good morning bacho good morning and I hope everybody is doing great your profession for gate is going really great better already we have covered simple mechanism in the previous video and today in this one short series in this today's video I will be covering again a very important topic of theory of machine I will be discussing about velocity and acceleration analysis careful and again this is actually a very big topic but today in this small session I will be covering all the key points from where the oceans have been already asked are or there are very high chances that questions can be framed only those points I am going to touch better so let me give you a glimpse that in this entire video about what points we are going to have you know we are going to have discussion I will be discussing about Eye Center method mostly this is ask beta I Center what are the Eye Centers how many number of Eye Centers are going to be there you know where are going to be the locations of basic Eye Centers how do we use this ice center method to calculate velocities of any mechanism all these things we are going to discuss so I Center method I will be discussing a little bit then we will talk about Kennedy's theorem this is part of this I Center method only candidates we are going to have some discussion then we will be talking about angular velocity theorem again a very important thing but a very important theorem then we have relative velocity method graphical method sometimes it may also play a very important role in examination and lastly I will be discussing brief about acceleration analysis and acceleration analysis say uh generally length equations are framed but objectives K point of you say acceleration analysis is less important coriolis acceleration is a bit more important part about mostly questions will be framed let's begin I will be discussing about uh what is a velocity analysis what do we mean by velocity analysis very very careful but they go in our syllabus we are having all the mechanisms of degree of Freedom 1 only and what is the meaning of degree of Freedom one voila mechanism that examiner will give you they have given some mechanism they have given you certain mechanism for example maybe mechanism or something like this this is a mechanism which they have given and in that in this particular mechanism this is pin joint this is pin joint this is pin join this is pin joint one link is fixed degree of Freedom that if I tell you only one link velocity so all other link velocity you can easily calculate this is the meaning of degree of Freedom one to Define velocities of all these links I need to tell you only velocity of one link here that is a beauty of degree of one mechanism now examine examination may they are going to give you input link velocity orientation they will give rest other link velocities you have to examine you have to find out and this is what when I say this is what I mean when I say velocity analysis of any mechanism for this mechanism if I have to analyze the velocities that means for any one link velocity they will give they will give and rest other links velocity I have to calculate and there are two beautiful approaches which we are going to follow two major approaches what are those approaches but a first one which I am saying as Eye Center method very popular and this is one of my favorite also because uh examinations this is also very important but examination may I Center method say majority of the questions you can easily solve but now this is very very less time taking as compared to this graphical method also I Center method second thing another approach which is known as relative velocity approach or some people also call it as graphical method better graphical method now look here very very carefully when I say I Center method what do we mean beta you go how to solve any uh how to solve those problems where link is having pure translations are from 12th standard we are studying that anybody which is having translatory motion linear motion I know how to handle that if anybody is having pure rotation I know how to solve that I I I know okay Center of rotation came out if any link is there which is having rotation if you can tell me how much is the Omega so easily I can tell on this link each point of the Velocity I can tell Omega just tell me what is the Omega Center just tell me how much is the Omega each and every Point velocity I can easily tell better now the problem arises vain we have certain link which is having mixed kind of motion neither pure translation nor pure rotation mixed kind of motion and mixed motion is something which we generally call as general motion and how any length will look suppose this is a link which is having some general motion General motion it's this particular point this is point a and this is particular point B point a on this link is having velocity in some random Direction somewhere here suppose somewhere here and point B on the same link is having velocity somewhere here some random velocity some random Direction there is no such relation here if you can identify where is the I Center of this body so you can very easily solve this kind of problems Buddha and how do we find out I Center Beta or any moving body you know with respect to fix link with respect to this board this link is having certain relative motion and that relative motion I can see point a is moving this side point B is moving the side the point a key velocity cup just drop perpendicular just draw perpendicular here and point B velocity you know you know this draw another perpendicular perpendicular to velocity of point B these two perpendiculars you have drawn and wherever these two perpendiculars are going to intersect that is known as I Center getting a point and from this eye center you can see you can get a feel by this length is going to have a pure rotation about which about which axis about which point about this particular point getting my point once you know any general Motion in this world any general motion can I very easily Connect into rotation this easily yes but yes add this instant if you sit at this particular location this is the magical location which is known as Eye Center or instantaneous Center of rotation or some people also call it as virtual Center of rotation if you are sitting somewhere here at this particular location so from this point you will see that from this point point a velocity is the line of sidecar perpendicular okay from the same point point B velocity line of side perpendicular Direction This is sir any link from this point velocities whenever I am looking at this link Point velocity is perpendicular to the line of side perpendicular to the line of side is that I am getting a rotation or a field this link is going to have a rotation with some angular velocity Omega now if I have already find out what is the location from where pure rotation feel I can get and if you can calculate this Omega sir now the problem is solved you know from where rotation of field you are going to get you know