1 00:00:00,060 --> 00:00:09,750 Well, gay people, I have decided to do a small project, OK, which is which I think which will be 2 00:00:09,750 --> 00:00:23,910 fun to do in order to understand forward kinematics more better and also put them into practice. 3 00:00:23,910 --> 00:00:33,750 And also how useful is for the kinematics shirtless for candidates will be much more useful than that. 4 00:00:34,160 --> 00:00:39,560 But it is, I think, is a pretty example to do. 5 00:00:39,640 --> 00:00:42,450 Pretty interesting project anyway. 6 00:00:43,830 --> 00:00:52,740 No need to do to speak up on this early and start to see what we will do. 7 00:00:53,160 --> 00:00:57,000 We will try to create our robot simulator. 8 00:00:57,030 --> 00:00:59,490 OK, but not the sophisticated one. 9 00:01:00,420 --> 00:01:02,550 So it will be just this stick. 10 00:01:02,910 --> 00:01:09,510 You know, there is some people can grow human rather can draw just stick humans. 11 00:01:09,510 --> 00:01:14,370 Yeah, like very simple and we will do exactly the same. 12 00:01:14,370 --> 00:01:20,100 We will not simulate robot, but we will try to simulate stick robot attempts. 13 00:01:20,220 --> 00:01:22,880 I mean, in this way, you can see to stick robots. 14 00:01:22,880 --> 00:01:23,130 Yes. 15 00:01:24,270 --> 00:01:25,620 So how do will do that? 16 00:01:25,630 --> 00:01:30,060 So our purpose is to create stick robots simulator. 17 00:01:30,150 --> 00:01:30,660 OK. 18 00:01:30,990 --> 00:01:31,950 This is our purpose. 19 00:01:31,950 --> 00:01:36,480 So what we have to do this one, I will say the steps to you. 20 00:01:36,810 --> 00:01:42,330 OK, so then we will see exactly how to this has been implemented in the code. 21 00:01:42,420 --> 00:01:42,810 OK. 22 00:01:43,740 --> 00:01:48,150 First, we have to write joint centers with respect to base frame. 23 00:01:48,630 --> 00:01:49,080 Why? 24 00:01:49,350 --> 00:01:51,300 So in order to plot them, yes. 25 00:01:51,300 --> 00:01:56,190 Because as you can see what are drawn centers, these are the joint centers. 26 00:01:56,200 --> 00:01:59,520 This is this is this is the joint center. 27 00:01:59,910 --> 00:02:01,270 This is the joint center. 28 00:02:01,290 --> 00:02:02,670 This is the joint center. 29 00:02:02,670 --> 00:02:04,320 And this is the joint center. 30 00:02:04,320 --> 00:02:05,520 And this is a joint center. 31 00:02:05,520 --> 00:02:05,790 OK? 32 00:02:05,850 --> 00:02:07,140 These are the joint centers. 33 00:02:07,350 --> 00:02:10,670 Yeah, this is not joint about this and the factor center, OK? 34 00:02:11,280 --> 00:02:17,550 And we will try to write them with respect to base frame. 35 00:02:17,550 --> 00:02:19,960 Base frame is which one base frame is this one? 36 00:02:19,980 --> 00:02:20,400 OK? 37 00:02:20,850 --> 00:02:23,340 With respect to base frame, why? 38 00:02:23,610 --> 00:02:27,240 In order to be able to put them in mutlak. 39 00:02:27,270 --> 00:02:27,840 OK. 40 00:02:28,440 --> 00:02:38,430 So when we try to plot them in three dimension, we will just give them plot and like X coordinates 41 00:02:38,430 --> 00:02:44,310 XCOR and let's include this X coordinate, you know, include not only one x comunemente x coordinate 42 00:02:44,310 --> 00:02:54,750 for first center x one x two x three four x five OK and x six pull x coordinate of these centers. 43 00:02:55,050 --> 00:02:56,180 We will plot them. 44 00:02:56,250 --> 00:02:57,920 We will write y coordinate. 45 00:02:57,930 --> 00:03:08,370 This will be y one again up to the the the device six and Z coordinate, which will also be Z one to 46 00:03:08,400 --> 00:03:10,830 the Z six. 47 00:03:10,860 --> 00:03:11,340 OK. 48 00:03:11,730 --> 00:03:14,430 So what will then not we'll do what? 49 00:03:14,430 --> 00:03:22,470 What will we take all these points and it will just it will just connect them with each other. 50 00:03:22,470 --> 00:03:30,060 So if the points are like that, OK, let's see in 3D space one two, three four, five and again six. 51 00:03:30,240 --> 00:03:32,100 Now let me do it in this way. 52 00:03:32,130 --> 00:03:34,360 OK, up, up up. 53 00:03:35,160 --> 00:03:37,950 Excuse me like that. 54 00:03:37,950 --> 00:03:39,150 Like that, like that. 55 00:03:39,150 --> 00:03:41,060 Like that and like that, OK? 56 00:03:41,110 --> 00:03:43,080 And this will be our end affected here. 57 00:03:43,380 --> 00:03:51,540 Then if we, for example, say, OK, if we change the angle, Tatooine or for example, here, let's 58 00:03:51,540 --> 00:03:51,900 change. 59 00:03:51,900 --> 00:03:54,000 For example, it change this angle. 60 00:03:54,630 --> 00:03:55,680 Peter, I don't know. 61 00:03:55,680 --> 00:04:03,210 Four or 03:52 then the position of points surely will change if, for example, they will be like that, 62 00:04:03,210 --> 00:04:06,060 like that, like that, like that, for example. 63 00:04:06,060 --> 00:04:09,570 And then we can connect and get another robot configuration. 64 00:04:09,570 --> 00:04:14,400 So we have to first be right. 65 00:04:14,400 --> 00:04:20,340 These joint centers with respect to the base frame so club can plot them OK easily. 