1 00:00:00,150 --> 00:00:09,540 OK, last time we have seen an example of getting the age parameters, assigning the age friend and 2 00:00:09,540 --> 00:00:10,830 getting the age parameters. 3 00:00:11,140 --> 00:00:20,400 And in this video, we will do one more example, which will also contain spherical Greece, which is 4 00:00:20,400 --> 00:00:21,450 interesting for us. 5 00:00:21,940 --> 00:00:29,630 OK, here, as you can see, I have summarized the the and the age parameter. 6 00:00:29,670 --> 00:00:31,740 What are the meaning of the age parameters? 7 00:00:31,950 --> 00:00:33,990 We have seen these in the last video. 8 00:00:34,230 --> 00:00:38,970 So I have written all of them here again, you know, for reference. 9 00:00:39,240 --> 00:00:45,930 And so key to the eight and I fossil be did for four parameters. 10 00:00:46,140 --> 00:00:47,760 Two of them rotation. 11 00:00:47,760 --> 00:00:56,220 So Theta and alpha and two of them translational parameters, which is the and a. 12 00:00:57,360 --> 00:01:06,300 So let's let me show you the whole robot to you, and you can see we will get the parameters for this 13 00:01:06,780 --> 00:01:07,800 robotic manipulator. 14 00:01:07,810 --> 00:01:11,910 So we will we will look forward kinematics for this robot manipulator. 15 00:01:12,300 --> 00:01:16,560 If you watch this robot manipulator, it consists of two parts. 16 00:01:16,590 --> 00:01:18,890 Okay, let me show you these two parts. 17 00:01:18,930 --> 00:01:21,510 The first one is this one. 18 00:01:21,540 --> 00:01:21,960 OK? 19 00:01:22,290 --> 00:01:25,680 This is called cylindrical robot. 20 00:01:26,010 --> 00:01:27,810 This is cylindrical robot manipulator. 21 00:01:28,110 --> 00:01:28,500 OK. 22 00:01:29,670 --> 00:01:38,240 So this part is only responsible for positioning the positioning in Cartesian space. 23 00:01:38,250 --> 00:01:41,910 OK, I presume space space. 24 00:01:42,240 --> 00:01:43,890 This is our end effector. 25 00:01:44,010 --> 00:01:51,120 OK, this is in the victor and the effector and this part. 26 00:01:51,540 --> 00:01:52,020 OK. 27 00:01:52,140 --> 00:01:58,710 This Part A is only responsible for positioning of the end effector. 28 00:01:58,710 --> 00:02:02,340 It doesn't affect the rotation, OK of the end effector. 29 00:02:02,340 --> 00:02:06,600 It's only used for positioning. 30 00:02:06,850 --> 00:02:14,040 OK, so but as you know, it's very it's not interesting for us. 31 00:02:14,040 --> 00:02:20,820 In order to be able to control only the position of the end effector, we want also to be able to control 32 00:02:20,820 --> 00:02:21,990 its rotation. 33 00:02:22,010 --> 00:02:24,990 Yeah, in three dimensions how we will do that. 34 00:02:25,380 --> 00:02:34,980 Indeed, if you've got your arm, you will see that the rotation part for your hand is due to the wrist. 35 00:02:35,040 --> 00:02:35,790 Your wrist. 36 00:02:35,790 --> 00:02:43,160 Yes, indeed, your wrist is a spherical wrist, and it consists of three rotational joints. 37 00:02:43,210 --> 00:02:46,410 Yeah, indeed we have seen before. 38 00:02:46,410 --> 00:02:54,260 During mentioning joints, we have said the spherical joint and this is nothing but a spherical wrist. 39 00:02:54,270 --> 00:02:57,400 OK, it's very cool breeze. 40 00:02:57,420 --> 00:03:07,320 And what we have said is that it consists of spherical joint spherical spherical joint, which was three 41 00:03:07,320 --> 00:03:13,350 degrees of freedom here because it provides three rotation in three Dimension X Y Z. 42 00:03:13,380 --> 00:03:22,440 So this part so this B part, which is spherical wrist, is only responsible for rotation, in part 43 00:03:22,440 --> 00:03:24,270 not positioning, but OK. 44 00:03:24,660 --> 00:03:33,750 So what we can do in any manipulator, you can attach spherical wrist in order to give dexterity to 45 00:03:33,750 --> 00:03:41,830 your robot's manipulators and effective so it can rotate OK in three degree of freedom over three axis. 46 00:03:41,850 --> 00:03:47,280 What we will do in order to calculate the age parameter, the H parameters on forward kinematics for 47 00:03:47,280 --> 00:03:54,990 this remote manipulator, we will first calculate we will separate these two parts A and B, OK. 48 00:03:55,230 --> 00:03:57,120 In order to make our job easier. 49 00:03:57,480 --> 00:04:01,430 What we will talk with VS will calculate the parameters for a part. 50 00:04:01,440 --> 00:04:04,140 Then we will calculate the age parameters. 51 00:04:06,640 --> 00:04:12,880 And then we will calculate the age parameters for the B part. 52 00:04:14,720 --> 00:04:24,430 It is OK for the B part after we will join these two together in order to obtain or obtain final homogeneous 53 00:04:24,430 --> 00:04:28,360 transformation matrix or so. 54 00:04:29,350 --> 00:04:33,670 Final forward kinematics for the whole robotic manipulator. 55 00:04:33,910 --> 00:04:35,860 Okay, so let's continue first. 56 00:04:35,860 --> 00:04:41,280 As you can see, we have taken the first part of the robot manipulator. 57 00:04:41,290 --> 00:04:43,800 This is the part a what we have said. 58 00:04:43,810 --> 00:04:44,810 Yeah, this is the part. 59 00:04:45,590 --> 00:04:48,190 So let's do. 60 00:04:49,000 --> 00:04:49,380 OK. 61 00:04:49,630 --> 00:04:57,430 As you can see, we have from here, we took out the spherical wrist and connected the victim directly 62 00:04:57,730 --> 00:04:59,670 to the robot manipulator. 63 00:04:59,680 --> 00:05:04,630 You can sing it like that in your wrist stuck, and it doesn't move. 64 00:05:05,350 --> 00:05:07,120 So it's something like this. 65 00:05:07,130 --> 00:05:09,970 Yeah, OK, so let's continue. 66 00:05:10,360 --> 00:05:13,300 Let's try to get the parameters. 67 00:05:13,420 --> 00:05:15,370 First of all, yeah, I forgot. 68 00:05:15,460 --> 00:05:21,530 First, we will just assign frames you important in the convention. 69 00:05:21,880 --> 00:05:25,170 Let's assume it was easy to assign. 70 00:05:25,180 --> 00:05:29,680 First, we assign a set axis as yes, this is for zero zero. 71 00:05:30,670 --> 00:05:31,660 How we would assign. 72 00:05:31,660 --> 00:05:35,560 Does it axis it axis has to be in the direction of motion. 73 00:05:35,560 --> 00:05:42,040 Yet as in our case, this joint is rotating in this way here in the rotation angle is teetering on. 74 00:05:42,110 --> 00:05:48,350 In this way we are doing the year. 75 00:05:48,370 --> 00:05:51,310 We are choosing our rotation axis in this way, OK? 76 00:05:51,820 --> 00:06:00,310 So in this case, the rotate, this is a prismatic joint, so its motion is in this way. 77 00:06:00,310 --> 00:06:03,820 So we will choose this, as is it one? 78 00:06:03,850 --> 00:06:04,330 Yes. 79 00:06:04,840 --> 00:06:11,170 And then the motion is like that, OK, we will rotate the two, OK? 80 00:06:11,790 --> 00:06:19,780 Then what we will do, we will talk, then we will choose that axis for this frame. 81 00:06:19,840 --> 00:06:21,210 OK, for this joint. 