### Lecture – 5 Parallel Manipulators

In the series I said briefly recapitulate what the head talking in last previous lecture and then I will go head further on so let us just recall what we are talk in the previous lecture Okay, in the previous lecture we had seen what are known as spatial and planar open change spatial and planar hope and change this we are look at so the degree of the freedom of open change how will you degree what are type of joint which are used open change okay, now we noticed that that we using some R ,P joint that is a review and the regarding joint so the these kind of powered that what we had seen more over we noticed that the axes can be parallel or perpendicular to this what we had seen in the last lecture okay, has we gone on we will seen much more about details about these your also seen what is known as direct kinematic where joint angle given you know where the end effect that what we have seen also we had briefly look that we know as inverse kinematic Where is the intersect or position is given you know valid what the to the joint angel inverse kinematic what are seen it last lecture in addition you had seen know has resolution accuracy and repeatable the most important of these repeatable because what are you robot does if it repeat continuously without error you are very happy accuracy yes more expensive robot you can very small workspaces must taken you need then resolution What is the minimum distance end of effect this can go that depend on the resolution of the various elements all so minutes are subject to forces continently to bend that back glass all desire all these parameter for the resolution accuracy and repeater you had seen that also okay, there all so look at the workspace we had seen that in a curtain robot the work space some sort a with cube and where seen that it is parallel the system occupies the lot that what we have seen yesterday there was a question after lecture some student ask me a question. I will briefly touch up on Before I go to what I am going to discuss today okay, let me look that you see yesterday was question was very simple, yesterday what I has told you people was this had taken a curtains robot something like this Okay, and then I had said where the workspace of the static robot is fairly not as much as one would desiring comprising to the overall size of the robot what I have seen so the student is asking I am not clear about that to be kindly look at it again so that why I visiting that and looking at it again .So let me show a draw a statical robot here I have got this and I have got one joints like this I have got the pneumatic joints here

Had grippers here I hope it does look like a static robot on this okay, right now I can drive this axis to various need and I am using pneumatic cylinder there is an pneumatic cylinder which powers this action the motion of this block to this motion a obtain by this solution this cylinder the whole block up and down motion where the something else and inward and outward motion of the gripper. So when you have the pneumatic cylinder like that let us say the cylinder length is L So you have that pneumatic cylinder where the piston in and that if this length is L The stock is also approximately L. so the pneumatic cylinder moves in and out and when you get a cylinder length of a L overall space occupied by the pneumatic cylinder is 2L now perhaps a workspace which is LxLXxL and I use three pneumatic cylinders one for the X motion one for the Y motion and one for the Z motion. And then the overall space occupied is 2Lx2Lx 2l\L are the work volume is into LxLxL Now if we move screws like in a lay in lay for the seed cutting you move this way and that way across you use a screw now the stock is L you want to go a distance L right from distant end to the other end then the overall length is also what similar to other, but there will be a motor here box and that position so may be one point 5 times then you will have multiply if use screws for this into 1.5xLx1.5Lx1.5 and it become overall space occupied whereas LxLxL is the now the next question that comes a piece Then you conduct the similar exercise for this what you called as spatial manipulator of the articulator then you conduct the similarities now remember when you stretched these two will line up and you will a length of a L1+L2 this is L1 and this L2 you will get that total length ,Then you fold it this comers somewhere here the L1=L2 this point will obviously come to the center then you conduct the similar it just to give you a feel of the workspace and relation to the overall system you can add a risk also once you had risk What will happen is there are many things you know the workspace is way you look at the workspace changes once you have the risk there So I have this robot okay, I have the mainly main body here then I have one more and then I have a added a risk here and put the gripper on the gripper or a end effective the correct ethnologies end effectors it tend to you the word the gripper now you when this poles and comes here then let lend let us say this is L1 and this L2 in this is L3 the distance from the center will depend on whether this fellow is in line these three are in line You can fold this back here you can stretched it out the outer edges workspace will be when all these three are stretched out When you bend this also you get or when you bend all of them together what are robot spaces and what is the relation have a look at it thus examine so these are things which we would like to do it on your own days of course the vertical axis though the whole thing is swapped all around oaky, that is what I was telling you yesterday when I talked out the workspace and you know the relative sizes of the system as a you relation to the oaky, so now having a spoken this let us go ahead with what are known as close chains these manipulators with close chains Are becoming quiet important in manufacturing particular what I call as what we call as flows change you had seen so far the open chains here is an example of the open chain

