link yeah link number four from one end it will come here it will take larger amount of time but returning may it will be fast getting a point examination they will ask questions tell me what is the quick return ratio quick return ratio it is defined as ratio of this beta by Alpha and from easily from this diagram easily you can check you can easily tell by Beta is more than Alpha energy beta by Alpha value more than one and that's why we call it as quick written motion mechanism quick return cutting time return time is less cutting slowly slowly it is doing and return it is doing fast this is going to be a question of simple geometry what you have to do simply make this geometry simply make this geometry extreme positions and once you have made Extreme position so from this geometry you can easily calculate how much is Alpha how much is beta one important relation let me tell you it will help you to find out Alpha and beta sir ratio is beta by Alpha and one more thing you can see sir beta plus Alpha this is nothing but 360 degree common sense now examination sometimes they will give sometimes they will give geometries they will they will tell you if I uh how much is the dimension of this link fixed link crank Dimension they will give you these values if extreme positions you can see clearly can I see sir this is the tangential this is the radius radius and tangent which we are going to have 90 degree angle so then I say can I say how much is this angle but e angle this is going to be 90 degree and if this is 90 degree look at this triangle from this triangle can I say sir this is 90 degree this half angle will become Alpha by 2. this half angle is nothing but Alpha by two so from this the right angle you can easily find out how much is Alpha by two Dimensions if you know the dimensions examination May Dimensions sometimes they will give if you know how much is this Dimension if you know how much is this dimension so from this right angle triangle can everybody easily find out how much is Alpha by 2 Alpha by 2 value once you know so alpha position you will get to know how much is beta beta no beta is known Alpha is known very easily you can find out equivalent ratio getting a point either they will give the dimension and they will ask okay try to find out how much is the quick return ratio yeah foreign ratio and they will ask how much is the dimension of Missing Link a simple geometry problem but if you can identify these configuration extreme positions to identify so very easily you can solve it but very easily you can solve it okay most of the time questions whatever questions they have asked they have asked questions about crank and slotted liver motion mechanism only clear enough and that's why I have discussed this otherwise there are few more types of otherwise there are few more types of quick return motion mechanisms but again questions are not asked so I will be limited to I will I will you know to make this video very short and crisp I'll I'll be limited to only those points only those parts from where you know chances of getting questions is very very high acha uh before concluding let me tell you another important thing we have double slider crank mechanism also over mechanism we have seen uh single slider crying mechanism we have seen that we have double stridocratic mechanism and how does it look double threaded crank mechanism before we proceed let me show you the animation also so that you can get more feel single slider crank mechanism uh crank and slotted liver motion mechanism just try to feel the you know motion how it is moving with respect to fix link this is the fixed link fixed link fixed link me about one point a link is there which is going to have oscillation about one point a crank is going to have rotation and crank K and by there is a piston there is a slider which is connected crank rotated with the help with the constant angular velocity and look at the motion of this slotted bar slotted bar slowly fast it is coming back slowly it is moving ahead past whenever it is coming back slowly it is going the side fast management is coming back that's why I am saying that this is your quick return motion mechanism and this kind of mechanism you are going to use uh in many applications shape or machine if you have seen we are going to use this planar mechanism we are going to use this Clearwater let's proceed for double slider crank mechanism you are going to have again four links because we are talking about simple mechanisms so four links and four lower pair but this time two turning pair and we are going to have two sliding pair and how does it look how does it look we are going to have a slotted plate something like this this is single link button single link slotted blade shape as I this is link number one link number one we are having a slider which I am saying as link number two so we are having like number three cases we have link number four and four is again making sliding pair building link number one both hands are careful link number three is having pin joint here pin joint here so between two three and three four we are having turning pair I have mentioned here two three three four we are having turning pair between link two and Link four whether this link plotted plate link 4 can have sliding in horizontal link 2 can have sliding in vertical arm player how will it look during motion something like this kuch something like this once this red Vala link slotted plate which I am saying this is single link inside this we are having two sliders which I have connected with the help of a link with the pin joints now again you may have choices here also we can talk about inversions you may have choices either you can fix link number one or glider either you fix this slider or the slider nothing but same same you will get something linked to or for any of the salary will fix you will get something if you will fix link number three you will get something plotted plate code if you are going to fix you will get elliptical tremel this is something which is used to draw ellipse ellipse let me show you plotted potato if you have fixed slotted plate is not moving other links are going to have motion once ladder is moving up down another sliding is moving left right and the link which