82 00:06:21,220 --> 00:06:26,380 OK, this is it to, in this case, all the extreme prismatic. 83 00:06:26,380 --> 00:06:32,800 So it will be something that these three and as we have said before, just could be the last one for 84 00:06:32,800 --> 00:06:33,820 the in the vector. 85 00:06:34,030 --> 00:06:35,830 This will be the three. 86 00:06:36,220 --> 00:06:36,610 Yes. 87 00:06:37,900 --> 00:06:41,320 OK, now let's assign x axis a smoking. 88 00:06:42,010 --> 00:06:47,530 Let's assign x axis in this way for this automatic manipulator, OK? 89 00:06:50,050 --> 00:06:58,960 And as we have said before, for the first run, we can assign in any way, we can also do this in this 90 00:06:58,960 --> 00:06:59,290 way. 91 00:06:59,500 --> 00:07:03,250 We can also do it in this way, but we have chosen it in this way. 92 00:07:03,700 --> 00:07:10,750 So out of the page and there you will see why, because it will make it our publication of parameters 93 00:07:10,750 --> 00:07:11,280 easier. 94 00:07:11,290 --> 00:07:12,010 You will see what. 95 00:07:12,430 --> 00:07:16,540 And now let's choose this one for the first frame. 96 00:07:16,780 --> 00:07:18,580 We can choose it in this way yet. 97 00:07:18,970 --> 00:07:22,840 What was the law for choosing the x axis? 98 00:07:23,470 --> 00:07:33,040 So this x one axis has to be perpendicular to the z zero axis and also has to be has intersected, OK? 99 00:07:33,310 --> 00:07:37,780 If we choose, as you can see x one in this way. 100 00:07:37,780 --> 00:07:47,410 So if it was x one in this race or endroit, it will surely be perpendicular to the Z zero and cut it 101 00:07:47,740 --> 00:07:48,640 so we can choose it. 102 00:07:48,640 --> 00:07:49,870 In this way, we can choose it. 103 00:07:49,870 --> 00:07:51,090 Also it in this way. 104 00:07:51,090 --> 00:07:54,990 Yeah, we can choose also it in inside the page. 105 00:07:55,060 --> 00:07:59,020 All of these cases, it will cut the z zero axis. 106 00:07:59,020 --> 00:08:07,600 But as we have said before, we always tried to do what we always tried to try to be as much similar. 107 00:08:07,610 --> 00:08:11,440 Um oh, sorry, yeah, we always tried to be. 108 00:08:12,730 --> 00:08:13,570 Um. 109 00:08:16,410 --> 00:08:20,790 Similar to the last previous frame. 110 00:08:20,970 --> 00:08:21,240 Yeah. 111 00:08:21,360 --> 00:08:27,670 So that's one of you will choose it in this way and will minimize the number of rotations. 112 00:08:27,690 --> 00:08:29,950 OK, so we will not choose it. 113 00:08:30,690 --> 00:08:32,920 Well, to the right or the left or inside the page. 114 00:08:33,510 --> 00:08:33,830 OK. 115 00:08:33,870 --> 00:08:38,010 In order to minimize the changes, we will choose it as exceeded. 116 00:08:38,370 --> 00:08:39,770 We can do the scene. 117 00:08:40,230 --> 00:08:47,460 OK, and one more thing for choosing the center, as we have said as at zero and that one is parallel 118 00:08:47,460 --> 00:08:48,210 to each other. 119 00:08:48,420 --> 00:08:54,870 We can choose the center for frame one or the Z one axis and in order to make it easier. 120 00:08:55,170 --> 00:08:59,430 And there is no meaning to put in offsets to put the center here. 121 00:08:59,610 --> 00:09:04,000 We will choose the center as the center of the joint, OK, the center of the frame as the center of 122 00:09:04,020 --> 00:09:05,940 joint for this one. 123 00:09:06,060 --> 00:09:06,960 And what will happen? 124 00:09:07,180 --> 00:09:08,280 What will be the center? 125 00:09:08,460 --> 00:09:13,770 As we have said, we have to first make it make for this axis longer. 126 00:09:13,770 --> 00:09:14,880 Is it one longer? 127 00:09:14,880 --> 00:09:16,620 And also this is it too. 128 00:09:16,620 --> 00:09:21,030 We have to continue and the intersection is the center. 129 00:09:21,030 --> 00:09:23,280 As you can see, the intersection is here, so. 130 00:09:23,920 --> 00:09:29,450 So so this will be the Frames center. 131 00:09:29,460 --> 00:09:38,910 OK, so we will choose again our X to it in this way because in order to minimize the number of minimize 132 00:09:38,910 --> 00:09:39,990 the changes, OK? 133 00:09:40,200 --> 00:09:45,370 And also X2 will be perpendicular and also cut or intersects with that one. 134 00:09:45,390 --> 00:09:45,780 OK. 135 00:09:46,770 --> 00:09:49,680 And we will copy the last one year. 136 00:09:49,830 --> 00:09:53,430 We will copy, as we have said, the previous frame for the end effector. 137 00:09:53,670 --> 00:09:54,660 And this will be. 138 00:09:55,500 --> 00:09:57,300 This will be our X three. 139 00:09:57,450 --> 00:09:57,870 OK. 140 00:09:57,960 --> 00:10:02,470 As you can see, we have finished assigning axis. 141 00:10:02,550 --> 00:10:08,190 I will not do y axis because, as you know, it will make only complex the drawing and also even not 142 00:10:08,190 --> 00:10:08,580 use it. 143 00:10:08,850 --> 00:10:12,990 But a year after assigning X and Z, it's very easy to assign y axis. 144 00:10:13,200 --> 00:10:16,050 You can just need to follow right hand rule. 145 00:10:16,350 --> 00:10:16,860 OK. 146 00:10:17,610 --> 00:10:26,490 So let's continue now to calculate T dot title parameter in what was the T done T towards. 147 00:10:26,700 --> 00:10:34,170 Let's remember it was rotation around zip ie minus won't be careful to match x i minus one and X I. 148 00:10:34,470 --> 00:10:38,510 So for the first joint, OK, if I equals to one. 149 00:10:38,520 --> 00:10:43,500 And so this for the second drawing, but for the frame, for the frame one. 150 00:10:43,680 --> 00:10:49,830 So how much we have to rotate both the left and put the rotation angles I have forgotten this year, 151 00:10:49,830 --> 00:10:52,800 we have put it in this way this is these three. 152 00:10:53,310 --> 00:10:54,310 Oh, OK, we have done. 153 00:10:54,720 --> 00:10:57,630 Yeah, we have put it the rotation and there's no need to do that. 154 00:10:57,660 --> 00:10:57,990 OK. 155 00:10:58,350 --> 00:11:06,240 So so how much we have to rotate frame is zero with respect to z zero. 156 00:11:06,390 --> 00:11:06,840 Yes. 157 00:11:07,140 --> 00:11:16,140 In order to match x one and x zero at the first time, you can see they are parallel to each other. 158 00:11:16,140 --> 00:11:22,470 So you can say that we don't need to anything because they are parallel and x one and it's zero parallel 159 00:11:22,470 --> 00:11:23,070 to each other. 160 00:11:23,070 --> 00:11:26,010 We don't need to do any rotation, but it's not correct. 161 00:11:26,220 --> 00:11:32,010 Yeah, as we have said before, you have to and you have to consider the angle. 162 00:11:32,280 --> 00:11:40,740 And if you watch from talk to the robot, if this is the first joint, OK, and this is OK, this will 163 00:11:40,740 --> 00:11:42,880 be our X0. 164 00:11:42,900 --> 00:11:44,700 Let's throw it at our X0. 165 00:11:44,730 --> 00:11:48,480 In this way, and this is our digits zero. 166 00:11:48,510 --> 00:11:50,340 Yes, this is our digits zero. 167 00:11:50,700 --> 00:11:54,330 And what will be the first frame first frames? 