66 00:04:20,700 --> 00:04:30,270 So however, in order to obtain these, I mean the center, the points of how, how we will provide 67 00:04:30,270 --> 00:04:31,950 them with respect to the base frame. 68 00:04:31,950 --> 00:04:38,850 First, we will write them in joint centers with respect to their own frame because it's easier for 69 00:04:38,850 --> 00:04:40,920 us to see because we know the link lengths. 70 00:04:40,920 --> 00:04:43,920 Yes, we know this is L1, this is L2. 71 00:04:43,920 --> 00:04:44,970 Yes, we know this. 72 00:04:45,540 --> 00:04:55,980 This is L3, OK, this is L4 or killed four and five and L six. 73 00:04:55,980 --> 00:04:59,820 OK, we know this and this is L6, so we can. 74 00:04:59,990 --> 00:05:05,780 Right, all these center points with respect to each frame is because it will be very easy. 75 00:05:06,020 --> 00:05:07,800 For example, it's still for the first one. 76 00:05:07,970 --> 00:05:12,050 What will be the center points for this center point coordinate? 77 00:05:12,230 --> 00:05:12,620 OK. 78 00:05:13,280 --> 00:05:15,320 With respect, it's on frame zero. 79 00:05:15,440 --> 00:05:17,810 Surely it will be zero zero zero. 80 00:05:17,960 --> 00:05:18,350 OK. 81 00:05:19,700 --> 00:05:21,420 Because it's a concern. 82 00:05:21,590 --> 00:05:22,200 It's frame. 83 00:05:22,550 --> 00:05:24,620 And what's going to happen for the second one? 84 00:05:24,620 --> 00:05:27,350 Surely it will also be zero zero zero? 85 00:05:27,380 --> 00:05:27,890 Yes. 86 00:05:28,290 --> 00:05:30,450 What will happen for the soon? 87 00:05:30,770 --> 00:05:35,950 Also, the center coincides with its own fair frame. 88 00:05:35,960 --> 00:05:37,580 It will be zero zero zero. 89 00:05:38,120 --> 00:05:38,960 And what will happen? 90 00:05:39,140 --> 00:05:40,820 OK, let me say that one. 91 00:05:41,060 --> 00:05:47,390 First, we have to assign surely the coordinate frames based on the date frame assignment. 92 00:05:47,390 --> 00:05:49,520 I have done this lot to explain this to you. 93 00:05:49,550 --> 00:05:51,170 You have to know this already. 94 00:05:51,440 --> 00:05:52,670 So you can practice. 95 00:05:52,670 --> 00:06:00,080 Also, I will give this to you that you see that and you can try to validate it that that this is correct. 96 00:06:00,110 --> 00:06:00,560 OK. 97 00:06:01,730 --> 00:06:02,120 OK. 98 00:06:04,910 --> 00:06:05,300 OK. 99 00:06:05,540 --> 00:06:08,420 So what I will say, I was saying yes. 100 00:06:09,380 --> 00:06:11,380 What about for the for this joint? 101 00:06:11,390 --> 00:06:11,700 OK? 102 00:06:11,720 --> 00:06:17,110 This is an interesting it's simple point is here is you can see this is the center point hole. 103 00:06:17,140 --> 00:06:18,290 Where is its frame? 104 00:06:18,470 --> 00:06:19,970 Its frame is here. 105 00:06:20,240 --> 00:06:26,360 So there is an offset and offset is in which direction is in three direction. 106 00:06:26,370 --> 00:06:29,750 Perfect, then it will be zero zero in the tree direction. 107 00:06:29,750 --> 00:06:30,530 But we will ride. 108 00:06:30,890 --> 00:06:33,830 The offset is illusory, so it will be illusory. 109 00:06:34,520 --> 00:06:35,960 OK, perfect. 110 00:06:36,200 --> 00:06:39,140 So what about this frame for this? 111 00:06:39,410 --> 00:06:40,670 What about for this joint? 112 00:06:40,670 --> 00:06:44,270 This joint center coincides with its frame, so it will be zero zero zero. 113 00:06:44,480 --> 00:06:45,980 What about this joint? 114 00:06:45,980 --> 00:06:48,320 Its center is here, but where is its frame? 115 00:06:48,530 --> 00:06:52,130 Its frame is these five and it is here. 116 00:06:52,370 --> 00:06:53,720 There is an offset. 117 00:06:53,720 --> 00:06:56,200 Yes, between its center and its own frame. 118 00:06:56,210 --> 00:06:57,230 And how much is that? 119 00:06:57,230 --> 00:06:58,970 It is L5 amount. 120 00:06:59,210 --> 00:07:04,980 So we will ride zero zero l five amount. 121 00:07:05,000 --> 00:07:06,380 OK, that's perfect. 122 00:07:07,100 --> 00:07:16,030 And for the last one, the last one, for the last one, for the end effector, OK, its frame and center 123 00:07:16,030 --> 00:07:16,630 to coincide. 124 00:07:16,640 --> 00:07:20,330 So it will be zero zero zero. 125 00:07:20,420 --> 00:07:20,880 Yes. 126 00:07:21,410 --> 00:07:22,100 Perfect. 127 00:07:22,640 --> 00:07:26,420 So no, these are nothing. 128 00:07:26,420 --> 00:07:30,700 But let me write for, for example, this is p one one. 129 00:07:30,890 --> 00:07:32,300 OK, p one one. 130 00:07:32,480 --> 00:07:36,380 Because it's on, it's it's on its own three year. 131 00:07:36,620 --> 00:07:38,230 This is P so. 132 00:07:38,480 --> 00:07:41,510 Second point with its own frame. 133 00:07:41,520 --> 00:07:42,280 Second frame. 134 00:07:42,290 --> 00:07:42,960 Yes, indeed. 135 00:07:42,980 --> 00:07:48,410 Let me just not p one one, but p zero zero zero zero. 136 00:07:48,680 --> 00:07:49,730 This is one one. 137 00:07:49,760 --> 00:07:50,990 This is P2 or two. 138 00:07:51,020 --> 00:07:52,900 This is P three three. 139 00:07:52,910 --> 00:07:58,580 Yes, P 44 P five five PS six six. 140 00:07:58,850 --> 00:08:03,480 However, in order to draw, we cannot use these coordinates right? 