how much is the Omega on this link any political velocity very easily you can find out very easily you can find out sir any point sir this is point C find out the velocity of this point Z what do you have to do nothing sir Center say connect this point C and perpendicular direction mean you are going to have the Velocity the velocity will be somewhere here this is going to be velocity of Point C perpendicular Direction Omega you know the Omega velocity of Point C I can write IC enter say from center location of Point C is how much just measure that multiplied by whatever is Omega velocity of Point C very easily you can find out Buddha getting a mind now you know the power of this I Center method okay sir just to find out in the space where is your eye center any emotion believe believe my words any emotion any emotion literally any emotion in this entire world if you want to see that motion as a rotation just find out where is the eye center and from I Center at least for this moment from this location pure rotational field you are going to get getting one point acha ecology examination when they will ask one question very important question if I for any given mechanism tell me first of all tell me how many number of Eye Centers are going to be there so today for each pair we are going to Define one eye center for each pair we are going to Define one eye center so for any mechanism for any mechanism which is having n number of links number of Eye Centers will be how much whatever is the number of pairs possible so that is nc2 permutation combination in the school days that thing I have written NC to two two pair I am going to make so with antibodies how many two two cup pair you can you can make sir nc2 the value of this comes out to be n n minus 1 divided by two this is going to be the formula and examination may they are going to ask question based upon this why just tell me how many number of Eye Centers are going to be there just calculate number of Eye Centers that's it the very first thing which you can expect occasion from the very first concept Clearwater acha once you know I Center is some some point in the space from where pure rotation of field you are going to get how many Eye Centers are possible if you know these basic things so you just have to do one thing by try to find out all the Eye Centers are location and once you know all Eye Centers collocation very easily very very easily you can calculate you can calculate velocities now let me tell you how do we find out some basic isometers some basic Eye Centers the very first thing few I centers you must know everybody must know better the very first thing if you are having turning pair turning pair means suppose I have two links this is link number one and it is connected to link number two these are two different different links and they are having a pin joint somewhere here this is the PIN joint button let me give it some name sir this is my link number three and this is my link number four intentionally I have not given it link one hello intentionally I have not said it link number one otherwise many people will get confused okay last class I have told link one is always reserved for fixed Wala link you know so just because many people will start getting feelings that's why I have written some some random name here this is link three and this is link four getting open two links I have and for these two links if you want to know where is the location of eye center here I Center means from where relative motion will be seen a pure rotation if you sit at this point center of the pin this becomes your eye center let me write this Center of pen is getting a point Center of pen itself becomes your horizontal you will write yeah this is my I Center and what is the name of this eye center for body three and four this is I three four everybody clear if you have turning pair location of y center becomes your pen is Center itself first thing second thing second thing okay sir careful careful careful second point doubles if you have rolling bear but in case of rolling bear as I keep in mind when I say rolling bear rolling pair means there should not be any slip no slip should be there if sleeping is happening for that condition you have to identify you have to find out again from the Zero from the scratch where is the eye center but if there is a no slip in that situation in that particular situation location of eye center will be where let me tell you sir you have a body a flat surface and fixed blood surface and on that fixed flat surface there is a disc which is going to have rolling motion purely motion there should not be any slip that's it that's the only condition this is a disc which is having pure rolling motion what is the meaning of pure rolling butter pure rolling that this risk is moving with a certain velocity V CM velocity say its Center of mass is moving and this is also having rotation meta with some angular speed Omega say it is also having rotation and I hope everybody knows what is the condition for North whip there are no slippery we have a beautiful condition that velocity of center of mass magnitude must be equal to R Omega getting moment this magnitude must be same now here actually this body is having translation as well as rotation both things are happening together General motion but if you want to get feel of pure rotation so just sit down at this point of contact this particular point of contact this is your eye center for these two bodies relative motion is link number one and this is my link number two so I Center one two collocation is this this is I one two everybody clear everybody clear ly whenever you see pure rolling the point of contact will become your eyes enter that's it same thing same thing you can also say you can also say for example again pure rolling example I am taking here suppose if you are having two gears or you can say frictional disks you are having two frictional disks you are having this is one disc it is in connection with another disc and these two discs are rotating about their fixed Center getting opened so yeah this is my link number one you are having link number two which is having rotation two this is link number three and again this is link Number One beta if you want to find out how many ice Hunters are there where are the locations sir length one and two k which you are having turning pair so this becomes this this point it is showing I one two location in joint adjust we have seen it one and three they are having pin join somewhere here to link one and three key you are going to have I one three this is somewhere here and between link two and Link three if you are having no slip if slipping is not there so Bhai this point of contact this contact point uh mark my word there should not be any slip if slipping is happening but this is not going to this is not going to be the valid result you have to again do your calculation carefully but if slipping is not happening pure rolling if you have some if you have pure rolling so this location will represent