again spatial open chain we had also seen a example as planar open chain okay, now we will see what are known as closed chain I will began with the very simple what you called at planar open chain planar close chain the simplest you plain a close chain I can think of is the plainer 5bar I will call this I will name this I will name at A B C D E it is a five sided right a equilateral is four sided I will call pentagon because that is special five sided at the okay, I will call it 5bar then count 1,2,3,4 and the six link as a fixed then you can see there are revolute pairs I could have prismatic also but I have right were revolute here also revolute I will it 5-R Close chain 5-R the dash is not subtractive it is a 5-R close chain actually I should remove the dash and simply write it as 5R closed chain this what it is now the question is how,, many degrees of freedom does it have there are formula which will give you is there any other way of doing it when we ask them I have fixed this link AE is already fixed once I have fixed this link how many degrees of freedom thus it have you know try to draw the psychiatry figure So let us say you fixed this link okay if you want to draw a equilateral there are four lengths available to use then you draw it just given four lengths equilateral what else additionally information do you require you need one angle now it is a five sided ,five so what else additional. I just give you these lengths A B, I will give you, BC I will give you ,CD I will give you DE and I will give A now I ask you the question Drawing what additional information you require you need 2 angels unless you given 2 angels you cannot complete it. Okay so it is a 2 degrees freedom because these are given now is there a way of finding out what are the number of degrees of freedom given something like in theory of machine you have a procedure which is known as the GUBLER’S I hope I have got the spelling right yes, I am sorry there is no R here GUBLER’S is called the GUBLER’S okay Now those we who are mechanical engineers are familiar with this formula but I will simply touch upon it we need it even in the spatial GUBLER’S we need a similar formula, what the formula says that given a set of endings number of links Okay Jn number of revolute pair all is the plain I am writing the formula for the plainer taste revolute joints then Jp is the number of prismatic joint when you connect two links you were revolute pair or a revolute joints how many degrees of freedom does this link progressive respect to this one if I give this angle you know where this link so in a plain how many degrees of freedom are there we know that are three degrees of the freedom in a plain So if this is one plain and this is another plain okay, with respect to this as long as these two links are 3,3 degrees of freedom

let it to be know but the moment I have put this revolute pair you have lost 2 degrees of freedom lost from 3 available from 3 available in a plain where is when I put a revolute joints then logic applied to this prismatic joints also you lose 2 degrees of freedom from this point When I fixed this link something to another link how many degrees of freedom do I lose when I fixed it in relation to other one I fixed these two on I have paste them together grove them together how many degrees are freedom I have lost all three degrees of freedom relate so when I fixed two joints, when I fixed two links each other I lead to lose three degree of freedom when have preferred one link through a revolute joint I lose 2 degrees of freedom When I connect to links to a prismatic joint I again lose 3 degrees of plain so what we does is in any mechanism when there are n links You have a total of 3n availability but you usually fix up one link that is reference link so you end up with 3(n-1) and each revolute pair removes 2 degrees of freedom so I lose 2x Jr and ecah prismatic pair removes 2 degrees Jp . Let us apply to the fiber n links which we had drawn there are 1,2,3,4,5 links 1 is fixed so n=5 one of them is fixed remember that so that is taken care of by this -1 when there are 1,2,3.4.5 revolute pairs Jr =5so when I muliply3x5-1-2×5 I get 2 degrees That is a number of degrees of freedom you know the formula has given to degrees of freedom but you can also find the degrees of freedom by drawing one of the reason why I keep repeatedly telling you to draw it is gives you a feel you know, how many angles do I required to draw this picture that is a number because all the lengths are given remember that provided the lengths okay, this is a close pneumatic chain I could replace these revolute pairs all these year in this particular chain all are revolute pairs R I could also have one width prismatic joints I will show that thus for the sake of The number of links are the base link is one the same base link is there the guide is also a base link remember that part of the base link so that is number one this is 2, this is 3 ,this is 4 and the fifth link is just slider , slider is also fifth link there is a joint between 5 and 1 that is a prismatic joint there a joint between 5 and 4 that is a revolute joint so I have R here .But I have a P here so 1,2,3 and there is an R inside ,here between 4 and 5 there is an R within and 1 there is a P so here also number of links is 1. I am sorry 5 the number of revolute pairs is =4 the number of prismatic pair =1 this can be here also, I can replace this R with the P and I will get some other p So these are known as parallel manipulator and these are plainer one side so far okay, in anyone of the those links in this parallel manipulator one could mount the end of it, you know for a example let me go back to this particular picture and I could mount the end