141 00:08:03,530 --> 00:08:09,380 You cannot use these coordinates because think about that as you can see, if you're right with respect 142 00:08:09,380 --> 00:08:17,630 to its own frame, even the robot moves, the joints will move and they, as their own frame is, stick 143 00:08:19,250 --> 00:08:21,200 in a hard way to it's joined. 144 00:08:21,440 --> 00:08:26,220 The joint joints will move with their frame with their frame. 145 00:08:26,240 --> 00:08:26,570 Yes. 146 00:08:26,810 --> 00:08:36,020 So if with the right points, with respect to their frame, then these coordinates will not change even 147 00:08:36,020 --> 00:08:37,280 if the robot moves. 148 00:08:37,290 --> 00:08:37,730 Yes. 149 00:08:38,330 --> 00:08:39,620 Think about it in this way. 150 00:08:39,620 --> 00:08:41,560 OK, this is our joint. 151 00:08:41,570 --> 00:08:43,010 This is our second joint. 152 00:08:43,010 --> 00:08:46,340 Yes, there is a frame here and there is a frame here. 153 00:08:46,730 --> 00:08:48,320 This is these frames. 154 00:08:48,740 --> 00:08:56,000 Stick to these joints, OK, in a hard way, so it will move with their joint. 155 00:08:56,300 --> 00:08:56,780 OK. 156 00:08:57,140 --> 00:09:03,350 So you might descend to the point of these coordinates, the center point coordinates with respect to 157 00:09:03,360 --> 00:09:10,650 this frame and for this joint, you will right with the expected this frame, which will happen either 158 00:09:11,030 --> 00:09:18,260 after this moves into one, for example, it became like that, OK, it became like that in this way. 159 00:09:18,350 --> 00:09:18,830 OK. 160 00:09:19,160 --> 00:09:20,810 And this joint is here. 161 00:09:21,110 --> 00:09:21,560 OK. 162 00:09:22,880 --> 00:09:24,830 How will be the frames? 163 00:09:24,860 --> 00:09:29,880 Again, the frames will be in the same way, OK, because they stick to their. 164 00:09:31,550 --> 00:09:34,900 They stick to their joints. 165 00:09:34,910 --> 00:09:35,420 OK? 166 00:09:35,840 --> 00:09:36,410 In the hallway. 167 00:09:36,410 --> 00:09:38,360 So they move with respect to them. 168 00:09:39,330 --> 00:09:41,180 Moving with them with joints. 169 00:09:41,210 --> 00:09:41,510 OK. 170 00:09:41,750 --> 00:09:48,310 So if you try to again express the joint center with respect to its own frame, the curtains will look 171 00:09:48,320 --> 00:09:48,780 change. 172 00:09:48,800 --> 00:09:49,280 OK? 173 00:09:49,610 --> 00:09:53,450 Because the joints moved with their own frames. 174 00:09:53,480 --> 00:09:54,430 OK, so we have. 175 00:09:54,470 --> 00:09:55,760 But they will change. 176 00:09:55,760 --> 00:09:59,330 When, if we would, if. 177 00:09:59,830 --> 00:10:07,390 Express these center points with respect to the base frame, because these frames will change their 178 00:10:07,390 --> 00:10:12,310 orientation or position with respect to base frame at each motion. 179 00:10:12,780 --> 00:10:13,260 OK. 180 00:10:13,630 --> 00:10:18,310 So that's why we have to express them in base frame. 181 00:10:19,300 --> 00:10:19,720 OK. 182 00:10:19,930 --> 00:10:21,410 Harvey will do that then. 183 00:10:21,430 --> 00:10:22,090 OK. 184 00:10:22,240 --> 00:10:25,870 We will just have to multiply these points. 185 00:10:25,870 --> 00:10:33,090 We have to take these points, for example, and multiply it with what age six zero times p zero zero 186 00:10:33,100 --> 00:10:36,340 in order to obtain what piece six zero? 187 00:10:36,760 --> 00:10:42,160 Did you see that we fund and the fact that a position with respect to the base frame? 188 00:10:42,490 --> 00:10:48,160 We can do the same for this one Page Six one times p one firm. 189 00:10:48,160 --> 00:10:52,450 OK, one one cause we get we got word piece six one. 190 00:10:53,110 --> 00:10:53,950 That's perfect. 191 00:10:54,070 --> 00:10:54,460 OK. 192 00:10:55,180 --> 00:11:04,390 As you can see, we have to calculate these at each iteration in order to to be able to express them. 193 00:11:04,420 --> 00:11:04,870 OK. 194 00:11:06,670 --> 00:11:07,120 OK. 195 00:11:09,340 --> 00:11:10,480 That's perfect. 196 00:11:10,660 --> 00:11:14,140 Then what we have to do? 197 00:11:14,440 --> 00:11:14,790 Okay. 198 00:11:16,030 --> 00:11:19,870 So that this is for the oh, excuse me. 199 00:11:19,900 --> 00:11:20,480 OK. 200 00:11:21,250 --> 00:11:27,880 We understood how people express OK and why we have the express with respect to the base frame. 201 00:11:28,180 --> 00:11:40,510 And also consider that this one if, for example, we have to calculate so the motion of this joint, 202 00:11:40,510 --> 00:11:43,570 OK, for example, this joint, let's take this joint again. 203 00:11:44,020 --> 00:11:47,170 The motion of this joint will affect the joints. 204 00:11:47,650 --> 00:11:49,900 It will this affect the base joint? 205 00:11:50,110 --> 00:11:57,430 Surely not because it is not after this joint, but before this joint. 206 00:11:57,640 --> 00:12:03,520 So if this joint moves, it will not affect the joints or leanings before itself. 207 00:12:03,760 --> 00:12:06,790 It will affect only the ones after itself. 208 00:12:07,060 --> 00:12:11,020 So that's why we have to update homogeneous transformation mattress. 209 00:12:11,240 --> 00:12:19,270 If, for example, moving this joint, we have to update only the ones after to it, not the ones before 210 00:12:19,270 --> 00:12:19,960 it's OK. 211 00:12:20,290 --> 00:12:22,270 But also consider this in your mind. 212 00:12:22,810 --> 00:12:23,380 Perfect. 