body 2 and body three a slipping is not there pure rolling you can get a feeling here also sir this will be location of this as your I 2 3 beta everybody clear I two three location you are going to have here third thing suppose if you are having sliding bear butter ing pair that means on a fixed surface this is a straight line and on that straight line fixed straight line if any slider is there and that slider is going to have sliding motion careful this is the slider and the slider is going to have sliding motion what do you mean by sliding motion sir it is having this kind of motion slide this is having sliding motion somewhere like this somewhere like this it is having sliding motion you are having for this relative motion one eye center I can Define and that I Center is on a line which is perpendicular to the surface where sliding is happening so this is the line on which sliding is happening draw a perpendicular line and on this line on this line at somewhere at Infinity you are going to have your ice interpreter getting appointed body one and two Kelly I one two will be on this line which is perpendicular Direction perpendicular to this length this line where sliding is happening at infinite distance you are going to have isometric and why why this why this is Hunter is at Infinity this link is having pure translation linear motion and linear motion could be if you want to see as a rotation so yeah you have to set at Infinity Infinity getting women obviously fourth thing these are the basic Eye Centers everybody must know about these things next suppose if you are having a slider which is sliding on a curved surface it may be on the convex part or it may be in the convex concave part slider sliding on curved surface sir it may be on convex part or it may be on the concave part it doesn't matter results are going to be same what I want to say is if I suppose this is a very big surface fixed surface and on that surface there is a slider which is going to have sliding motion this is a slider and the slider is going to have sliding motion how this sliding motion is going to work so sliding motion is something this link is going to have sliding motion this is the block and this block is going to have sliding somewhere somewhere like this getting a point getting a point now I Center if you want to find out what where is going to be is under this is link number one a link number two habitat and this is the center of curvature of that surface where sliding is happening sliding may be inside means at the concave Wala part or even if this slider is sliding at convex part sir outer surface may it is sliding something like this this is going to have this motion even in this condition both of these conditions location will be at this Center of curvature getting a point but this is going to be your i1 2 Beta for this also for this also clear everybody is cleared in this point no sir some basic Eye Centers you have already calculated some basic Center you you have already calculated listen carefully rest of the Eye Centers Kelly you have to have some uh some more theorems and what are going to be those theorems the very important theorem is Kennedy theorem py centers few basic I centers I have already got rest of the Eye Centers you can calculate how do you calculate better careful careful careful careful uh according to Mr Kennedy's he says or any mechanism suppose if you are having feelings which are having relative motion with respect to each other any Three Links it is not necessary this is my link number one leg number two and Link number three that these three links are together now or any mechanism which is having link one two three four five six so many links are there it is your choice take Link one take Link four and take Link six no direct connection it is not necessary any Three Links which are having relative motion with respect to each other for these three links for these three links for let me write if Three Links are having relative motion with respect to each other relative motion with respect to each other so for all the three Eye Centers associated with them all three Eye Centers associated with them they will be in a line with them will be in a straight line they have to be arrested and they don't have any choice but now they don't have any other choice now listen carefully sir if I take link number two link number four and Link number five so for these three links which are having relative motion what are going to be the eye center sir whatever pairs you can imagine those isometers are possible sir length 2 and 4K you are going to have I two four two and five kilo you are going to have I two five and Link four five kilo you are going to have this is I four five these three eyes centers they have to be in a line they have no other choice but one more example suppose if you are having link number one link number three link number six some random links again I'm saying it is not necessary that link one two three link four five six no no no they may have direct connection or not link one link three link six for any mechanism these are three links which you have taken into consideration what are going to be the Eye Centers but you are going to have link one and three kill a pair I one three beta one and six K you are going to have I one six beta 3 and 6K you are going to have I three six and these three Eye Centers they have to be in a line these three isometrics they have to be in a line getting a point getting my wind how we are talking how do how we are calculating everybody is getting my point okay now one theorem is Kennedy's theorem another is angular velocity theorem before we go before we go for angular velocity theorem let me take one example where I will where I will show you how do we calculate location of all the I centers but very very careful suppose we have a link some some general some random example I am taking uh this is link number one which is fixed yelling number two hey this is link number three and this is link number four beta let me show you when join this is pen joint this is pin joint this is pen joint they go some basic ISO enters call location you know already Kennedy's theorem you know now you are comfortable you can find out all the Eye Centers very easily very very easily beta sir this one is fixed how many links you can see here so link number one this is link number two earring number three has this is link number four let me write down where are going to be the Eye Centers sir one and two Kelly you are going to have one eye center this is I one two three k you are going to have this is your I 2 3 3 and 4K you are going to have this is your I three four four and one kilo you are going to have this is your I Center I one four these four eyes centers you have calculated and somebody who can tell me why how many I shoulders are going to be there there are total number of links number of links are going to be four so I centers number of Eye Centers will be how many n and the minus 1 divided by 2. 