effectors here on this main they are stiffer than this serial chain this serial chain tend to handle series of link in serial chain you have a series of link like this only one So when you apply of a force something tells you this can be stand be forces better than this right serial here the motors have to in case you have got 2 things parallel coming and holding on to the supporting the end effectors in this case two parallel parts to end effectors to the ground whereas there is an single path from the end effectors to the ground so this is tends to this thicker though the work volume of the parallel chains is not has much as that of the series Work volume available that is one of the problems you could of course have a serial if you have a two degree of freedom system you have then you orient the end effectors in any direction you will like when you have a 2 degree of freedom plainer system can you orient n effectors whichever way you like their plain we require three degrees of freedom system so should go for a 3 degree of freedom system close chain. I will draw 1, may not be best in the world 1, 2,3 4 ,5 and 6 so this is link 1,link 2, link 3,link 4 ,link 5 let us write the formula 3(n-1)-2Jr We do not have any prismatic so I will leave it here is the degrees of freedom formula n=6 how may revolute pais are there R1, 2,3,4,5 so Jr =6 I may right, check 3(6-1)-2×6 =3 this guy can oriented an object supposing I could may n effectors here not only position where you want but again remember the workspace here is count ably smaller than what you getting the serial chain it would be instructive if you could workout the workspace of the 5 plainer chain Which is try to work out by drawing the workspace how will know where the boundaries of the workspace R in the case of the fire where are the boundaries of the workspace just like you know in the case of a static an main body of a serial chain we could find the boundaries of the workspace then you find the boundaries of the workspace of this plainer chain the 5R at least tried for an 5 R also you know we had looked at this problem Or number of possible orientation for a given position then you look at that parallel I will just write here Chain 5-bar then we will find workspace boundaries right then 6-bar close chain okay remember that number of orientations either I should use the word range of orientation that is the more a proper word not number range of orientation for given position of end effectors will it change in the workspace these are question one have to admit to answer this is plainer case remember that I think these are the question once should admit answer as we goes to chain I would like you to try it out on your own and a feel of the workspace and other degrees when now it is not very difficult actually to workout use your compose pencil yeah, I assume the rangers of motion sometimes it

may lock up all link lengths assume the set of link lines assume the rangers of motions sometimes that is are reason why I am asking you to do the exercises you Chaney that you cannot go beyond a particular bond Depending on the toys your made use a compose and a ruler and do it okay, that is as per as the parallel plainer chain are concern we will have a look at the we had a seen the GUBLER’S formula for the plainer chain and messengers now let us just look at the direct and inverse kinematics use the feel of that okay Direct inverse I will give you a figure here also now direct kinematics of the 5-bar plainer chain ,5-bar planar close or parallel you know I can use both in the direct kinematics what we do we say the angels are given and you have to find the position of the end effector Let us try to draw it link, length are given that is assume so link length are given specified there is a correct word as should used angles are given find were the end effector is position of end effector I call it E not electric engineer End effector okay, so what you do, how to you go robot you first will draw the base link then you are given the 2 angle so you will draw this link and this link at this angle then other two link length are known how you will put your compose here draw one arc and put the compose here draw another arc and you will get two possible assemblies of the arc this is one assembly as assembly I am sorry I did draw this circle properly one circle will be I draw it again On another sheet so I am given the base I drawn the base, I have drawn the two cranks one is here the angle is to me this particular angle it is given if I draw the other crank the other angle is also given to you when I put my compose here on this revolute pair draw curve like this circle then I put my compass here take that corresponding link length draw another circle I get two intersection so I can assemble the 5-bar either this A or okay I called it 2 modes of assembly that is very important we can figure out can you fix from this mode of assembly to that during g motion that one of our concern will have to find out there is thick from this mode ,this is let us call this mode 1 to mode 2 during motion as you rotate these two input using may be not you figure it out, so these are 2 modes of us okay, now comes this is the direct kinematics So let us go the inverse kinematics quickly have a brief look what is it inverse kinematics the position of the end effector is given and you have to find the angles all the link lengths are given inverse Link lengths are specified okay and what else is specified the position of end effector