213 00:12:24,820 --> 00:12:27,460 I will make it in this way so you can see everything. 214 00:12:27,760 --> 00:12:32,020 As you can see, this is nothing but our the edge table. 215 00:12:32,020 --> 00:12:35,900 You can again verify that it is correct for yourself. 216 00:12:35,920 --> 00:12:36,430 OK. 217 00:12:36,840 --> 00:12:41,380 Um, so and then one last thing to explain to you. 218 00:12:41,620 --> 00:12:44,590 So you will understand in the code how we will draw. 219 00:12:45,490 --> 00:12:52,420 Let me show you how we will draw the end effector, OK, in the fact that it is easy indeed in order 220 00:12:52,420 --> 00:12:53,110 to drive it. 221 00:12:53,140 --> 00:12:58,600 So in order to drive this shape, how we will drive it, how we will plot in MATLAB. 222 00:12:58,930 --> 00:13:02,970 So what we are doing for this one in order to do this one, I wrote it here. 223 00:13:03,370 --> 00:13:05,710 Also here first, we have to choose an offset. 224 00:13:05,890 --> 00:13:07,510 What does it mean by the offset? 225 00:13:07,510 --> 00:13:11,740 Is this one, for example, how much do you want this offset to be here? 226 00:13:11,980 --> 00:13:13,450 For example, this is all offset. 227 00:13:13,750 --> 00:13:15,790 This is our offset. 228 00:13:15,790 --> 00:13:17,020 OK, offset. 229 00:13:17,110 --> 00:13:17,510 OK. 230 00:13:17,560 --> 00:13:21,370 And this is our offset, and this is our offset. 231 00:13:21,370 --> 00:13:26,560 Why this is called offset, I will show it because this is our end effector center. 232 00:13:26,560 --> 00:13:28,390 Yes, this is the center point. 233 00:13:28,390 --> 00:13:29,410 This is this point. 234 00:13:29,410 --> 00:13:31,090 OK, we know this, OK. 235 00:13:31,510 --> 00:13:33,180 We know it's card in it. 236 00:13:33,190 --> 00:13:34,900 This is nothing but P6. 237 00:13:34,900 --> 00:13:35,380 Zero. 238 00:13:35,530 --> 00:13:36,070 OK. 239 00:13:36,400 --> 00:13:38,790 So if we want to calculate it. 240 00:13:38,860 --> 00:13:43,750 So in order to plot this, we can create four different points. 241 00:13:44,020 --> 00:13:45,670 Let's call these points C. 242 00:13:45,910 --> 00:13:51,590 Let's call this point a let's call this point B, and let's call this point. 243 00:13:52,240 --> 00:13:55,120 Now we can put this in MATLAB. 244 00:13:55,120 --> 00:13:58,450 By using this, we applaud a b. 245 00:13:58,600 --> 00:14:01,360 Yes, this will draw this line. 246 00:14:01,600 --> 00:14:04,960 Then we will do a plot, a c it. 247 00:14:04,960 --> 00:14:12,620 This will draw this line and we will see plot b d, which we applaud this line. 248 00:14:12,640 --> 00:14:15,430 Yes, that's perfect. 249 00:14:16,180 --> 00:14:21,100 So how we will calculate a c b d, it's indeed very easy. 250 00:14:21,460 --> 00:14:22,520 What is there? 251 00:14:22,540 --> 00:14:29,530 Let's first try to express the a point with respect to their sixth frame, OK, its own frame. 252 00:14:29,540 --> 00:14:32,290 So in order to find it, let's write it over the right. 253 00:14:32,290 --> 00:14:33,220 It was offset. 254 00:14:33,490 --> 00:14:34,930 Offset A. 255 00:14:35,290 --> 00:14:35,820 OK. 256 00:14:35,860 --> 00:14:37,000 With respect to which? 257 00:14:37,090 --> 00:14:37,900 Six. 258 00:14:38,680 --> 00:14:39,220 Six. 259 00:14:39,280 --> 00:14:39,710 OK. 260 00:14:39,730 --> 00:14:41,770 So in this one, six is enough. 261 00:14:41,770 --> 00:14:45,280 I think, OK, we write it into its own frame. 262 00:14:45,310 --> 00:14:47,470 I mean, the frame of the last point, OK? 263 00:14:47,800 --> 00:14:48,280 Six. 264 00:14:49,450 --> 00:14:52,250 So let's do that. 265 00:14:52,270 --> 00:14:53,050 Let's do that. 266 00:14:53,100 --> 00:14:54,160 How people write this. 267 00:14:54,370 --> 00:14:59,550 If you can see a e um doesn't move in the direct. 268 00:15:00,280 --> 00:15:00,750 OK. 269 00:15:00,910 --> 00:15:02,360 Look at that, look at that. 270 00:15:02,380 --> 00:15:08,950 It is here it moves only in which direction in the direction you're from, right, Andrew. 271 00:15:08,980 --> 00:15:11,740 You can move the direction of why. 272 00:15:11,740 --> 00:15:16,600 Let me throw it for you at the direction of why it is in this way. 273 00:15:16,870 --> 00:15:17,200 Why? 274 00:15:17,200 --> 00:15:21,100 Six You can know it from what? 275 00:15:21,550 --> 00:15:22,620 By using right hand. 276 00:15:23,080 --> 00:15:28,690 OK, as you can see a move upward, which is opposite to devise six. 277 00:15:28,990 --> 00:15:30,790 Which is negative right now. 278 00:15:30,880 --> 00:15:33,880 How much it moves as an offset? 279 00:15:33,940 --> 00:15:37,450 OK, but it doesn't move in the direction of X, or does it? 280 00:15:37,450 --> 00:15:41,170 So what will be its coordinate with respect to the last? 281 00:15:41,560 --> 00:15:43,270 It doesn't move in X. 282 00:15:43,600 --> 00:15:48,010 It did move in as offset on Y, but minus offset. 283 00:15:48,250 --> 00:15:51,460 But it also didn't move in it. 284 00:15:51,490 --> 00:15:51,910 OK. 285 00:15:52,210 --> 00:15:54,490 We can ride for B. 286 00:15:54,490 --> 00:15:58,090 Also, let's check what's b how much be moved. 