4 into 4 minus 1 divided by 2 how many sir this comes out to be six total six I centers are going to be there what are going to be the I centers but uh sir one two hoga one three hoga one four hookah two three two four and three four these are the Eye Centers these are the Eye Centers we generally practice a rough work also here you will draw a circle why let me tell you you will draw a circle and you have to mark these many how many these many four whatever is the number of Link these many Eye Centers you have to Mark Sir this is link number two this is link number three this is link number four rough work we are doing you know for these four points are representing four links and what are the Eye Centers you have already got one two you have already got sir this is line is representing I Center for one and two for this pair Eye Centers we have already calculated getting a point similarly link two and three one two you have known you have got I two three you have got I three four you have got one four you have got one two you have got two three three four you have already find out and one four you have already find out what is left beta you have to calculate where is I one three and can I write can I write from the Kennedy theorem okay this I one three I 1 3 have to be in line with one two two three one two two three as per Kennedy Forum by Kennedy theorem what does it says it says it says for link one two three all three I centers one two two three one three they have to be in a line so that's what I have written one two two three one three will be in a line and similarly if I consider link one four three so for these three links one four three four one three they have to be in a line so can I write by this one three will also be in line with one four and three four let me write it better very easily one three will also be in line with one four three four one four three four now where is one two two three you know these things where is one two two three the one two yeah this is the two three one two and two three go please connect three a and wherever these two let me draw a line a little bit thinner sir this is the line which you have drawn one two and two three on this line you have you will get your I13 the location it is also in line with one four three four one Fourier three four yeah sir one four three four you have you will get I one three allocation somewhere here one person is saying if one three is on this line one person is saying I13 on this line is the intersection point you are going to have your eye center I13 beta this intersection point is representing I one three now everybody is getting my point similarly one three is known now you can talk about I two four can I write so where is going to be 2 4 or 2 4 Glee I can write look here 2 4 will be in line with the two three three four also in line with one two one four foreign you will get a line which looks like this wherever these two lines are going to have intersection can I write butter this is going to be location of I24 once you know all the ice Hunters location now you can start calculation of speeds velocities how do we calculate how do we do that for that we have a very beautiful theorem which is known as ice and first the very first thing which you have to do is calculate find out location of all the isometers further process we will start now but sometimes in examination they will ask a question simply don't do any calculation just tell me just tell me where are the Eye Centers location only location they have asked for to do marks question number now we will come back here we will come back here but before that let me tell you another beautiful theorem which is angular velocity theorem what does it says angular velocity theorem says angular velocity theorem says angular velocity theorem says careful angular velocity theorem say is suppose link to Velocity they have given and from link two this is your link to the velocity they have given and they are asking to tell me what is going to be linked angular velocity of Link number five directly from link two I can tell you link five angle velocity how for that you have to you have to have three Eye Centers what I centers One Eye Center from here absolute motion of link two is seen which is I one two beta you must know this I one two collocation one eye center you must know from where link five absolute motion you can see I one five which we call I one five and one eye center which is common for these link two and Link five which is I two five if you know all these three eyes centers again again I am repeating what Eye Centers you must know one eye center from where absolute rotation of link two is seen one I center from where absolute rotation of Link five is seen and one common I Center for link two and Link five clear beta if you know these eyes genders you can very easily write angular velocity theorem says Omega 2 distance must be equal to Omega 5 I 1 5 say I25 distance look at this formula very carefully and try to understand what I have written I have written angular velocity of Link 2. 1 2 say 2 5 contestants then Omega 5 1 5 say to five conditions what is this two five two five commonweal Center what is this one five from where absolute velocity of Link five is seen from where Omega 5 is seen similarly what is this one two from where link to the absolute velocity is seen from where Omega 2 you are seeing killing a point getting a point sir take our example sir hello let me tell you another example for example for example for example for example suppose sir from length three to link four velocity you have to identify imagine length three to link four velocity you have to identify how we write equation better how do we write equations are one eye center from where link three absolute motion I13 one eye center from where link four absolute motion is seen i14 I 1 4 1 Eye Center from where relative motion length three and Link four common wallet Center I three four you must know these three Eye Centers you must know now Omega 3 is given Omega 4 you have to calculate how do we write equations are Omega 3 I 1 3 is a I 3 4 distance Omega 4 times I 1 4 say I three four conditions everybody clear everybody clear password now as an angular velocity theorem will also it will not only help you in finding out uh magnitude because beta Omega 3 is given one thing will be given another thing you have to find out this thing you have to find out re the rest of these Eye Centers distance I centers we just have calculated all the isometers we have find out where are going to be the locations these distance I13 say I three four distance you have to measure i14 say i34 car distance you have to measure from the diagram you have to measure these distances but ah getting a point now coming back coming back so suppose this in this question you have calculated all the I centers collocation you have calculated I you have find out in locations of all the I centers let me copy this diagram to a new page so that few things I can remove let me remove these these things a high centers identified now