is position specified when I say position I used the word very loosely .I kill you what I am use both the position and oriented is given that is I should say more clearly the locational the end effector with the respective to the base of the 5-bar now you have to give it on so will it be you know in the case of potential we saw there are multiple solutions, multiple ways it could be right What would be similar here? Figure it out use a compass and a pencil and do it, and these are things if you do with a compass and a pencil it hardly takes any time to draw a figure of a picture and get a feel of what happens that is very important you cannot do it for a 3D the spatial manipulators it is very tuff to draw use a pencil and a compass and a ruler and figure out all these things but it base you know you are a bit enhances you are understanding if it do it weather I suggest to do it select your own link lengths you may do it for the 5-bar or you may do it for 6-bar specify draw it and then try to figure out what is going on what I will like it request you to do okay, now we have sees the plainer 5-bar close chain as well as 6-bar close chain if 5-bar close chain allows you to position the object 6-bar allows not only to position but also orient because it has 3 degrees substations let us go to the spatial one that is a ,let us just look at a spatial I will draw the spatial manipulator it is known as the STEWART PLATFORM so this has been used the Stewart platform I will stretched it here ,whatever I will draw essentially two platform consist of two what you called disks one at the top ,one at the bottom the disk at the top ,and there is a disk at the bottom these are connected together there are two disks then they are connected that together to some linear actuators I am showing the linear actuator here this could be out small screw they will by a motor embedded inside the actuator or it could be a hydraulic or pneumatic cylinder typically the hydraulic cylinder is used now is the leaner activator Two leaner activators this distance and coming out This is the cylinder to you notice this particular leaner activator is private to the bottom here. Okay this one and private to the top We will see what are the joiners here we are not conventional revenue this is something heals. I will come to that let me complete the picture first here is another activator and this follow is private here so some for form this is the activity. So you see two pars to the activator at the top more the distance ends are connected to a specific joint on the top this. At the bottom separately Okay this is the ball end to the serial jointer I call it here at the bottom what is known has serial join is here so you have writ down has four activator there are two more there are six activator in all This degrees freedom in this stage you will sensually need this axis. Okay these are the now there is one more here the joint is connected And is here, you got the picture now responsibility fine a top of the elicitor jell motor with the jell on is the end effecter that is the motor jell. Imagine it is a jell now the top pluck and jell and move with the respect to the bottom floor has these activator are completed There are six activator these six activator

has I said to connected with the bottom play the serial join the ball and short term. At the top they are connected to Hooke’s joint All of familiar with the Hooks joint to hooks joint is found of auto mobiles that we draw is. Okay the hooks joint is found in auto mobile you can draw that sketching that I will just beefing sketch in hooks joint. How many degrees of freedom ahookes joint you just think a in the automobile how many? Two or three are you sure, very sure he here the hooks joint let we put that paper on top and show you the hooks joint it is a very tiny one Okay now these rotation is possible also this part that’s all this is not possible is I just pay here otherwise this is not to rotate to not so how many degrees of freedom of rotation of this respect that Okay one rotate okay right and the presented. So let me show you the looks hooks whiled your sketching the manipulator I draw the hooks joint here now any other auto mobiles of start with hooks joint of ward axis. Okay it is a two degree of freedom here I want to picture the hooks joint Let us start let us you know across you know a have a cross and one side of cross the whole edge other side of the cross. There are four reveal of spares in a there has been shown I am sorry thorough there are it’s not four it will be called two axis. If you know the two axis in. This like a door you do not have a single keys you have one of the bottom and one of the middle and one in that top. Is still one reveal between door and the wall? So something like that there are in two revenue I think I guess four. So this is the Hooks joint so is space how many degrees of freedom does you have two how many degrees of freedom of there in space takes. So how many a removed by this Hooks joint four the spherical joint are how many degrees of freedom three okay he space there are six degree of freedom so the spherical joint revues three degrees of here. So using this knowledge and using the same equation of same will have to realize the regular equations. Shall we realized let us be will realized now how many degree n=no of joint; So you will write this let we just adjust the n= no of joints I am writing the we count the no of links equations. N= no of joint we will count that I am sorry no of links I am extremely sorry we count the no of links do not worry Js is the no of spherical joint alright what is other think were use the Hooks joint we call it Jh =no of hooks joint alright is it clear no of Hooks joint. So shall we write the formula now we are working in the space remember so we add 3 into n- has the first term of the degrees of freedom equation in explain Now how much should be have here six into