is connected is connecting to the sliders on that link if you take any points per path any any point connect pencil to that so it will trace a ellipse getting opened so this is something which is known as elliptical tremel to draw ellipse we are going to use this instrument then we have any of the cylindrical if you are going to fix who is Adder link 4 or link two nothing but same you will get scotch York mechanism and this is something which is used to convert rotation into reciprocution you can see sir link number one which is fixed length number one which is fixed one case we have length which is going to have rotation rotation go it is converting into reciprocution this is also known as a simple harmonic motion generator beta and last if Rod which is connecting with ladder this is the rod which is connecting both these sliders if Rod who you are going to fix so link to and Link Force okay rotations can be transmitted into each other if link two go somebody is going to rotate length 4 will rotate in the same direction with the same velocity and this concept is used as old hands coupling to connect shaft butter to connect shafts you can see here you can very easily see here if everybody is comfortable till this point foreign topics what is mechanical advantage and what is the transmission angle how do we define mechanical advantage let's have a look what is the meaning of mechanical advantage beta mechanical advantage is defined as ratio of output effect output way how much force or Torque you are going to get divided by input effort input how much force or Torque you have applied you have given keep in mind mechanism May it is not generating power you are going to give the power at certain link and it is getting transformed from one link to another to another to another and lastly you are going to collect the output input by whatever power you have given exactly same power output link so you can collect but during this transmission from links this power this motion has transferred so in this transformation some format may change input May input May you have given uh some torque some omega torque into Omega this is power input you have given but input May uh you have given very high velocity but very small amount of torque but output way when you are collecting it output link may you can see you will get some output multi some torque into Omega but output whatever power you have given this power it will be exactly same as output torque let me write it uh somewhere whatever power you have given output by exactly same power you are going to get input when you power the other same power output you are going to get in the output also but output Maybe angular velocity is very very less but torque has increased this product have to be remained same obviously whatever is the input power it will be exactly same as output power input torque into Omega power output torque into output Omega power these powers are same power format changes getting a point power format change and this ratio this ratio output effort divided by input effort in terms of torque if you are talking talk in terms of torque in terms of forces if you are talking talk in terms of forces only output my effort output torque divided by input by effort input cut or this ratio is called as mechanical advantage can I write output torque upon input torque output torque upon input torque core reciprocal of velocity input Omega divided by output Omega now one very interesting things one interesting fact you will be surprised sir generally we want a mechanical advantage should be more than one we want it more than one hoga so we will enjoy input may very small amount of torque I will give output a very large amount of torque very small with very small effort very heavy work we can do at the expense of his speed I can understand but very small amount of force I file apply Force by this little finger you know I can even raise you know 1000 kg weight with the help of my this little finger that's a different thing okay I will have to apply force with large velocity but output May with a very small velocity that heavy weight will be lifted clear enough one interesting thing one interesting thing is sometimes a situation may arise for example if you are talking about mechanism which is crank rocker mechanism this is crank and this is going to be your rocker beta you have given input here motor you have connected and you are going to collect output here it is very important for me to tell you okay which is my input length which is my output link okay input Omega divided by output Omega this is going to give you the formula of mechanical advantage if I if I say output I am collecting here the formula will be reversed getting open Everything Will Change so very carefully you have to write if whatever whichever is your input link angular velocity you have to write here getting a point result otherwise results now this is the crank you have connected motor can you feel motor connector key motor is going to rotate with constant Omega Omega constant rotate correct continuously it is going to have rotation whereas The Rocker it is going to have oscillation Dollar Motion sir add this extreme position at this extreme position it is going to stop these are the two extreme position between this this rocker is going to have motion beta and can you imagine at this toggle position and this another second toggle position there are two toggle position and add this toggle position output triangular velocity is going to be 0 bit a input Omega is always constant and output Omega will become zero at some position not always but at some position at whatever moment input way speed is there output zero okay imaginary a input my speed is there continuously output Omega is zero something upon zero you will get infinity and that's what examination multiple times they have asked you add toggle position what is going to be mechanical advantage mechanical advantage at toggle position becomes Infinity becomes Infinity becomes Infinity getting a point at toggle position mechanical advantage will become Infinity but keep in mind input is this output is this if I do it reverse these are input I am giving here Infinity add certain toggle positions input will become zero output continuous input