they have given some information that Omega 2 is something something this is whatever something radiant per second direction is clockwise clockwise they are asking to find out what is going to be location of Omega what is going to be uh Omega 4 distance but uh will be equal to Omega 4 I 1 4 say I 2 4 distance getting a point now everybody is comfortable how I am writing this equation very fast there's a link to selling 4K which you have to write down the equation the one I Center from here absolute rotation of 2 is seen I 1 2. when I Center from here absolute rotation of Link force in i14 one common eye center I24 I24 getting a point one two three two four questions into Omega two one force a two four distance into Omega 4. they have given some information this value is given this value is given one two three two four resistance how much is this where is one two three two four distance measure this distance how much just calculate measure this distance put down this value here foreign and put measure and put it here can you easily tell me these are Omega 4 you can easily calculate but everybody comfortable this is given this this value we have already measured so something radian per second you are going to get something you have got your answer better comfortable now magnitude to this formula will tell but whatever Direction how can I be sure about Direction and for Direction let me tell you one important thing that that if common values enter I24 if one two and one four if these are on the one side only one two and one four I two four K on the one side either they are on the right only or they are on the left only I will say that Omega 2 Omega 4 will be in the same sense same direction getting a point Omega 2 and Omega 4 same direction if this is a situation or another case may be these are I24 is somewhere here one side you are having one two other side you are having one four means one two and four this two for common eye center is at the mid in this situation I will say Omega 2 and Omega 4 they are going to have opposite direction for this example what we have taken can I say sir sit down at 2 4 where is 2 4 that 2 4 is this one two is this side where is one four so one four is on the same side this side both one two one four are on the same side so if Omega 2 was given as clockwise but a if Omega 2 was clockwise so Omega 4 whatever you have calculated it will be in clockwise Direction same direction same as Omega 2. everybody clear my clear how I am writing this everybody clear examination May once they have asked one question and what is the question let me tell you let me draw the diagram a bit more clear diagram they have given that in a figure is given they have given a link something like this one slider is here another slider is here and these sliders can slide on horizontal and vertical actually many people can feel eraser this is double slider crank mechanism this is double slider crank mechanism getting a point they have given it some name this fixed wallet is holding number one yelling number two the other one this is link number three and this is your link number four proper diagram they have made they have said they have given one as our daughter lines they have given they have marked some points also this point they are saying that this is your point l this is Point N beta and this is your point M this is your point m the ocean may they are asking question mainly are asking the figure below shows a planar mechanism with a single degree of Freedom that instantaneous Center to four for the given configuration is located located at Water positions I 2 4 you have to calculate I 2 4 you have to calculate and they have given some option okay by I 2 4 will be at L M N or Infinity where will this I Center be hoga they are asking this question they are not asking about velocity analysis they are simply asking why just tell me where is the I Center Eye Center how do we write that sir few basic Eye Centers we already know let me Mark those basic Eye Centers I one two will be at somewhere Infinity where infinities are this side horizontal Infinity somewhere there now linked to a link three they are having pin joint they are having pin joined and I write sir you will be having link two or link three which you are going to have I two three beta this pin joint pain Point L pay you are having I two three three and four are connected at this point you are having link three and Link four car I Center i34 at this at this point at Point m getting a point link four one this is making sliding pair horizontal this is going to have sliding sir just draw perpendicular and on this perpendicular line somewhere here I one four again infinite sir perpendicular Direction whoa Infinity is going to have i14 location one two locations in finite we are going to have I one two vertical May or perpendicular Direction at Infinity distance we are going to have i14 beta sir somebody is saying sir what if I say 1 4 is it will be on this perpendicular perpendicular line but it will be upside infinity or downside Infinity your wish your wish it should be on a line perpendicular to the surface on which sliding is happening so this is the surface draw perpendicular line on this perpendicular line either this side infinity or this side Infinity getting a point now now py centers you have calculated few Eye Centers you have already calculated what they are asking they are asking about two four two four draw that Circle draw that Circle this is link one link two length three this is link number four one two but I had two three but I had three four but I have one four but I have there is going to be two four beta can I write two four will be in line with one two and four also in line with the two three three four can I write this exactly where is one two one four sir where is one two one four one two so one to it is that infinite way horizontal infinite pay outside the board where is one four sir one four perpendicular Direction May outside the board Infinity Within connect these two lines sir one two one horizontal Infinity you are going to get a line from that point to that point a line which is going to be diagonal shape getting a point sir I have drawn this line but this line is not here you give 1 4 is not here one two is not here these two points are at in finite distance this is at infinite distance so draw that diagonal draw that diagonal in finite distance P getting opened but diagonal shape it will be somewhere here only as the shape you are going to get getting a point this is the line outside the board I have drawn imagine career and where is i2334 Sir draw this line this line and this line where these two lines are going to have intersection so these two lines are going to have intersection at Infinity where at Infinity many people will give answer is infinity sir I I agree answer is going to be Infinity but where in infinity infinity May at least tell me the direction it will be horizontal infinite or vertical infinite or where let me write on this line let me write sir along this