n-1 so you will write 6(n-1) the spherical joint remove three degrees of freedom so 3(0) and the Hooks joint is removes so it is 4(Jh number of okay now let us work out for the other edges is now what about the revenue joint how do that remove in space a revenue joint has five so mines into Jr -5 into J p there are depending of the joint degrees of freedom in space. Let us apply to the situate flat form let has go back to the situate flat form and applied here. How many links are there let is cow it is always better to leak numbers of the drawing with him let us what to play at the top place so I called is one I called it two Okay what else there is leak connecting the fisted to the top plait pistol and pistol and is only they are connected two Stewart spare to the cylinder right cylinder whatever is the mounting of the cylinder is another so we have one more leak here will call it three will call four. Fine, is it okay now can you give the number of links. Well there is six cylinder in the cylinder they the piston and the so that is the well plus the top plait and fourteen so n equal to fourteen I hope the formula works out otherwise you will be travel. So it will be six into the l= what about the apiculture joints there are six here at the movement so I call there what about the number of Hooks joint again six how can you have just because you can see let us say the window you know have connected this here I have a revalue joint here right have connected another here I have another revenge joint here do you how does it look say supposing this is I am sorry I could have one more here okay let us we drawing here There I got one link have connected one more link here and it can rotate to a revenue Okay then I have connected one more wear also one more that is the draw should be complete this okay These two were connected to the earth then one of you come has to save one more link I want to add here. So we connect one more here so there are three wings here 1, 2,3 And there is what appear to the single revolution actually there are two revolution one connecting the provide accommodating the relative motions will one and two here one revolution another accommodating the relative motion between 1:3 similarly here is situate platform the pistol rod of this he is accommodated connected to the top plat to into joint the other pistol rod is also connected. So there are six has there has I exacter we have counted all the joints are is there anymore joints here Fix the agnatic joint how you see where there the formula words it be does not and were all in trouble something is wrong then let we go back to the formula I have whole thing is here how many degrees of here prismatic is checks oh sorry is not a six. So how many degrees of freedom is communicate fourteen into six degrees of freedom okay. This flute platform is used in this for call aircraft simulators the word of the receptor stimulated that is spillers of a train all six cylinder are moved in certain passion under computer control and spilt get the feel of you know that the aircraft baking or diving or going a of course the activation I do not know were there you can really feel them

You know the aircraft really goes in a so many actuator in velocity in craft. So we cannot some extended cannot be here what the held the lead this is what you use for now a days it come become very important because by mounting grill you know you will have in your machine what you doing you have this third state form to sticking out like this with the driblet and it keep going distance this way that way that way drill whole ten several. Oriented this very step so many connections to the base from the portion link so this very simple and use the hydraulic you can use the balls. So you look all the electric to a planet Remain you to show you a picture of that emotion I forgot the file lecture today one of the lecture I will show you that in the morning The state platform emotions it became a very popular in machine tool originally conceived for aircraft then now there is a cringing making die all these things the tool may be carried on the stair platform or the job may be tool were is cringing for example some time the tool will be grinding wheel it spinning and the platform in tinkling like this. So that is what it known go slowed platform so we are team the steward platform the Hooks joint I hope I would have tower that wheel Okay now we has seen water known has serial manipulator water known has baler manipulator in the process were are look at ways of use of finding the degrees of freedom by counting the number of links and number joint you known the remember the degrees of freedom equation simply counting. We have to be very carefully out to number on the links do not forgot that fixed links you really know what will do particularly if the prismatic Paris on the spiking you simply tell to forgot about the link You do not count the slider to the typical mistakes student make for once he get hang of nothing with you got just what tell so we have now a sparkly good idea of various cynamatrics starters and some of the property were learn something about invest cynomatrics direct cynomatrics were seen the degrees of freedom some idea of industrial manipulator you have in your mind. The four we go to the advance of is. There is one more thing I want to prove I pose it a question to you robots is sitting here on the table It is plainer robot of you all this is one you have okay this is end effecter who subway in this objects sitting like this okay now remember how many degrees of freedom that is plainer robot has R three degrees of here Now find out the final position of orientation of the object thinking this one robot. Can I find can I use robot has a measuring devise can one use robot manipulator I use the word robot manipulator that is the more appropriate work. Do not call everything robot robotic aircraft robotic manipulator robotic chip that is better robot manipulator is robot manipulator has a measuring the design what I want to measure. The position and orientation of the equation answer them we a no or no opinion. I do not know which answer you want to know Yes what I do it I pick up the end of the effect robot and ring it and I do this I will match the end effectors with the objects I strictly to take end effecter and match it object. Object is perform the table like like that then what do you do next I know the links lines because when I give with the robot you give me the robot with the definitely plan these going to change there is link parameter