168 00:11:54,330 --> 00:12:01,260 It will be the same again because as the first joined, the rotation is about the Zetec says it will 169 00:12:01,260 --> 00:12:01,770 not change. 170 00:12:02,070 --> 00:12:09,270 It will be that one, but X1 will be change and it will change in this direction as the rotation is 171 00:12:09,270 --> 00:12:10,320 like that here. 172 00:12:10,920 --> 00:12:15,810 As the rotation is in this way, the X1 will become like that. 173 00:12:15,810 --> 00:12:20,430 As you can see, the difference between them is nothing but theta one. 174 00:12:20,790 --> 00:12:29,820 So we have to make T to one of rotation in order to match x zero and x one. 175 00:12:29,820 --> 00:12:31,680 So let me write Theta one here. 176 00:12:32,190 --> 00:12:40,770 So what about Frame two or how much we have to rotate frame one with respect to Z volume in order to 177 00:12:40,770 --> 00:12:45,150 match X two and X1 as joint two is prismatic? 178 00:12:45,360 --> 00:12:47,520 It will not provide any rotation. 179 00:12:47,730 --> 00:12:55,720 So X2 and X1 will be always parallel to each other, so we don't have to do any rotation yet. 180 00:12:55,740 --> 00:12:58,250 This will be zero two. 181 00:12:58,510 --> 00:13:04,950 So they are on the same plane and as they will not, they never leave the same plane. 182 00:13:05,010 --> 00:13:08,830 You will never leave this plane because the joint is prismatic. 183 00:13:08,850 --> 00:13:09,300 It's not. 184 00:13:09,450 --> 00:13:11,070 It doesn't provide rotation. 185 00:13:12,660 --> 00:13:15,110 They will be always parallel to each other. 186 00:13:15,300 --> 00:13:21,450 OK, now let's come for the last one in the last one, also it's prismatic joints, so how much we have 187 00:13:21,450 --> 00:13:27,910 to rotate frame to with respect to the two in order to match X to X three? 188 00:13:27,990 --> 00:13:33,450 We don't have to do anything because it is the prismatic joint, so they will be always parallel to 189 00:13:33,450 --> 00:13:34,260 each other. 190 00:13:34,500 --> 00:13:35,640 We have finished with data. 191 00:13:36,000 --> 00:13:44,310 OK, let's continue with the what was Dee Dee was translations through that I'm on this one to merge 192 00:13:44,310 --> 00:13:50,860 origins of origins of sequential or subsequent frames. 193 00:13:50,880 --> 00:13:51,210 OK. 194 00:13:51,770 --> 00:13:54,220 Um, let's do that. 195 00:13:54,270 --> 00:13:54,700 Okay. 196 00:13:54,720 --> 00:13:57,180 How much we have to move. 197 00:13:57,210 --> 00:13:59,130 Origin of frames zero. 198 00:13:59,520 --> 00:14:00,120 OK. 199 00:14:00,450 --> 00:14:03,750 In the direction of z zero. 200 00:14:03,780 --> 00:14:04,230 Yes. 201 00:14:04,290 --> 00:14:08,580 Or the direction of Z zero is upward in the direction of Z zero. 202 00:14:08,790 --> 00:14:12,660 In order to match it with all this origin, how much we have to do. 203 00:14:12,660 --> 00:14:16,880 As you can see, the offset is once, so we need to do it. 204 00:14:16,890 --> 00:14:17,670 And one. 205 00:14:17,880 --> 00:14:19,530 Yes, it was easy. 206 00:14:19,770 --> 00:14:22,260 So this split me. 207 00:14:22,890 --> 00:14:23,220 Oops. 208 00:14:23,800 --> 00:14:24,210 One. 209 00:14:24,240 --> 00:14:24,990 OK. 210 00:14:25,230 --> 00:14:27,600 Let me clear this one, this one. 211 00:14:28,410 --> 00:14:36,240 So for this, uh, second frame, how much we have to move the frame? 212 00:14:36,330 --> 00:14:43,380 OK, this frame so frame one in the direction of Z one, which is also upward in order to match it with 213 00:14:43,380 --> 00:14:45,210 the origin or frame two. 214 00:14:45,450 --> 00:14:49,950 As you can see, this is nothing but L to the offset is able. 215 00:14:50,820 --> 00:14:51,210 OK. 216 00:14:51,280 --> 00:14:57,030 People write it here L two and I want to remind I want to say one thing not once into you. 217 00:14:57,030 --> 00:15:03,450 As you can see, L2 is not only the length of the robot manipulator, for example. 218 00:15:03,450 --> 00:15:10,040 Here L1 is constant because this is a rotary joint, but in L2, you have to consider also the two. 219 00:15:10,050 --> 00:15:14,770 Yeah, because they're the prismatic joint moves upward and downward. 220 00:15:14,790 --> 00:15:16,770 And there is a link connected to it. 221 00:15:17,070 --> 00:15:22,690 The links of the link and these together, which is the two, is coincided at L2. 222 00:15:22,710 --> 00:15:26,380 Yes, OK, I am writing you by considering both of them. 223 00:15:26,400 --> 00:15:26,790 OK. 224 00:15:27,120 --> 00:15:34,890 So while in the first joint, I mean, in the rotary joint L1 is constant in a prismatic joint, L2 225 00:15:34,890 --> 00:15:38,380 is not constant because of the two changes yet. 226 00:15:39,510 --> 00:15:47,160 So no, let's go for the last one, for the last one, as we have said, how much we have to move the 227 00:15:47,160 --> 00:15:55,850 the frame to in the direction of the two, which is in this direction in order to match two with origin 228 00:15:55,860 --> 00:15:56,760 to the origin. 229 00:15:57,030 --> 00:15:57,450 Three. 230 00:15:57,720 --> 00:16:05,070 And as you can see, this is nothing but L3 again in L3 considers the three prismatic joint movement. 231 00:16:05,160 --> 00:16:05,430 Yeah. 232 00:16:05,880 --> 00:16:07,030 Okay, perfect. 233 00:16:07,590 --> 00:16:12,300 Now, as we have done this one also, we have finished with D. 234 00:16:12,300 --> 00:16:15,120 Also, let's go to parameter eight now. 235 00:16:15,660 --> 00:16:22,370 How we will do parameter h parameter h was translation through X arm to match the origins. 236 00:16:22,380 --> 00:16:22,660 Yeah. 237 00:16:23,610 --> 00:16:30,510 So let's go for the frame one how much we have to move the original frame. 238 00:16:30,540 --> 00:16:31,440 Zero. 239 00:16:31,710 --> 00:16:32,160 Yes. 240 00:16:32,520 --> 00:16:37,830 In the direction of X one, the direction of X one is in this way, yes. 241 00:16:38,130 --> 00:16:45,650 In order to get that, in order to match the origins of frame zero and frame by frame zero and frame 242 00:16:45,660 --> 00:16:50,620 one, as you can see, we don't have to do anything in this direction yet. 243 00:16:50,640 --> 00:16:52,800 We don't have to move them in this direction. 244 00:16:52,800 --> 00:16:58,020 We have to move them in this direction, but not in this direction because there is no movement in this 245 00:16:58,020 --> 00:16:58,530 direction. 246 00:16:58,530 --> 00:17:00,390 There is no offset in this direction. 247 00:17:00,660 --> 00:17:07,890 They are, um, they don't need to be displaced in direction of x one. 248 00:17:08,160 --> 00:17:10,140 So we it is zero. 249 00:17:10,530 --> 00:17:10,950 Yes. 250 00:17:12,420 --> 00:17:16,140 And let's two for water. 251 00:17:16,140 --> 00:17:19,080 For, um, yeah. 252 00:17:19,080 --> 00:17:22,470 Uh, for the second joint or the second frame. 