287 00:15:58,330 --> 00:16:01,960 As you can see, b move to exactly opposite to their A.. 288 00:16:02,170 --> 00:16:11,170 It also didn't move in exit, but it moved in positive y direction as an offset amount a offset and 289 00:16:11,230 --> 00:16:14,710 zero, excuse me, zero offset and zero. 290 00:16:15,520 --> 00:16:17,200 What will be about C. 291 00:16:17,920 --> 00:16:18,370 OK? 292 00:16:18,400 --> 00:16:20,590 What about C about C? 293 00:16:20,590 --> 00:16:26,620 You can see it both moved in upward, which is in negative y direction. 294 00:16:26,620 --> 00:16:29,650 And also it moved in the direction of Z six. 295 00:16:29,650 --> 00:16:31,340 How much as an offset again. 296 00:16:31,360 --> 00:16:31,810 OK. 297 00:16:32,200 --> 00:16:40,480 So what we've tried for X is zero, but for in the direction of why it's minus offset in the direction 298 00:16:40,480 --> 00:16:41,500 of is it? 299 00:16:41,500 --> 00:16:42,460 It is offset. 300 00:16:42,760 --> 00:16:47,360 We can ride the same for D, which is the exact opposite of this one. 301 00:16:47,380 --> 00:16:50,320 It moved as an offset to the double. 302 00:16:50,620 --> 00:16:50,990 OK. 303 00:16:51,010 --> 00:16:54,220 As you can see, the first move like that then moved like that. 304 00:16:55,840 --> 00:17:01,510 Both of them are offset among offset amount down in the bi directional offset amount in this positive 305 00:17:01,510 --> 00:17:02,470 Za'atari action. 306 00:17:03,100 --> 00:17:05,800 OK, we have found these points also. 307 00:17:05,800 --> 00:17:09,190 But again, these are with respect to this sixth frame. 308 00:17:09,400 --> 00:17:17,830 So if the robot moves as the last joint will move it its own frame, these cardinals really don't change, 309 00:17:17,830 --> 00:17:20,140 so we have to take into account updates. 310 00:17:20,320 --> 00:17:27,610 We will take this into account by expressing all of these offsets with respect to base frame so that 311 00:17:27,610 --> 00:17:34,380 we will just do this will just take Page Six zero and multiply it with a six. 312 00:17:34,390 --> 00:17:38,140 We will get, excuse me, offset. 313 00:17:38,230 --> 00:17:38,950 OK. 314 00:17:39,280 --> 00:17:40,810 A in zero. 315 00:17:40,960 --> 00:17:41,300 OK. 316 00:17:41,320 --> 00:17:44,590 As you can see now, we can plotted OK. 317 00:17:44,620 --> 00:17:49,810 And now we will take into account the motion of all the joints. 318 00:17:49,840 --> 00:17:50,210 OK. 319 00:17:50,230 --> 00:17:58,420 All these joints will affect the robot manipulator because we take each six zero, which include all 320 00:17:58,420 --> 00:18:02,320 of these points, homogeneous corners of transformation. 321 00:18:02,830 --> 00:18:04,540 We will do the same for this one. 322 00:18:04,540 --> 00:18:08,670 We will do the same for this one and for this one, and we'll just plop them. 323 00:18:08,680 --> 00:18:15,670 And this is the stick simulation of our robot and I make it in this way so you can clearly see everything 324 00:18:15,670 --> 00:18:16,240 from this. 325 00:18:16,630 --> 00:18:17,080 OK. 326 00:18:17,110 --> 00:18:18,490 This is like that. 327 00:18:18,500 --> 00:18:19,990 Let me just put it in this way. 328 00:18:19,990 --> 00:18:20,830 This our robot. 329 00:18:21,130 --> 00:18:25,930 This is our, um uh, homogeneous transfer. 330 00:18:26,200 --> 00:18:31,060 Excuse me, say that the H matrix and this is for the end effector. 331 00:18:31,060 --> 00:18:31,810 OK, no. 332 00:18:31,810 --> 00:18:39,490 I think result we have almost we lose time in way, but we can go to the MATLAB and to see what's happening. 333 00:18:40,480 --> 00:18:41,860 This is our muscle, of course. 334 00:18:41,980 --> 00:18:43,450 So we will use. 335 00:18:44,080 --> 00:18:45,250 Let me see. 336 00:18:45,640 --> 00:18:48,790 We will use what we will use at designers. 337 00:18:48,850 --> 00:18:49,450 OK. 338 00:18:49,880 --> 00:18:58,090 Um, designers, um, for my club, how you can get up designer just right here up designer, designer 339 00:18:58,090 --> 00:19:00,400 and press enter. 340 00:19:00,610 --> 00:19:02,290 You will get up. 341 00:19:02,290 --> 00:19:05,230 Designer, OK, you will get this design view. 342 00:19:05,230 --> 00:19:08,040 Just take and access and put it here. 343 00:19:08,050 --> 00:19:08,920 Drag and drop. 344 00:19:08,950 --> 00:19:09,460 OK. 345 00:19:10,180 --> 00:19:13,540 If you work this, we programming. 346 00:19:13,600 --> 00:19:14,140 OK. 347 00:19:14,290 --> 00:19:15,520 You have to know this. 348 00:19:15,550 --> 00:19:16,030 OK. 349 00:19:16,210 --> 00:19:18,360 Because it's very easy and it's very easy. 350 00:19:18,370 --> 00:19:22,480 Grip programming is at least dragging and dropping section is easy. 351 00:19:22,780 --> 00:19:25,330 Yeah, and you just it. 352 00:19:25,870 --> 00:19:31,600 And then you have to take a slider here, as you can see where it's like, OK, this slider and put 353 00:19:31,600 --> 00:19:32,600 them all here. 354 00:19:32,620 --> 00:19:33,130 OK? 355 00:19:33,670 --> 00:19:34,390 Slide them. 356 00:19:35,590 --> 00:19:39,640 Now, after doing this one, you can go to the code section. 