Lecture – 5 Parallel Manipulators

Just another WordPress site

Lecture – 5 Parallel Manipulators

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

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