253 00:17:22,470 --> 00:17:28,350 Look at how much we have to move frame one in the direction of x one. 254 00:17:29,280 --> 00:17:38,580 Excuse me, X2, which is again in this direction in order to match the original frame to frame one 255 00:17:38,580 --> 00:17:40,080 with original frame two. 256 00:17:40,470 --> 00:17:45,600 As you can see again, we don't have to do anything because there is no offset in this direction between 257 00:17:45,600 --> 00:17:46,260 these two. 258 00:17:46,440 --> 00:17:47,910 Origins of these two frames. 259 00:17:48,180 --> 00:17:49,650 And this is also zero. 260 00:17:49,950 --> 00:17:59,430 And for the last one, as you can see how much we have to move frame in the second frame origin in the 261 00:17:59,430 --> 00:18:06,480 ex-city direction, which is again in this phase of of the page OK x direction in order to match the 262 00:18:06,480 --> 00:18:09,180 origin of frame to with original frame three. 263 00:18:09,180 --> 00:18:13,540 And as you can see again, there is no offset between them. 264 00:18:13,560 --> 00:18:14,040 OK. 265 00:18:14,280 --> 00:18:14,610 There is. 266 00:18:14,670 --> 00:18:21,870 Offset in the $2 addiction, but there is no offset in X to, excuse me, x direction, OK? 267 00:18:22,770 --> 00:18:31,120 So it will be also zero and the last parameter for IFR rotation around excitement is it ie minus one? 268 00:18:31,150 --> 00:18:32,190 And is it all right? 269 00:18:32,490 --> 00:18:33,930 So let's do this one. 270 00:18:33,930 --> 00:18:41,940 Also, when you have to be careful a bit with the rotation parameters because you need to take the joint 271 00:18:41,940 --> 00:18:45,600 rotations, yes, you have to visualize in 3D. 272 00:18:46,050 --> 00:18:49,980 So OK, that's in a fast way to this one. 273 00:18:49,980 --> 00:19:01,830 Also, so how much we have to rotate frame zero frame zero years frame zero over which axis over x one 274 00:19:01,830 --> 00:19:02,670 axis yes. 275 00:19:03,060 --> 00:19:09,210 X one axis um, in order to match z one zero zero. 276 00:19:09,420 --> 00:19:15,510 As you can see, there is no need to match because it one two zero zero because they already match even 277 00:19:15,720 --> 00:19:19,830 the robot rotates to two degrees in this way. 278 00:19:19,830 --> 00:19:22,320 Yeah, this is, excuse me, two to one degrees. 279 00:19:22,320 --> 00:19:28,370 In this way, they will always get one and the two will always match with each other, OK? 280 00:19:29,250 --> 00:19:32,890 The X, the x one and x zero will be different. 281 00:19:32,910 --> 00:19:38,790 Excuse me, this is not is that this is a zero four x one and X0. 282 00:19:38,790 --> 00:19:45,330 As we have said before, there will be um, there will be offset between them. 283 00:19:45,330 --> 00:19:51,180 OK, there will be a difference between them, but there will not be anything different between that 284 00:19:51,180 --> 00:19:51,390 one. 285 00:19:51,390 --> 00:19:54,390 And it's, you know, they will always be parallel to each other. 286 00:19:54,390 --> 00:20:01,350 So and it will be the first and there will be nothing but zero. 287 00:20:01,800 --> 00:20:09,660 So what what about the second frame in terms of second frame, how much we have to rotate frame one 288 00:20:09,930 --> 00:20:19,800 in the direction or so through also now through the X two OK x two axis in order to match that one? 289 00:20:19,800 --> 00:20:26,310 And is it two OK, OK, as you as you can see, we are rotating in x two direction. 290 00:20:26,310 --> 00:20:26,640 Yes. 291 00:20:26,910 --> 00:20:31,800 And so in the external direction, the rotation angle is positive. 292 00:20:31,800 --> 00:20:32,370 In this way. 293 00:20:32,370 --> 00:20:38,280 If you put your finger in extra direction the same before extra direction and curl your fingers, the 294 00:20:38,280 --> 00:20:40,860 rotation positive rotation is this way. 295 00:20:41,310 --> 00:20:50,210 So however, in order to match it one with the two, we have to rotate frame one in this direction. 296 00:20:50,220 --> 00:20:54,780 Yes, along x x tour in order to match is that one and the two? 297 00:20:55,020 --> 00:21:00,140 This is 90 degrees because the difference between that one and the two is 90 degrees. 298 00:21:00,160 --> 00:21:07,050 But however, it is opposite to the positive direction, so it will be minus PI over two. 299 00:21:07,480 --> 00:21:08,000 OK. 300 00:21:10,350 --> 00:21:10,690 Okay, 301 00:21:13,620 --> 00:21:17,520 so let's see what will happen for the last joint. 302 00:21:17,820 --> 00:21:18,750 OK, last frame. 303 00:21:19,080 --> 00:21:22,110 So as you can see, there is nothing to do here. 304 00:21:22,110 --> 00:21:23,390 Because why? 305 00:21:23,400 --> 00:21:31,520 Because the frame we don't have to rotate frame two in x three axis in order to merge the two ends its 306 00:21:31,520 --> 00:21:34,830 three because they all already match with each other. 307 00:21:34,830 --> 00:21:42,900 And as the Z two, excuse me, the joint two of the three assert joint is nothing but prismatic joint. 308 00:21:42,900 --> 00:21:49,350 It will not provide the rotation, so the Z two and the the three will always be parallel to each other, 309 00:21:49,350 --> 00:21:51,570 so we don't have to do any rotation. 310 00:21:52,080 --> 00:22:00,270 As you can see, we have obtained each parameter table for this cylindrical part, OK, for part, and 311 00:22:00,660 --> 00:22:09,600 from here, what we can do from this is using these parameters, I can find this edge one zero. 312 00:22:09,960 --> 00:22:15,390 Yes, I can find H2 one from here and I can find it three two from here. 313 00:22:15,750 --> 00:22:23,970 So how can I find the h, uh, uh, zero and three? 314 00:22:24,210 --> 00:22:29,880 So the relation between this frame, the base frame and the end of the frame, how can I do that? 315 00:22:30,180 --> 00:22:37,320 I can do that by multiplying each one zero by age two one and this by age three two. 316 00:22:37,470 --> 00:22:40,350 Okay, this will give us age zero three. 317 00:22:40,650 --> 00:22:41,370 That's perfect. 318 00:22:41,770 --> 00:22:47,010 Let's go with the second part, which was cylindrical arm, a wrist, OK? 319 00:22:47,250 --> 00:22:54,240 And as we have seen, the cylindrical wrist is nothing but the combination of steering a joint rotational 320 00:22:54,240 --> 00:22:54,730 joints. 321 00:22:54,750 --> 00:22:58,990 OK, now let's try to find the 322 00:23:02,130 --> 00:23:04,080 the parameters for this also. 323 00:23:05,550 --> 00:23:07,360 Okay, first, let's assign frames. 324 00:23:07,380 --> 00:23:07,700 OK. 325 00:23:08,100 --> 00:23:10,890 We will try to assign the frame for it. 326 00:23:11,340 --> 00:23:13,280 OK, let's do how we can. 327 00:23:13,560 --> 00:23:14,490 First, we will choose. 