will be zero at toggle position input 0 hoga so there's zero upon something this is zero so very carefully most of the time they have asked question okay at toggle position what is going to be mechanical advantage but if very clever manner if I say that this is my input and this is my output if your answer will be 0 not Infinity but now okay last topic for this session the last topic I hope everybody has enjoyed transmission angle recently they have started asking about this we will not go into much detail let me just give you a glimpse here what is the transmission angle suppose four bar mechanism if I'm saying add any instant when I saw Links of my mechanism were having motion something like this Links of my mechanism are having motion like this this is my fixed link okay this is my input link I have connected motor here this is my input link add any instant when I saw my input link was making some angle Theta input angle voltage but this is called as input angle Theta is input angle again pegs link and input link whatever angle you have that is called as your input input angle coupler this is your coupler and this is your output link add any instant coupler and output link whatever is angle that is something which is known as the transmission angle mu is called as transmission angle getting my point now examination May sometimes Google if they have asked generally they won't ask if I at any position try to find out how much is the transmission angle with the help of simple geometries all these Dimensions they will give they will tell you this is the dimension a this is the dimension B they will tell you all these Dimension this is the dimension C this is the dimension d all these dimensions most of the time they will ask you might for this mechanism transmission angle minimum value and maximum value without how much it is going to be okay so again derivational part I am skipping just giving you results and I many of you already know about this transmission angle it is not independent thing it will depend upon Theta Theta value when it is 0 degree and 180 degree these are the two positions when your transmission angle is going to have minimum and maximum value beta so whenever if they are asking if they have given you a mechanism and they are asking to try to find out what is going to be a mu minimum value mu maximum value so Theta is 0 and 180 degrees corresponding you are going to get mu minimum and mu maximum beta formulas there is there is no such formula many people might have remembered few things key sir this is the formula now there is no formula here configuration if you will draw very easily sir zero degree how how this mechanism is going to look sir zero degree May how this mechanism is going to look let me give ah little bit color combination so that it will be easy for everybody to understand this listen carefully for zero degree wall of configuration how will it look the zero degree may it will look something like this is the white color or a link when Theta is 0 this length composition is somewhere here it will be so a has a zero degrees you are going to have this position better input link is making zero degree angle and then we have coupler coupler and outputting they have no other option they are going to make they have to make a triangle something like this this is Theta 0 position this is pin joint this is pin joint can you see this was the given mechanism Theta give zero only position one position you have seen here you will have mu minimum value all these values these Dimensions they have given year Dimensions also also known to you you know all these dimensions are known very easily you can identify this is Mu minimum very easily you can find out how much is the value of mu minimum again let me tell you this Dimension is given this Dimension is given this Dimension is given this is also given that means you also know this Dimension better so in this triangle a dimension this Dimension is known all three dimensions are known mu value they are asking cosine very easily we can find out and how do we use cosine rule please don't ask this and now please don't ask this array beta this is angle a this is angle B and this is angle C opposite to angle a we have Dimension a opposite to angle B we have Dimension B opposite to angle C we have Dimension C is small C cosine rule says angle a if this angle you have to identify cos angle a can be written as b square plus C Square minus opposite value Dimension a square divided by two b c if all these Dimensions you know so angles go easily we can find out Buddha clear enough so just draw the configuration one configuration I have drawn for Theta is equal to 0 and similarly if all Theta is equal to 180 what you will have for 180 degree input link will be somewhere here a this is your 180 Wala link input on a link at 180 degree other tooling they have no other options so they have to make a triangle beta they have to make a triangle it will look something like this as another Hobby this is pin joint this is pin joint a b my dear this is pin joint and this is the position Theta 180 degree corresponding and this angle is your mu maximum beta symbols about again you have to do what sir in this triangle Dimension this is known this entire Dimension is known a link a link everything you know mu maximum very easily we can identify beta so sometimes transmission angle maybe they may ask questions that's all so uh what we have seen here in this entire chapter what we have seen we have seen examinations by degree of product they will ask question we have seen what is the formula and how do we use that crash of law what is grasshop's law how do we use that we have seen that inversion of mechanism I have told you some inversions of mechanism how do they look animations I have I have told you that and examinations wherever numericals can be asked I have discussed that medical mechanical advantage and transmission angle baby we have had a very crisp discussion better I hope you have enjoyed this session I hope you have learned something I hope it has helped you in revision part also so thank you and in the next session of this one short series we will meet and we will discuss some beautiful concept of velocity and acceleration analysis thank you love you all