the word we used for use link lines see link parameters. They do not say robots anything any dimension of links excreta are even the angle between links you know I said the axis parallel The axis are per perpendicular an angle between one axis another it could be another a link parameters because the does not change in the emotions of the robots. Okay whatever changes the angles that change has we move the robot of the joint angle that change their known has motion parameter You slowly start using these words rather then in a prismatic joint is use then the leaner motion of the slider is the motion parameter motion parameter in link parameter he just come the terminal link so I can use robot has a measuring devise it is I am note the parameters and I can measure the motion parameters to part to the encoders or the potential meters here the one side you know the music .I can tell you were this particular objectives. It is very import thing because you stanching the head and felt figure out where the objectives you say I put camera and all that somebody come just put in case I lead the encoders and that the information I want Okay so now remember once your match this other multiple are only one once you brought physical robot is there is there is unit of a angle call are the multiple the physical robot has been brought here remember lead. The soling the equation the multiple solution when you brought the robot like that physically and musket with the outgoing your position that yourself so you handle are a unlike were solve the equations you will find it that is draw contract you all find. But when your work the physical robot sitting here you brings it we want to use it. So I can capture the information of all the objects on the table simple were using the robot has a mastering devise And I can say for this particular object is a where it is. I can write the twice a corner are I simply write this. Correct I could need not anything more I can say that after the measurement is complete I could write : X, Y, gamma is angle orientation if recall yesterday I use the word gamma okay has the angle of oriented remember with execs the gamma oriented. It is my definition you can define that way you want the positive exacter and gamma is there. So object one I tell this gamma X,Y, gamma or: You can write down ?1 how many anglers are there But these information has to be use along with the link parameters to arrive the this so object two I can use the same robot to figure out the were that is find the X,Y, gamma or again I can make the table like this for each object. No do not any suspected machine are anything just using the robot itself has measuring devise one can be we worry about the later why should I worry about that okay you worry about that shall we do it with the close joint okay a such nice question I can capture for the examination you know quizzer can we do this closing remember the physical robot is there do not drawing it you must keep it in mind. With a okay remember that you got the physical system you can build using the Lecco set like I did you know you can build it using cardboard you build that then you figure it down do that with the physical system not take a pen or pencil and all you can get the feel with the pen and pencil do it Because you have the robot in sitting in front of you infusions are known okay parallel manipulator Is the question you ask the good you could read out if I tell you everything I want to anything to ask you for the examp0le right so right of course sometime I am not know