328 00:23:14,570 --> 00:23:19,600 Again, does it access this and as we have said, that exercise will be in which direction that access 329 00:23:19,600 --> 00:23:21,930 is will be in the direction of motion, OK? 330 00:23:22,380 --> 00:23:26,330 And also for in this case, then it will be in this way. 331 00:23:26,350 --> 00:23:28,680 This will be that one and four. 332 00:23:28,680 --> 00:23:31,950 In this case, this will be what is it? 333 00:23:33,210 --> 00:23:34,020 Excuse me. 334 00:23:34,080 --> 00:23:40,770 Let me start from before we start from not one, but instead it will be three. 335 00:23:40,890 --> 00:23:41,300 Why? 336 00:23:41,560 --> 00:23:43,050 Because anyway, this will. 337 00:23:43,410 --> 00:23:50,370 This reset will be connected to the end effector saw these two friends will coincide with each other. 338 00:23:50,430 --> 00:23:55,640 As you can see, this third frame instead of this third frame, there will be this frame. 339 00:23:55,650 --> 00:23:57,080 So we are right. 340 00:23:57,090 --> 00:23:58,470 And is it three two here? 341 00:23:58,470 --> 00:24:03,830 Is it four to here, Z five two here and the copy of the last one? 342 00:24:03,840 --> 00:24:05,610 It will be that six here. 343 00:24:06,060 --> 00:24:06,570 Perfect. 344 00:24:06,960 --> 00:24:08,910 Now there's an interesting scene here. 345 00:24:09,780 --> 00:24:17,370 As you know in, though, it is interesting seeing is that choosing the origin for the frames if the 346 00:24:17,790 --> 00:24:21,250 we can choose the first frames origin as we want. 347 00:24:21,270 --> 00:24:21,720 OK. 348 00:24:22,320 --> 00:24:24,060 We have said this one arbitrarily. 349 00:24:24,060 --> 00:24:24,810 We you can choose. 350 00:24:24,930 --> 00:24:26,120 OK, let's keep it. 351 00:24:26,310 --> 00:24:29,340 Then this joint destroying this frame like that. 352 00:24:29,350 --> 00:24:31,500 OK, for now, we will not touch it. 353 00:24:31,500 --> 00:24:36,100 But what will happen for this joint, this frame? 354 00:24:36,100 --> 00:24:36,420 OK. 355 00:24:37,020 --> 00:24:43,200 In order to find its center, we have to make this in this way and we have to make this in this way 356 00:24:43,200 --> 00:24:45,960 and its intersection will be the center, OK? 357 00:24:46,380 --> 00:24:48,570 As you can see, this is the same to the point. 358 00:24:48,570 --> 00:24:49,320 So. 359 00:24:53,500 --> 00:24:58,900 Okay, let me make this again back, go back, think OK in this way. 360 00:24:59,110 --> 00:25:02,650 So the center will be for the fourth free will be here. 361 00:25:02,890 --> 00:25:06,520 Let's check for the fifth frame how we will find for the fifth frame. 362 00:25:07,300 --> 00:25:13,550 We will again let me do it in this way so that the data will be easy. 363 00:25:13,570 --> 00:25:16,000 We will make it longer like that. 364 00:25:16,330 --> 00:25:18,100 We will also make it longer life. 365 00:25:18,100 --> 00:25:20,590 That intersection point is again here. 366 00:25:21,070 --> 00:25:27,560 So we have to bring this frame from here. 367 00:25:27,580 --> 00:25:33,770 We have to take frames from here, OK, and bring it to back to here. 368 00:25:33,790 --> 00:25:36,550 Yes, because its center will be here. 369 00:25:37,240 --> 00:25:40,180 No, I think it's much clearer to you how we find the same. 370 00:25:40,520 --> 00:25:45,340 OK, so what about the Z6 in order to find the center of Z six? 371 00:25:45,580 --> 00:25:47,110 Let's take it also. 372 00:25:47,130 --> 00:25:48,760 Let's make it longer. 373 00:25:49,120 --> 00:25:52,130 And as you can see, it doesn't intersect with Z five. 374 00:25:52,150 --> 00:25:53,130 It's parallel to that. 375 00:25:53,140 --> 00:26:02,140 Five So we can choose as it seeks alongside the frame of the original frame frame six alongside the 376 00:26:02,170 --> 00:26:08,710 is it six OK like distortion in any point and in order to make our job easier, as we have said before, 377 00:26:08,710 --> 00:26:10,750 we will choose it to stay here. 378 00:26:11,560 --> 00:26:12,010 OK. 379 00:26:13,400 --> 00:26:18,070 However, in order to make the calculation of the H parameters much more easier. 380 00:26:18,280 --> 00:26:22,060 What we will do, we will take this frame. 381 00:26:22,080 --> 00:26:25,640 OK, the first frame, the short frame, I mean, OK. 382 00:26:26,260 --> 00:26:30,510 And we will, as we have said, we can assign it center arbitrarily. 383 00:26:30,510 --> 00:26:33,670 It will take it and we will put it also here. 384 00:26:33,880 --> 00:26:34,300 Yes. 385 00:26:35,020 --> 00:26:37,300 This will be also in this way. 386 00:26:37,330 --> 00:26:40,150 This will be the Z three. 387 00:26:40,990 --> 00:26:41,400 OK. 388 00:26:41,650 --> 00:26:47,050 As you can see, this is now how we assign the D.H parameters. 389 00:26:47,590 --> 00:26:53,460 OK, now let's calculate, excuse me, how we assign the frames. 390 00:26:53,470 --> 00:26:57,770 Now that's calculated the Oh, I have forgotten the x axis. 391 00:26:57,790 --> 00:26:59,880 Now that's the x axis. 392 00:27:00,160 --> 00:27:00,670 OK. 393 00:27:01,660 --> 00:27:11,020 So as we have said, and let's assign, does it exist for the, um, third frame because it is the first 394 00:27:11,020 --> 00:27:13,690 one and we can assign it arbitrarily. 395 00:27:13,690 --> 00:27:16,570 As we have said earlier, this is x three. 396 00:27:16,870 --> 00:27:19,750 Let me go that this one, I will put it here. 397 00:27:23,830 --> 00:27:25,120 OK, this is our thought. 398 00:27:25,720 --> 00:27:28,270 Look at yeah, for itself. 399 00:27:28,270 --> 00:27:30,520 Or indeed, yes, it's in the therefore. 400 00:27:30,520 --> 00:27:30,820 Yes. 401 00:27:31,120 --> 00:27:31,500 OK. 402 00:27:31,720 --> 00:27:34,100 So this is extreme. 403 00:27:34,120 --> 00:27:36,700 OK, what will happen with X four? 404 00:27:36,700 --> 00:27:44,800 Then X four has to be in such a direction that it will intersect X3. 405 00:27:45,010 --> 00:27:45,430 OK. 406 00:27:45,670 --> 00:27:49,600 So we can g we can use this direction. 407 00:27:49,600 --> 00:27:55,630 We can put it also in the direction of X three in order to minimize the changes. 408 00:27:55,810 --> 00:27:58,780 So a calculation of the H parameters will be easier for us. 409 00:27:59,110 --> 00:28:07,170 And as you can see, X four will intersect z three axis and OK, which we which is required for the 410 00:28:07,180 --> 00:28:10,200 H parameter assigning frame assignment. 411 00:28:10,240 --> 00:28:10,630 OK. 412 00:28:10,960 --> 00:28:12,760 And we can do the same. 413 00:28:13,060 --> 00:28:21,670 Indeed, we can choose the same direction for X x five also y because x five have to, it has to intersect. 414 00:28:21,670 --> 00:28:23,200 Z four OK. 415 00:28:23,500 --> 00:28:28,890 And if we choose it, it as a as part of the page in this way. 416 00:28:28,900 --> 00:28:33,700 Yeah, the same way as you can see, if you make it longer, it will cut again. 417 00:28:33,700 --> 00:28:41,470 Is it for Intersect at Fort, which is required for the frame assignment and we can copy the last frame 418 00:28:41,470 --> 00:28:44,210 for them, as we have said. 419 00:28:44,230 --> 00:28:49,240 And so if we have a, we can copy X five to here in order to get X six. 420 00:28:49,660 --> 00:28:54,730 OK, now we have frames assigned, we can easily calculate the H parameters. 