357 00:19:39,850 --> 00:19:41,500 This will be automatically created. 358 00:19:41,500 --> 00:19:46,210 This great sections are automatically created and you cannot change them. 359 00:19:46,540 --> 00:19:50,110 The MATLAB doesn't allow for this one in the way of the blah blah. 360 00:19:50,120 --> 00:19:53,200 Let's go to the code and see what we will do. 361 00:19:53,530 --> 00:19:57,940 First, we will add some, uh, some. 362 00:20:00,170 --> 00:20:06,110 Callbacks, OK, let me make it OK, I can make it bigger, OK, let me make it bigger for you, OK? 363 00:20:06,530 --> 00:20:07,700 We will add callbacks. 364 00:20:08,000 --> 00:20:09,290 What are callbacks? 365 00:20:09,500 --> 00:20:17,600 Callbacks is this one, for example, you tried to take this slider zero and slide it to its slider. 366 00:20:17,600 --> 00:20:17,950 OK? 367 00:20:19,140 --> 00:20:22,640 How you will know that this changed. 368 00:20:22,640 --> 00:20:23,060 OK? 369 00:20:23,630 --> 00:20:26,940 You want to grab this change and read the slide there as well? 370 00:20:26,960 --> 00:20:27,900 You will be. 371 00:20:28,100 --> 00:20:30,470 You will do this using sliders. 372 00:20:30,710 --> 00:20:33,530 So you just come to the code view. 373 00:20:33,710 --> 00:20:35,980 You choose your slider from here. 374 00:20:35,990 --> 00:20:38,900 OK, competent browser Cube zero slider. 375 00:20:38,900 --> 00:20:43,730 You come, you just right click OK and callbacks. 376 00:20:43,730 --> 00:20:52,300 And there you are, adding go, you are adding here's shows go to about a because I have already added, 377 00:20:52,310 --> 00:21:00,050 but you will see add value changing, not value changed because you want to have a callback while the 378 00:21:00,050 --> 00:21:04,200 value is changing in order to change the robot in real time manner. 379 00:21:04,220 --> 00:21:07,430 OK, go to zero slider changing. 380 00:21:08,270 --> 00:21:16,040 You will have add value changing callback OK, and add this for each of these joints in for each of 381 00:21:16,040 --> 00:21:20,270 these sliders of these sliders will control the joint of the robot manipulator. 382 00:21:20,270 --> 00:21:21,830 OK, joins a little bit manipulated. 383 00:21:22,250 --> 00:21:32,540 So and in each slider value changing callback what we will do even read the value of the slider. 384 00:21:32,810 --> 00:21:38,370 OK, then the four in each of them, and we will then draw our robot. 385 00:21:38,390 --> 00:21:38,750 OK. 386 00:21:38,930 --> 00:21:43,130 Because we have changed joined, we have to update the plot of the robot. 387 00:21:43,130 --> 00:21:45,290 We will draw robot again and again. 388 00:21:45,500 --> 00:21:49,080 The robot takes what function drone robot takes for. 389 00:21:49,490 --> 00:21:56,290 First of all, the joint value because we changed and get new joint value. 390 00:21:56,300 --> 00:22:04,580 I am sorry and we then pass from which, no, the joint, which joint changed. 391 00:22:05,150 --> 00:22:10,790 But we know this half by looking at, for example, choose zero controls the first joint. 392 00:22:10,790 --> 00:22:11,120 Yes. 393 00:22:11,330 --> 00:22:16,880 So if it changes cues zero slider change, then we know that joint one is change. 394 00:22:16,880 --> 00:22:21,470 So the pass, it's no this will help us in order to do some calculations, OK? 395 00:22:21,680 --> 00:22:24,770 As you can see, we are doing the same for each of this slider. 396 00:22:24,860 --> 00:22:27,200 OK, now let's see. 397 00:22:27,200 --> 00:22:29,820 What's our draw robot function? 398 00:22:29,840 --> 00:22:30,170 OK? 399 00:22:30,320 --> 00:22:32,360 This is our start-up function, OK? 400 00:22:32,540 --> 00:22:34,100 We will seat, as you can see. 401 00:22:34,100 --> 00:22:35,750 Let me explain this one for an example. 402 00:22:35,990 --> 00:22:44,140 This is in order to put the limits for the to put the limits for the robot manipulator. 403 00:22:44,240 --> 00:22:44,750 OK. 404 00:22:45,050 --> 00:22:46,820 Excuse me for this slide. 405 00:22:46,820 --> 00:22:56,600 This, you know, because it has to change between what a minus p or p or minus two p i. 406 00:22:56,600 --> 00:23:02,000 Just say that because its angle OK generally change from minus P2P. 407 00:23:02,300 --> 00:23:06,920 So we we can put only the integer for the slide that it limits. 408 00:23:06,920 --> 00:23:08,540 So I put minus three. 409 00:23:08,810 --> 00:23:09,350 OK. 410 00:23:10,700 --> 00:23:18,410 In order to be as much, you know, how can I say as much? 411 00:23:19,250 --> 00:23:22,010 Uh, close to a pi lets. 412 00:23:22,010 --> 00:23:23,000 You can do also. 413 00:23:23,000 --> 00:23:29,320 You can do a minus four to four, but not eat to the minus three point minus PI two Pi. 414 00:23:29,330 --> 00:23:29,610 OK? 415 00:23:29,750 --> 00:23:32,360 By mapping, you can do this. 416 00:23:32,720 --> 00:23:41,810 But I didn't do that because I want to do that just simply to withdraw the robot. 417 00:23:42,290 --> 00:23:45,560 The other things are just accessories, and you can do it by yourself. 418 00:23:45,570 --> 00:23:47,870 It's very easy to do these kind of things. 419 00:23:48,140 --> 00:23:48,500 OK? 420 00:23:48,530 --> 00:23:55,730 You can even look for the limits of the robot on the blade rocket, for example, I didn't take into 421 00:23:55,730 --> 00:23:57,080 account the limits of the joint. 