line can I write sir here I24 will be at Infinity along this line beta so what is the answer here answer is option D but getting my point peeling that's why I am saying that's why I usually say if I many people will say my this is going to be at Infinity but Infinity where nobody knows nobody knows that's where I say always just solving question is not enough but now you must have a feeling of the concepts you must feel the subject essay questions they are going to ask now getting opened how do we saw if they are asking to solve question we can easily solve the question because IC underscore location once you have calculated once you have find out the location we have angular velocity theorem just put down the values measure these distances and you will get the answer okay if simply sometimes they are asking location you can tell very easily location getting a point now another methods I don't think anybody is having problem till this point you know uh if in in case anybody is having any problem related to these videos you can drop your message in the comment section definitely either us the teachers or anybody from our technical team will definitely reply but we will consider your valuable suggestions now listen carefully we are talking about relative velocity methods graphical method or in short let me write graphical let me show you with one example beta directly one example and I will draw the velocity diagram for the same question for the same question which we have already taken now for the same question I am showing you how velocity triangle is going to look I have taken example of forward mechanism it was looking something like this doubles the suspend joint this is pin joint this is pin joint this is going to be your PIN joint this is the flexible link all links cut Dimension is given they have also given that at this instant what is the configuration this Theta is given and this link input all a link it is making some angular speed Omega 2 say it is rotating all other links are Velocity they are asking they are asking to draw relative velocity diagram and how do we do that let me Mark some points this is point a this is point B this is point C and this is your point d how do we draw velocity diagram all fixed point you are going to mark this is point a this is point D these are fixed points they are going to have zero velocity or zero velocity you are going to represent by a point vector this is a vector whose length is a zero this is my point D all the fixed points I have represented here only you're gonna now with respect to point a if I look at b sir this link is having only rotation now Omega 2 I know Omega 2 this link this link can have rotation only so from point A if you look at this point B so point B has no other choice it will have a velocity perpendicular to the link somewhere here velocity you are going to have perpendicular Direction perpendicular and sense will be somewhere here if Omega was anti-clockwise so I would have drawn this Vector opposite direction by getting a point you have drawn this vector copy this copy this this Vector getting moment this vector magnitude is also known better velocity of point B with respect to point a sir you have directly drawn it a b distance multiplied by Omega 2 magnitude is known Direction just draw this vector and you will get location of point B beta what is this Vector representing this Vector is representing velocity of point B with respect to a HR this is customary everybody does this we are also doing the same in this entire world everybody has agreed that velocity diagram we are going to represent points by small letters and everybody does that we are also doing the same once you know the point B point B is standing here you can draw velocity of Point C pin joint here with respect to point B this link has no other option rotation and rotation with what velocity it is rotating I don't have any idea no idea I have but sir rotation whether clockwise or anti-clockwise no idea but sir rotation so can I say Point velocity perpendicular to the link it will be whatever is the velocity link okay perpendicular Direction getting a point copy that from point D draw a vector somewhere like this draw a vector somewhere like this on this line somewhere maybe this side or maybe this side you are going to have your point see I don't know I don't know how much is the length of the vector even I don't know that but wherever is Point c will be on this line only same point C same point C with respect to D if you will talk velocity sir whether it is clockwise or anti-clockwise how much is the magnitude literally I have no idea but just draw the line kisser whatever is the velocity it will be in the perpendicular direction to the link is maybe this side or maybe this side getting a point this line you have copied you have drawn copy that line from where you are drawing this point D say where is Point D this is point D rocker beta and wherever these two lines are going to intersect that will tell you location of Point C but a your calculation is saying by a point c will be on this line your idea is saying the point c will be on this line and there is only one point which satisfied both of these lines is the intersectional point once you have got Point C draw one thing draw a vector in this direction what you will call you will call it as velocity of Point C with respect to point d Point draw a vector sir somewhere like this draw of vector array draw a vector what you will call this Vector this is the vector which is one sec velocity with respect to B it is showing velocity of C whether it will be getting a point once you have drawn this velocity triangle whatever the unknown velocities you can easily calculate getting a point getting my point how do we draw velocity diagram now everybody is comfortable you can anyway again uh examination you must know both these things what is the I Center method what is the relative velocity method you must know both of these things but examination May most of the time I Center method is going to help you a lot Clearwater acha next we will talk about acceleration analysis we have to keep this you know video to the point very crisp so only important points I am going to discuss with you otherwise this entire chapter when I am when I'll be teaching with you when I'll be teaching you in our detailed comprehensive courses it is going to take approximately velocity and acceleration come combined it will take not less than 10 hours 10 hours it is going to take okay minimum 10 to 10 to 15 hours but now okay now how do we draw acceleration for any rotating body we are talking about acceleration analysis careful acceleration analysis again it is going to be a little bit lengthier why I am saying this beta because for any body which is having rotation suppose for any link this is the link which is having rotation about some point yeah this is the point Point okay respect me there is there is there is some point a and if for this point a you have to draw the accelerations this link this link is having