the answer so I can getter the answer you answering okay this is one way of doing thing Now these are some terminology which we have to I will introduce the few more terminologies; Some of the terminology which will require has we go along there is a table on which the some objector sitting and the robots it also sitting on the same table. Again plain has just for the sake of understanding okay we called is the world has a robot. Now the robot is fix somewhere and is particular table okay so it somebody comes various robot fixed on the table I would like to tell you obtusely what would like here I given in this corner you go up by 20 centimeter and go like this right 10 centimeter to gather so reticular way of telling you inside what I will say I could format the system all that W. were w stand for the world yw at the corner of the table I tell you the orient of coordinate system are called Xw,Yw fixed this corner of the table bottom left of the corner in this coordinate system this point the base of the robot is that 10, or 5, 10. Centimeters Right then he ask me where is objects the robot which is the scale I measure were the objective correct and he know that of course add my sick my point off and televise just here okay that is no I can do then I tell you to bring a measuring tape and then measure all these things an can on. The robot of course based there is sample were find out where the robot based is using by a measure in looking at the drawing based on a robot can fixed in a table it can. But the object of transfer here and there that is solves to ever time run a round bring a measuring tape and find out they expect cornated the option. And still the angle is left out the oriented so you will say I bring the product or and measure the angle to get the oriented. That is few orientation so what you do you have the robot there use it has a measuring devise in table Correct just bring it of here and find out where the objectives. You can capture the X,Y and the oriented now that X,Y oriented if you capture You will end of the sincerely the world and here is the Xw, Yw Using the robot has a measuring devise you know in all polity you would capture that information in the x robot y robot for pick at to the robot they I am right. see you have this link this line this link line note you and these angles what you work out will essentially we did position of this object from disco ordinate from the base of the robot so it is world correlate is robot coordinate okay so you will has we go then I can sit the a coordinate same to the object also ,I will call it as a job then the implementation of the orientation of the object is a implementation of the x job axis with the robot axis I will paste the paper containing these two axis on the job so I have that I will test the paper on the base of the robot origin of the robot coordinate and this is the base coordinate system that we I think I should

use the word base rather than the robot because the base on the robot and the world is here see in a shop floor on the table when objects are kept and there is no robot there you want to install a robot you want to know where the objects are moving in all problems the worker will read drawings and say he will give you information in which coordinates the world or the he will give the ,he will say that these objects are going to be placed here Essen tally he is giving you on the table he is giving you information in the world coordinates system whereas the robot requires information in the robot coordinate system in order to approach top this all the equations I may right so you know should be a transformation to be a soul we tend to fit several coordinate system in order to does this exercise this is known as the terminology of the various coordinate system there is another coordinate system which is used ,what is known as the tool coordinate. I will just touch up on it as I end this lecture So here is the base of the robot I have got a base coordinate system here with base I would not use word robot I will call it x base y base remember this is touch base of the robot it does not turn a ring it there ,then what is known as the tool, coordinate system that is sub content to this gripper I will draw are gripper as plate y tool and I have my job sitting on the fugue I have fitted one coordinate system called the x job correct ,now obviously when I want the gripper I will show you these are the gripper finger As this is I shown know when I want the gripper to graph the job like this obviously the which coordinate should align with x job the x tool should align here or parallel to depending g how we are define and sometimes you know foe examples in this titanic you see in that movie the summary going down and there are two arm and whole summary is going it is though somewhere that robot there is to operate this lever, the lever is here and the hand is here okay Essentially what you want supposing you are sitting in the hand you will say if I goes straight ahead I can grass the lever oh you are expressing the motion in the tool, coordinate system your saying that since you sitting on the gripper you are sitting you imagine yourself to be dorgel to a tool coordinate system you will say if I go along this axis the x axis or y axis what about you are defining that the I will go and take it the information can be given to the robot from various coordinate when your cycling okay you are pedaling From the road when somebody says you have to take a right turn in which coordinate system the information given in your cycle as to turn orient 90 degrees turn to 890 degrees that is in your own tool, you are the tool go straight ahead if it is in a word coordinate system you are in a cycle or in a car or in a mobike you are travelling along your own In the world coordinate system the road is of course turn this is the world these are road branching into two direction in the world coordinate system there is some angle and all but supposing you are in a car it is moving in this direction in your own car for system in the tool coordinate system as I would call it your still moving straight ahead it is take a left and keep moving in the same direction That is how the information is fast so there

are several types of coordinate system the world you should world using keep this terminology In your mind as we go ahead in the more advance topics base, tool each as shown the tool is a particularly very useful when you want a object to be gripped and the gripper as approach the object this is a gripper approaching the object, the object is sitting here you have come close when you simply tell it move ahead means in the tool coordinate system along the particular axis keep going in that direction you will give that answer okay, I think with it I will close today’s lecture

## Recent Comments