422 00:23:57,080 --> 00:23:59,210 I just write minus pipeline. 423 00:23:59,420 --> 00:24:05,000 OK, you can move it if it's minus Pi Pi, the robot, the manipulator, even though it's links or joints 424 00:24:05,000 --> 00:24:06,320 are cold anyway. 425 00:24:06,860 --> 00:24:09,740 Um, we we change it in this way. 426 00:24:10,160 --> 00:24:10,650 OK. 427 00:24:10,680 --> 00:24:20,600 And then we just put the limits for the axis OK x limited by the Medsafe limit for our this graph. 428 00:24:20,960 --> 00:24:21,530 OK. 429 00:24:22,040 --> 00:24:23,720 Then what we are doing? 430 00:24:23,730 --> 00:24:28,530 OK, let's go to the code section, which is Draw Robot. 431 00:24:28,560 --> 00:24:28,970 OK. 432 00:24:29,210 --> 00:24:31,100 OK, let me just show you this one. 433 00:24:31,400 --> 00:24:34,690 Also, this is this is link lengths, OK? 434 00:24:34,700 --> 00:24:37,430 We have seen for the robot manipulator this link lengths. 435 00:24:37,430 --> 00:24:39,590 You can change link legs here, OK? 436 00:24:39,650 --> 00:24:40,840 These are emitters. 437 00:24:40,850 --> 00:24:43,700 OK, just put arbitrary numbers. 438 00:24:43,700 --> 00:24:47,900 Don't judge me because of this, then this is nothing. 439 00:24:47,900 --> 00:24:54,920 But these are initial values for our, um, joint centers. 440 00:24:54,920 --> 00:24:55,160 OK? 441 00:24:55,190 --> 00:24:57,050 I mean, these are our joint centers. 442 00:24:57,050 --> 00:24:59,390 As we have said before, these are our joints. 443 00:25:00,020 --> 00:25:03,350 With respect to its own flame, OK, we have seen this. 444 00:25:03,680 --> 00:25:07,820 These are the joint centers with respect to their own reference frame. 445 00:25:08,630 --> 00:25:11,880 This will, however, this will take this will. 446 00:25:12,050 --> 00:25:21,620 This P will stop the joint values with respect, not with respect to its own frame, but each joint 447 00:25:21,630 --> 00:25:24,770 center calls with respect to the base frame. 448 00:25:24,980 --> 00:25:31,520 But first, I will make it equal to the be equal to this one, but we will update it. 449 00:25:31,700 --> 00:25:32,150 Yes. 450 00:25:32,150 --> 00:25:32,680 Okay. 451 00:25:34,840 --> 00:25:38,410 This is our homogeneous transformation mattresses, OK? 452 00:25:39,140 --> 00:25:44,510 This is a four by four because homogeneous transformation matrix is four by four and four six because 453 00:25:44,670 --> 00:25:45,780 for each of the joints. 454 00:25:45,800 --> 00:25:46,160 OK. 455 00:25:46,340 --> 00:25:50,690 It will hold a homogeneous transformation between two subsequent. 456 00:25:50,840 --> 00:25:51,230 OK. 457 00:25:51,260 --> 00:25:56,600 Be careful between two subsequent frames, not between the base frame and the given frame. 458 00:25:56,930 --> 00:25:57,290 OK. 459 00:25:57,450 --> 00:26:02,910 And this is all your did node heartwarming parameter table. 460 00:26:02,930 --> 00:26:06,110 OK, well then what we are doing, we have to first. 461 00:26:06,530 --> 00:26:08,570 At the first time, we have to draw. 462 00:26:09,130 --> 00:26:12,620 Um, we have to draw the robot moments later. 463 00:26:12,650 --> 00:26:13,000 Yes. 464 00:26:13,260 --> 00:26:20,060 At initial time versus startup, we have to draw the robot because if you don't draw, then we will 465 00:26:20,450 --> 00:26:21,280 see the robot. 466 00:26:21,290 --> 00:26:25,640 We will throw the robot on the after moving the slide sliders. 467 00:26:25,850 --> 00:26:27,840 And we don't want this, OK? 468 00:26:27,860 --> 00:26:32,870 We have to we want to know the robot in initial position first, OK? 469 00:26:33,140 --> 00:26:38,300 And we are doing what in order to do that we are, we have to create a homogeneous transformation. 470 00:26:38,300 --> 00:26:40,960 Methodists, we send it there. 471 00:26:41,570 --> 00:26:42,350 This is nothing. 472 00:26:42,680 --> 00:26:46,130 This is this is abbreviated since OK. 473 00:26:46,160 --> 00:26:47,900 I will not go deep into this one. 474 00:26:48,080 --> 00:26:54,560 But if you know C++ because the here classes are used, you know you have to know this easily. 475 00:26:55,610 --> 00:26:56,030 OK. 476 00:26:56,060 --> 00:26:58,190 These are language related things. 477 00:26:58,190 --> 00:26:59,990 So I have a lot go into these details. 478 00:26:59,990 --> 00:27:01,970 OK, your vpas. 479 00:27:01,970 --> 00:27:09,560 First of all the teacher angle, I will assume the teacher angle at zero, OK, because at first we 480 00:27:09,560 --> 00:27:10,610 are zero. 481 00:27:10,910 --> 00:27:11,360 OK? 482 00:27:11,780 --> 00:27:14,870 The slider will be in zero position, so it will read zero. 483 00:27:15,110 --> 00:27:22,970 Then we I have said I send a D and I four parameters in order to calculate homogeneous transformation 484 00:27:22,970 --> 00:27:27,960 matrix for each of the joints, and I stored the tommasini homogeneous transformation mattresses. 485 00:27:27,980 --> 00:27:35,480 OK, then I'm doing what I'm doing just after I have initialized this adjacency mattresses, I draw 486 00:27:35,720 --> 00:27:36,950 my robot manipulator. 