at this instant it is having angular velocity Omega and add this very same instant it is also having some angular acceleration Alpha Alpha opposite direction I have shown that means it is nothing but retardation angular velocity will be in radian per second common sense Alpha will be in radian per second Square Common Sense common sense you know Alpha may also be in the same sense of Omega then I will say that this is the acceleration a Omega key magnitude this is going to increase if Alpha is in opposite direction that means Omega magnitude over the period of time it is going to decrease because this is retardation D acceleration later now now whether it's better 2.0 if point a acceleration you are going to draw there are going to be two components whenever a body is rotating the very one first component which is called as a radial acceleration radial acceleration of a with respect to Point O yeah this is nothing but R Omega Square beta tendril acceleration always towards the center foreign doesn't matter whether you are moving clockwise or in the clockwise doesn't matter centripetal acceleration radial acceleration always towards the center so point a car radial acceleration you will draw where sir rotation agar hey so for radial acceleration towards the center another something like this this is the radial acceleration this is the radial acceleration of point a with respect to O how much is the magnitude that I have shown what is the value of r r is point O say point a the distance getting a point similarly Alpha tangents angular acceleration is here and due to this angular acceleration you are also going to have some tangential acceleration and what is that tangential acceleration we represent that by a on the top of that t acceleration of a with respect to O tangential acceleration of a with respect to O it is nothing but R Alpha Beta radius is nothing but Point O say point a the distance and direction of this tangential acceleration is perpendicular to link o a clockwise Direction so you will draw a line perpendicular in this sense if it was clockwise Direction so where you would have drawn something like this as a coach getting a point but here in this case we will draw this anti-clockwise remember so we will draw this you have calculated magnitude this is the tangential acceleration of a with respect to O if somebody is asking to tell me what is the resultant foreign total acceleration acceleration of a with respect to O Vector summation radial and tangential Vector summation these are the vectors add curly Jupiter under root magnitude will be how much under root initial acceleration square plus radial acceleration Square getting a point this is the magnitude beta and if I want to show you the resultant resultant will be where sir resultant will be somewhere somewhere somewhere resultant is this age of vector I have shown this vector radical so this is velocity acceleration of a with respect to O absolute acceleration whatever they are asking they are asking magnitude sometimes they will also ask how much is the angle very easily we can tell very easily we can tell this angle if somebody is asking why what is this angle so tan Theta can I write tan Theta will be equal to perpendicular upon base perpendicular is how much tangential acceleration divided by radial acceleration that's it very easy very very easy for one link velocity diagram drawing drawing velocity diagram was easy why the only one vector you have to draw but this time you have to draw two vectors first you will draw the radial acceleration then you will draw the tangential acceleration then you will take resultant and this is representing acceleration again from point A you will draw some other point B radial acceleration tangential acceleration then resultant then you will get point B getting opened so it is again going to be a little bit complicated complicated in the sense not tough but it will be time taking and that's why examination where they will not ask question here but examination May they will ask question definitely definitely from a topic which is known as coronis acceleration why because here tricky questions can be framed very easily they are not lengthy but they are going to be trigger again gate examination they are never examination yet examination is trying to judge your aptitude getting a money they are never trying to judge your memory skills they are never trying to judge your uh how lengthy questions you can solve Nevada your calculator no they are not interested they are just willing to check your common sense and general aptitude of engineering whatever basic things you have is to read do you know how to apply them clear and that's what you need to learn when you are studying your College Wala subjects University point of view say the approach is going to be different than the questions how do we solve this then the definitions how do we memorize them hate me they are saying just forget all these things approach is completely different and in fact every competitive exam approach is totally different and for clearing any examination you have to understand need of that examination meta the day you will understand need of that examination you will start you know tracking those examinations sir for so many days I was not able to uh clear any examination but all of a sudden during my preparation Journey there was a point there was a time when I cracked my first competitive examination one after other after other after other so many examinations whichever examination I was appearing I was getting good rank in that you just have to cross that threshold you have to understand what examiners are thinking what is the need of that examination and gate May you have to build good conceptual Clarity feeling again I'm saying feeling once you feel the subject you can very easily crack the gate examination but again coming back to the correlates acceleration acceleration what is the correlation beta doubles for any rotating link there is a link which is having rotation okay this link is rotating with some angular velocity Omega this is also having some angular acceleration Malo be but we are not going to consider that you know I will I will introduce Alpha later on but we are going to focus only on correlation for any rotating link which is having instantaneous angular velocity Omega and on that link if we are having a slider the slider is this this is the slider and this slider is sliding on that link either outward or inward it is having sliding sliding motion simultaneously rotation in parallel to that simultaneous to that your slider was also sliding slider car sliding velocity suppose outward Direction This is the velocity of sliding if both of these things are happening simultaneously this link is on our rotating body so rotations related both of these accelerations which we have already studied they will come definitely they will come additional acceleration will be there this acceleration and that correlation acceleration is given as a on the top of that c it is given as 2 V