421 00:28:54,760 --> 00:28:57,550 OK, let's calculated the H parameters. 422 00:28:57,550 --> 00:28:59,050 Let's start with to. 423 00:28:59,920 --> 00:29:05,560 So Peter, was this one how much we have to rotate frame? 424 00:29:05,680 --> 00:29:06,620 Three. 425 00:29:06,640 --> 00:29:07,790 Yes frames. 426 00:29:07,790 --> 00:29:07,990 Three. 427 00:29:07,990 --> 00:29:10,090 How much we have to rotate frame three. 428 00:29:10,480 --> 00:29:20,740 In our view, in so and through Z, the three, how much is through that? 429 00:29:20,740 --> 00:29:21,250 Three. 430 00:29:21,400 --> 00:29:26,560 In order to make X three and x four to match each other. 431 00:29:26,740 --> 00:29:30,340 So we want to match X three and four with each other. 432 00:29:30,550 --> 00:29:30,970 Yes. 433 00:29:31,480 --> 00:29:37,220 And we have to do a rotation in which along which direction is it? 434 00:29:37,220 --> 00:29:37,540 Three. 435 00:29:37,570 --> 00:29:37,870 Yes. 436 00:29:39,170 --> 00:29:40,600 So let's see. 437 00:29:42,340 --> 00:29:48,730 Um, the first time x three and X forward seems that they are match with each other. 438 00:29:48,730 --> 00:29:52,360 Yes, they seems that they are matching with each other, however. 439 00:29:52,790 --> 00:30:00,500 You have to take into account which rotation the angle of the again, you have to take the angles into 440 00:30:00,500 --> 00:30:01,430 consideration. 441 00:30:02,150 --> 00:30:05,300 So four x three let me at right angles. 442 00:30:05,300 --> 00:30:07,980 Also, I forgot to put them x three. 443 00:30:08,600 --> 00:30:12,920 The positive rotation will be in this way for this one. 444 00:30:13,400 --> 00:30:15,840 This will be five this one. 445 00:30:15,860 --> 00:30:17,800 This will be three to six. 446 00:30:17,810 --> 00:30:18,200 Yes. 447 00:30:18,800 --> 00:30:19,880 This will be Theta six. 448 00:30:20,870 --> 00:30:21,320 Perfect. 449 00:30:22,670 --> 00:30:23,060 No. 450 00:30:23,780 --> 00:30:28,940 So how much we have to rotate is so are if there is a full rotation. 451 00:30:28,950 --> 00:30:29,360 Yes. 452 00:30:31,910 --> 00:30:34,280 Oh my gosh, what would I have done? 453 00:30:34,760 --> 00:30:37,000 Put it for the x axis. 454 00:30:37,310 --> 00:30:38,030 I'm sorry. 455 00:30:38,510 --> 00:30:39,680 I forgot. 456 00:30:40,190 --> 00:30:42,820 Okay, they they should be x axis. 457 00:30:43,190 --> 00:30:45,730 Yeah, that was stupid mistake. 458 00:30:45,760 --> 00:30:47,540 So for us, it's three. 459 00:30:47,720 --> 00:30:49,730 It will be in this way. 460 00:30:49,730 --> 00:30:53,780 So the positive rotation is in this way three to four for Z. 461 00:30:53,780 --> 00:31:01,850 For the positive direction will be in this way T to five and for Z five, the positive direction will 462 00:31:01,850 --> 00:31:02,850 be again in this way. 463 00:31:02,850 --> 00:31:04,580 If this is Theta six. 464 00:31:04,580 --> 00:31:05,310 Yeah, perfect. 465 00:31:05,330 --> 00:31:05,690 No. 466 00:31:06,710 --> 00:31:14,720 If the if the first joint will rotate, if you watch from for direction, you will see that, um, it 467 00:31:14,720 --> 00:31:17,150 will be in this way and this will be. 468 00:31:18,260 --> 00:31:25,700 So we try to match X three and explored the there will be a rotation between X three and X4 because 469 00:31:25,970 --> 00:31:28,310 X three will come like that. 470 00:31:29,210 --> 00:31:34,910 Excuse me, x four will become a will become like that and X3 will be in this way. 471 00:31:34,910 --> 00:31:35,330 Yes. 472 00:31:35,720 --> 00:31:42,800 And in order to match these together, in order to merge this together, we need, as you can see, 473 00:31:42,800 --> 00:31:44,040 two to four angle. 474 00:31:44,090 --> 00:31:44,630 OK. 475 00:31:45,140 --> 00:31:46,520 We need data for angle. 476 00:31:47,420 --> 00:31:49,480 However, we have. 477 00:31:49,990 --> 00:31:59,360 So our first key to this will be data for so we need in data for rotation in order to match x with X 478 00:31:59,360 --> 00:31:59,660 four. 479 00:32:00,230 --> 00:32:00,970 That's perfect. 480 00:32:01,000 --> 00:32:05,630 Now let's go with, um, table two. 481 00:32:05,840 --> 00:32:06,270 OK. 482 00:32:06,370 --> 00:32:07,760 And in order to find it. 483 00:32:08,210 --> 00:32:10,940 So the title parameter for the second frame. 484 00:32:11,210 --> 00:32:17,900 So how much we have to rotate the frame one with respect to an excuse me, I say frame one. 485 00:32:17,900 --> 00:32:22,490 But as we have said from frame three, how much we have to rotate frame four. 486 00:32:22,790 --> 00:32:31,910 Yes, with respect to Z four, in order to match X4 and S5, as you can see again, you can see that 487 00:32:31,910 --> 00:32:37,670 exponent X-File are the same, but you have to take into account the rotation. 488 00:32:37,700 --> 00:32:41,420 OK, let's take into rotation account. 489 00:32:41,780 --> 00:32:52,100 And in this case, if joined this joint, OK, which is the second joint rotates, OK, if it rotates 490 00:32:52,610 --> 00:32:59,510 theta five degrees, what will happen if it rotates to five degrees, then this will happen. 491 00:32:59,690 --> 00:33:00,080 OK. 492 00:33:01,820 --> 00:33:08,600 Um, the X for X four will be in this way. 493 00:33:08,960 --> 00:33:12,750 But X five will become in this way. 494 00:33:12,770 --> 00:33:13,970 OK, x five. 495 00:33:14,090 --> 00:33:21,940 There is angle of three to five between them, so we have to rotate in positive direction. 496 00:33:21,950 --> 00:33:23,540 Among the how long is it? 497 00:33:23,540 --> 00:33:28,040 Four in order and three to five degrees in order to match x for with x five. 498 00:33:28,070 --> 00:33:28,490 OK. 499 00:33:29,300 --> 00:33:35,720 So we have three to five here and in the same way and four in the same reasoning. 500 00:33:36,080 --> 00:33:45,230 You can you can understood that this will be a six in order to match with in order to match what in 501 00:33:45,230 --> 00:33:49,310 order to match x five with x six year excuse me. 502 00:33:50,210 --> 00:33:56,840 X five with a six book and rotation will be among which axis. 503 00:33:56,840 --> 00:34:01,350 It will be a moment alongside a Z five access through Z five axis. 504 00:34:01,370 --> 00:34:14,000 Yes, because if frame if joined in, if this sort of joint rotates by an angle of T to six, then as 505 00:34:14,000 --> 00:34:18,050 you know, the X x five will be in this way. 506 00:34:18,050 --> 00:34:20,390 X five will be in this way, OK? 507 00:34:20,410 --> 00:34:24,890 But again, X will become like that pick six. 508 00:34:24,890 --> 00:34:29,210 So there will be three to six angle between them that we have to consider. 509 00:34:30,590 --> 00:34:35,730 OK, if we consider this angle, also, it will be status. 510 00:34:35,730 --> 00:34:36,050 Six. 511 00:34:36,110 --> 00:34:37,760 OK, I want you. 512 00:34:37,910 --> 00:34:45,620 Um, if you cannot, if you couldn't catch it, please stop and go step by step by pondering and trying 513 00:34:45,620 --> 00:34:46,520 to imagining. 514 00:34:46,550 --> 00:34:47,210 Yes, everything. 515 00:34:47,210 --> 00:34:48,050 It's very easy. 516 00:34:48,770 --> 00:34:52,340 You have to just watch it by step, by step and. 517 00:34:52,510 --> 00:35:00,580 I want you also drove it in your paper and tried to make you try to follow me in each step. 518 00:35:00,610 --> 00:35:09,460 OK, so we have finished with Theda, then we can go with the parameters and indeed this translation 519 00:35:09,460 --> 00:35:09,700 problem. 520 00:35:09,700 --> 00:35:11,200 This will be very easy for us. 521 00:35:11,410 --> 00:35:13,660 They will be all of them will be zero. 522 00:35:14,350 --> 00:35:21,790 I know from where surely I know it because all the frames are out on top of each other. 523 00:35:21,890 --> 00:35:26,080 See, it makes it easier to do the calculation. 524 00:35:26,350 --> 00:35:27,310 So what was? 525 00:35:27,460 --> 00:35:28,990 But anyway, let's see this. 526 00:35:29,010 --> 00:35:39,970 What was d d was that how much we have to move if the centre of frame three OK in the direction of Z 527 00:35:40,060 --> 00:35:42,740 three, which is like that, OK? 528 00:35:42,830 --> 00:35:48,880 This is like that in order to match origin of three and fours frame. 529 00:35:48,910 --> 00:35:49,300 OK. 530 00:35:49,510 --> 00:35:56,680 As you can see, their origin matches with each other and there is no prismatic joint that will separate. 531 00:35:56,680 --> 00:36:00,130 These make distance between these two sensors. 532 00:36:00,370 --> 00:36:01,810 So it will be zero. 533 00:36:02,050 --> 00:36:02,530 OK. 534 00:36:03,070 --> 00:36:12,220 So the same way how much we have to move the origin or frame forward in order to move out of the frame 535 00:36:12,220 --> 00:36:14,520 for in order to match it with the original frame. 536 00:36:14,530 --> 00:36:18,760 Five Among which direction z for the direction? 537 00:36:18,760 --> 00:36:19,090 Yes. 538 00:36:19,420 --> 00:36:23,600 As you can see, there's four directions upward and we don't have to do anything. 539 00:36:23,620 --> 00:36:24,100 OK? 540 00:36:24,670 --> 00:36:30,430 Because there is no offset in this direction between these two centers, so it will be zero and the 541 00:36:30,430 --> 00:36:33,610 four the last one, how much we have to move. 542 00:36:33,910 --> 00:36:36,030 Origin of frame five. 543 00:36:36,070 --> 00:36:38,080 OK, which is here. 544 00:36:38,080 --> 00:36:42,160 Origin of frame five in the direction of Z five. 545 00:36:42,490 --> 00:36:42,910 Yes. 546 00:36:46,170 --> 00:36:52,590 How much we have to move the order in the direction of five in order to obtain in order to make what? 547 00:36:53,220 --> 00:36:58,330 In order to match that five vs six. 548 00:36:58,530 --> 00:37:00,030 Excuse me, origin of five. 549 00:37:00,690 --> 00:37:04,500 Origin of six news how much we have to do that. 550 00:37:05,490 --> 00:37:09,990 As you can see, this is nothing but the sum of L5 and L6. 551 00:37:10,380 --> 00:37:15,270 Okay, these two things, because the offset in this dilution in Z590 chain is like that. 552 00:37:15,720 --> 00:37:20,200 So we have to ride these two five plus IL six. 553 00:37:20,220 --> 00:37:20,790 OK. 554 00:37:21,420 --> 00:37:23,010 We have to move like that. 555 00:37:23,220 --> 00:37:25,570 OK, now let's. 556 00:37:26,310 --> 00:37:27,660 Oh my gosh, don't do that. 557 00:37:30,990 --> 00:37:31,290 Yeah. 558 00:37:34,430 --> 00:37:35,740 By clicking OK. 559 00:37:40,200 --> 00:37:41,270 Not necessarily. 560 00:37:41,940 --> 00:37:42,180 Yeah. 561 00:37:42,900 --> 00:37:43,210 No. 562 00:37:43,530 --> 00:37:44,820 Let's do this one. 563 00:37:45,210 --> 00:37:47,470 We have finished with the parameters. 564 00:37:47,550 --> 00:37:56,900 OK, now let's continue with parameter e OK for parameter A. What we will do for parameter A. It's also 565 00:37:56,910 --> 00:38:02,580 translation parameter how much we have to translate the center of frame three. 566 00:38:03,840 --> 00:38:05,040 Central Frame three. 567 00:38:05,520 --> 00:38:08,640 OK, here center of frames three. 568 00:38:09,060 --> 00:38:13,410 In the direction of which direction x four by addiction. 569 00:38:13,410 --> 00:38:20,690 OK, in the direction of x four, which is in this way in order to match the origins. 570 00:38:20,700 --> 00:38:25,520 OK, and the original frames leave its original frame for. 571 00:38:25,740 --> 00:38:30,450 And as you can see, there is no need to do anything because they are on top of each other in the way. 572 00:38:30,720 --> 00:38:31,060 OK. 573 00:38:31,110 --> 00:38:32,070 This is zero. 574 00:38:32,520 --> 00:38:42,600 And again, what we will do for the frame and the other frame, OK, how much we have to move the original 575 00:38:42,600 --> 00:38:50,790 frame forward in the direction of X five, OK x five, which is also in this direction in order to match 576 00:38:51,360 --> 00:38:53,610 the original frame for with original frame. 577 00:38:53,610 --> 00:38:54,000 Five. 578 00:38:54,240 --> 00:38:57,240 As you can see, there is no offset in the direction of X five. 579 00:38:57,450 --> 00:39:04,470 So we don't need to do and it will be, but it's certainly OK. 580 00:39:05,040 --> 00:39:06,660 It will be zero. 581 00:39:07,710 --> 00:39:16,410 The last one for the last one is, as you can see, how much we have to move in the direction of which 582 00:39:16,410 --> 00:39:25,050 x six direction, which is like that in order to match the original frame five, which is here with 583 00:39:25,050 --> 00:39:27,780 the original frame six, which is here. 584 00:39:27,830 --> 00:39:31,470 As you can see, there is no offset in the direction of X six. 585 00:39:31,770 --> 00:39:37,590 There was an offset in the direction of Z six, which was Influentials six, but in the direction of 586 00:39:37,590 --> 00:39:41,550 X six, there is no offset, so it will be zero. 587 00:39:41,880 --> 00:39:42,160 OK. 588 00:39:42,180 --> 00:39:45,480 As you can see, much of the translation parameter is R zero. 589 00:39:45,540 --> 00:39:45,930 OK. 590 00:39:46,320 --> 00:39:52,080 Because they are, um uh, on top of each other. 591 00:39:52,440 --> 00:39:52,960 OK. 592 00:39:52,980 --> 00:39:55,680 And the last parameter, which is rotation. 593 00:39:55,980 --> 00:39:56,300 OK. 594 00:39:56,360 --> 00:40:01,380 I find how much we have to rotate the frame. 595 00:40:02,040 --> 00:40:03,230 Uh, three. 596 00:40:03,240 --> 00:40:03,660 OK. 597 00:40:05,010 --> 00:40:15,950 Uh, alongside so through X in the direction of X forward in order to match what Z is three and is thought 598 00:40:15,960 --> 00:40:16,410 OK. 599 00:40:16,620 --> 00:40:20,530 As you can see, there is an offset already between the three and Z four. 600 00:40:20,550 --> 00:40:23,820 OK, and this is how much this is 90 degrees. 601 00:40:23,820 --> 00:40:25,140 Yes, Pi over two. 602 00:40:25,290 --> 00:40:28,920 But we want to know if it is positive or negative. 