Omega what is this v v is the sliding velocity Omega is at this instant angular velocity of this link on which slider is sliding foreign acceleration unit if you have kept velocity in meter per second Omega in radian per second acceleration you are going to get this acceleration okay very easily very easily we can calculate now the question arises these are acceleration here this is the vector quantity can you please tell me the direction let me tell you the direction direction clear what you will do direction of coriolis acceleration sir take velocity Vector there are two steps basic steps first one take direction of velocity number two rotate it by 90 degree in sense of Omega getting a mind sir this is the velocity or velocity any Vector if you want to do if we want to rotate that Vector always about its tail you have to rotate so Omega clockwise about this tail velocity Vector go clockwise Direction you will get what sir rotation you have got this Vector this is correlates acceleration this slider will experience this correlation acceleration rotated clockwise Direction 90 degrees acceleration on which body this is acting sir on this slider the slider was also experiencing some more acceleration so examination they may ask they may ask why you tell me what is the corollary acceleration you will tell me this 2v Omega value if somebody is asking to tell me what is the total acceleration I am not interested in coriolis tell me the total acceleration absolute acceleration or simply they will say tell me the acceleration Sky acceleration they will tell you acceleration without any point on this ladder is there any point the ladder keeper there is a point a point a acceleration though simply they have said point a acceleration with respect to 2.0 how much is that sir point a is on that slider is also threading so coriolis acceleration V I got it will also be there rotations related all those accelerations which were already there they will come radial acceleration tangential acceleration they will come new acceleration correlation acceleration will also come into picture now careful careful careful careful for example let me take one beautiful cushion foreign they have given a link Omega angular velocity so this is link is rotating we have a slider over here this is slider both very very careful but very very careful one example and from here every doubt will be cleared so sir this slider is sliding uh for example in this direction inward Direction velocity see this is sliding inward and there is initial acceleration also tangential acceleration is sorry angular acceleration Alpha is also given Omega is there Alpha is there simultaneously sliding is also there sir there is a point on this link which is point a Point O say point eight occur distance is given as suppose r this distance is given as r that tell me what is the total acceleration and total acceleration how do we calculate that sir total acceleration of point a with respect to O sir this is slider Point e is on a rotating link rotations related radial acceleration will be there pictures radial acceleration will be towards the center always towards the center this is going to be radial acceleration this is going to be radial acceleration tangential acceleration Alpha is anti-clockwise tangential acceleration green color say I am showing it will be in this direction so what is this tangential acceleration and what is that what is the correlation acceleration so correlation acceleration will be 2 into V into Omega but direction direction will be velocity Vector in the sense of Omega rooted Omega is clockwise Omega clockwise about its tail clockwise clockwise you will reach somewhere here you will reach and the acceleration which you will get that acceleration let me show you my yellow color corolla's acceleration will be somewhere here this parallel line parallel line getting a point this is the correlation acceleration beta it's a before that we have seen a situation where corollary acceleration was in this direction what we have seen it is in this direction it may be this direction or this direction to sir someday this tangential acceleration and correlis they may also be in opposite direction they may be in the same direction you know so depending upon your case to case can I write total acceleration magnitude these two are parallel maybe in the same direction or in the opposite direction sometimes they will be added sometimes they will be subtracted depending among different different cases under root resultant of these two Coral is acceleration either plus or minus in this case we are going to do plus you know but I am writing the general formula total is acceleration plus or minus tangential acceleration square plus perpendicular Direction you are having radial acceleration that's it that's it that's it that's it that's it everybody comfortable put down all these values you will very easily get radial acceleration what is the formula I know tangential acceleration I know correlates acceleration I know add to this instant r k value is known so radial acceleration R Omega Square tangential accelerations every value put every value here you will get the answer this is the magnitude getting a point now you know now you know everybody knows the acceleration analysis May questions will be framed here Gateway and doesn't matter how much I tell you but many of you are going to commit mistake why it's a simple mistake very easy this is very easy concept but you will commit a mistake foreign they have they have asked tell me the acceleration answer I have selected that option that was showing correlation if they are asking coriolis acceleration they will clearly mention my Coral is acceleration if they are asking radial acceleration only they will clearly mention but if they have written tell me what is the acceleration that means they are asking total acceleration getting opened so in these points you have to be extra cautious better so that's all these were all the important points from where the oceans can be framed in velocity and acceleration analysis already we have covered mechanism chapter I hope everybody has learned something new something important and in this chapter I have covered all the important points from where questions can be framed these are the Those portions these are Those portions from where mostly questions are asked but again beta this is a very crisp video very crisp video in detail in comprehensive courses whenever we are going to study this and this only this chapter I will teach you for not less than 12 to 15 hours beta clearer we will again go into much deep we will solve some more numerical some more subjective questions also you know again uh I hope you people have enjoyed you people have learned something new if you are literally enjoying this session this series so please let us know in the comment box okay and do share this informative video with all your friends who are really looking for good content of theory of machine we will meet in the next video till the time thank you goodbye