603 00:40:29,220 --> 00:40:36,330 So as you know, we have to rotate, we have to rotate which frame sort of frame in order to match the 604 00:40:36,330 --> 00:40:36,780 Z four. 605 00:40:36,790 --> 00:40:42,000 So we have the angle of rotation is PI over two and it should be in this direction. 606 00:40:42,300 --> 00:40:52,500 But in a alongside which axis, scroll through which axis we are providing the rotation X for and alongside 607 00:40:52,500 --> 00:40:53,430 X for direction. 608 00:40:53,430 --> 00:40:59,640 If you put your index for direction and curl your fingers, the positive rotation direction is like 609 00:40:59,640 --> 00:41:03,540 that and we are turning in this direction here, as you can see. 610 00:41:03,540 --> 00:41:04,920 So it will be positive. 611 00:41:05,160 --> 00:41:11,130 If it was like that, the rotation, it was like that, then we would take it as negative. 612 00:41:11,310 --> 00:41:11,670 OK. 613 00:41:12,090 --> 00:41:15,060 So the first one is positive pi over two. 614 00:41:16,140 --> 00:41:16,830 That's perfect. 615 00:41:17,160 --> 00:41:20,280 Now let's check for the other one. 616 00:41:20,310 --> 00:41:21,090 What will happen? 617 00:41:21,090 --> 00:41:22,380 Let's say for the other one. 618 00:41:22,800 --> 00:41:23,100 Cool. 619 00:41:23,640 --> 00:41:24,000 OK. 620 00:41:24,570 --> 00:41:35,880 So how much we have to move the frame, how much we have to rotate frame for with respect to yes x five 621 00:41:35,880 --> 00:41:36,990 in order to match. 622 00:41:37,320 --> 00:41:44,100 Z four and a Z five, as you can see it again, there is an offset of PI over two between the four and 623 00:41:44,100 --> 00:41:48,360 the five, and we have to rotate Z four in this direction. 624 00:41:48,360 --> 00:41:49,440 Pi over two. 625 00:41:49,680 --> 00:41:50,750 In order to match. 626 00:41:50,760 --> 00:41:51,540 Is it fast? 627 00:41:51,540 --> 00:42:00,510 But let's again see what is the sign of the rotation via rotating alongside x five axis, which is, 628 00:42:00,510 --> 00:42:06,420 as you can see, the positive direction is like that, and in this case, as you can see, our rotation 629 00:42:06,420 --> 00:42:08,820 is opposite to this positive direction. 630 00:42:09,060 --> 00:42:12,450 So it will be minus PI over two. 631 00:42:12,660 --> 00:42:15,000 Yes, it will be at minus PI over two. 632 00:42:16,770 --> 00:42:17,200 Perfect. 633 00:42:17,910 --> 00:42:27,720 We have finished for this one also and the last one, how much we have to rotate frame five in order 634 00:42:27,720 --> 00:42:32,160 to match in order more alongside execs. 635 00:42:32,160 --> 00:42:35,960 OK, along six axis in order to match. 636 00:42:35,970 --> 00:42:37,520 Is it five with. 637 00:42:38,200 --> 00:42:47,530 And as you can see, we don't need to do anything in execution because of these five and six already 638 00:42:47,530 --> 00:42:49,570 match with each other. 639 00:42:49,600 --> 00:42:49,980 OK. 640 00:42:50,410 --> 00:42:52,390 It will be so zero. 641 00:42:52,450 --> 00:42:54,190 We don't have to do it in the rotation. 642 00:42:54,670 --> 00:42:54,980 OK. 643 00:42:55,000 --> 00:43:00,670 As you can see, we have finished our the table for the cylindrical vest also. 644 00:43:01,090 --> 00:43:01,930 But what we can? 645 00:43:02,170 --> 00:43:05,840 Let me just change these numbers because these are not correct. 646 00:43:05,860 --> 00:43:11,570 This should start from I'm sorry, this should start from Portlaoise. 647 00:43:11,590 --> 00:43:13,840 This should start from Ford this far. 648 00:43:13,870 --> 00:43:14,860 This should be six. 649 00:43:15,280 --> 00:43:21,370 So this first one will give us what this will give us h four. 650 00:43:21,400 --> 00:43:21,790 Three. 651 00:43:22,270 --> 00:43:28,990 This will give us age five four and this will give us Page Six. 652 00:43:28,990 --> 00:43:29,430 Five. 653 00:43:29,500 --> 00:43:39,820 OK, now how can we find the relation between the center of this frame, which is here and this one? 654 00:43:39,850 --> 00:43:40,450 OK? 655 00:43:40,810 --> 00:43:50,880 We have two front Page Six three, which will be given by H four to three times. 656 00:43:50,890 --> 00:43:54,490 Page five four times Page Six four. 657 00:43:54,640 --> 00:43:59,260 OK, now we have in our hands h x age six three. 658 00:43:59,260 --> 00:44:01,700 OK, and we have eight zero three. 659 00:44:01,720 --> 00:44:03,640 Let me make it in this together. 660 00:44:03,940 --> 00:44:10,330 As you can see, we have eight zero three in this part and we have eight six three in this part. 661 00:44:10,390 --> 00:44:17,410 And for this robotic manipulator, in order as we have seen to find in order to find the relation between 662 00:44:17,410 --> 00:44:25,870 these base frame and the fact that we have to find what Page six zero, because the frame attached to 663 00:44:25,870 --> 00:44:27,970 this one is six frame splits. 664 00:44:28,250 --> 00:44:29,650 Let's draw the frame. 665 00:44:30,040 --> 00:44:32,530 The frame was a six frame. 666 00:44:32,530 --> 00:44:34,180 Yes, this was it six. 667 00:44:34,180 --> 00:44:36,430 And this was x six. 668 00:44:36,850 --> 00:44:37,960 And this was. 669 00:44:40,890 --> 00:44:44,950 Is it zero and this was X0. 670 00:44:45,140 --> 00:44:46,910 Yes, that's perfect. 671 00:44:47,240 --> 00:44:53,540 Now, in order to find the relation between these two frames, we have to find age six zero. 672 00:44:53,840 --> 00:44:57,830 And how we will find age six zero we have in our hands. 673 00:44:57,860 --> 00:45:01,350 Age three zero. 674 00:45:01,370 --> 00:45:04,010 And we from this is from a. 675 00:45:04,220 --> 00:45:07,400 And we have in our hands eight six three. 676 00:45:07,400 --> 00:45:08,730 Yes, which is won't be. 677 00:45:09,110 --> 00:45:17,140 If you multiply these together, I will get the relation between age is six zero and this is our forward 678 00:45:17,150 --> 00:45:24,210 kinematics for this cylindrical robot arm vs spherical joint, which is very important. 679 00:45:24,230 --> 00:45:24,530 Yes. 680 00:45:25,400 --> 00:45:35,750 Keep in mind that they always try to remove the spherical restock to complete her, and he can't wait 681 00:45:35,750 --> 00:45:36,920 for the age parameter. 682 00:45:36,920 --> 00:45:44,360 Um, for this list and for the robot and then combine them in this way. 683 00:45:44,510 --> 00:45:44,870 OK. 684 00:45:45,050 --> 00:45:54,790 And also, let me say to you one thing this point for the spherical wrist is called wrist center or 685 00:45:54,800 --> 00:45:55,600 wrist point. 686 00:45:55,610 --> 00:45:58,890 OK, this is the wrist centre or wrist point. 687 00:45:58,910 --> 00:46:01,910 This is called for this vertical wrist. 688 00:46:02,630 --> 00:46:03,560 That's perfect. 689 00:46:03,800 --> 00:46:05,870 I think that's enough for it. 690 00:46:06,080 --> 00:46:11,360 As an example to the parameters, we have seen many things how to calculate it.