487 00:27:37,190 --> 00:27:41,810 Don't I just say zero here? 488 00:27:42,020 --> 00:27:44,900 Zero, because this is our joint value. 489 00:27:44,910 --> 00:27:48,740 One is the joint number. 490 00:27:48,740 --> 00:27:56,750 But this is not needed actually, because this draw robot draw the whole robot's structure. 491 00:27:57,890 --> 00:28:06,750 Because as I assign parameter input parameters like that for the draw robot, I have to send some value 492 00:28:06,800 --> 00:28:08,750 and I just send zero and one. 493 00:28:08,760 --> 00:28:16,070 But for now, I mean, for this step, it is not important what you have put inside because you didn't 494 00:28:16,070 --> 00:28:17,660 even changed the slider. 495 00:28:17,810 --> 00:28:23,510 However, this shows how much is the slider changed, how its value and which slider is changed. 496 00:28:23,810 --> 00:28:28,370 But we didn't change even any slider, so I just put random numbers zero and one. 497 00:28:28,430 --> 00:28:28,770 OK. 498 00:28:29,160 --> 00:28:30,110 And there's no need 499 00:28:33,050 --> 00:28:35,240 to stick that here to make it the problem. 500 00:28:35,660 --> 00:28:41,360 OK, if we do our robot now, let's see what's our true robot function? 501 00:28:41,390 --> 00:28:41,930 OK. 502 00:28:44,000 --> 00:28:45,380 Here is our draw. 503 00:28:46,220 --> 00:28:50,210 First of all, this is calculate homogeneous transformation matrix, which return homogeneous transformation 504 00:28:50,210 --> 00:28:50,570 matrix. 505 00:28:50,570 --> 00:28:53,420 I just put the formula of this. 506 00:28:53,420 --> 00:28:54,500 I will make it like that. 507 00:28:54,500 --> 00:28:58,850 OK, as you can see, this is nothing but the formula for the calculation of homogeneous transformation 508 00:28:58,850 --> 00:29:04,820 matrix from the given the parameters and in the draw robot, we get the teeter angle. 509 00:29:04,880 --> 00:29:09,740 OK, Hall, what if the fear, if we change, for example, a slider tool? 510 00:29:09,890 --> 00:29:11,480 What's its key to now? 511 00:29:12,080 --> 00:29:12,390 OK. 512 00:29:12,410 --> 00:29:14,740 Because we have to know what it's T to yes. 513 00:29:14,990 --> 00:29:21,320 Um, then which slider is changed and the changing slider is number two. 514 00:29:21,890 --> 00:29:27,950 OK, then we are calculating the homogeneous transformation matrix. 515 00:29:27,950 --> 00:29:30,950 OK for this joint only. 516 00:29:31,100 --> 00:29:33,110 OK, because this join changed. 517 00:29:33,110 --> 00:29:33,670 OK? 518 00:29:33,980 --> 00:29:35,720 These joints join changed. 519 00:29:35,720 --> 00:29:41,130 So it's a homogeneous transformation matrix has to change also, because for others, it doesn't change. 520 00:29:41,510 --> 00:29:42,460 D doesn't change. 521 00:29:42,470 --> 00:29:45,920 It doesn't change all photos and changed anyway. 522 00:29:46,640 --> 00:29:48,800 There is, therefore the homogeneity is homogeneous. 523 00:29:48,800 --> 00:29:52,070 Photo with a homogeneous transformation matters. 524 00:29:52,070 --> 00:29:58,640 In this case, the only changing available will be theta, and this variable is changed for only. 525 00:29:59,530 --> 00:30:01,300 MS joins, OK. 526 00:30:01,370 --> 00:30:08,000 The M.S. here, for example, if this is the second slider, then for the second joint it is changed. 527 00:30:08,020 --> 00:30:08,320 OK? 528 00:30:08,980 --> 00:30:19,030 It's for the searching joint because we started from two zero, then we will just update this and homogeneous 529 00:30:19,030 --> 00:30:24,250 transformation matrix in our mattresses of homogeneous transformation matrix. 530 00:30:24,640 --> 00:30:32,060 OK, then what we are doing, we are just initializing our values again. 531 00:30:32,080 --> 00:30:41,440 I mean, you know, you know what I have said, I have said that during the was we were watching the 532 00:30:41,440 --> 00:30:43,110 picture of the robot manipulator. 533 00:30:43,120 --> 00:30:49,630 We have said that if ends joined changes, then which links has to change, not the previous ones, 534 00:30:49,630 --> 00:30:51,940 because they are not affected, but after a while. 535 00:30:51,950 --> 00:30:55,070 So we are starting from an up to the end. 536 00:30:55,090 --> 00:30:55,540 Six. 537 00:30:55,720 --> 00:31:01,300 And we update the positions of all the if a phrase. 538 00:31:01,600 --> 00:31:10,100 First of all, we are not updating but resetting the positions of these points. 539 00:31:10,120 --> 00:31:10,630 OK. 540 00:31:10,990 --> 00:31:19,390 Then after we have done this, OK, uh, what we are doing, we are just 541 00:31:21,820 --> 00:31:24,050 taking this. 542 00:31:25,780 --> 00:31:26,360 OK? 543 00:31:26,710 --> 00:31:31,240 Because below you can see why we are doing this one. 544 00:31:31,240 --> 00:31:40,840 Because if we don't do it in this way, then this the links lengths will be increase increase increase 545 00:31:41,080 --> 00:31:45,130 because this will save as this is global variable. 546 00:31:45,130 --> 00:31:45,970 I mean, global. 547 00:31:46,210 --> 00:31:47,920 This is not global. 548 00:31:48,160 --> 00:31:57,280 It's not correct term in terms of programming, but as it is the parameter for the know, not parodied 549 00:31:57,610 --> 00:31:58,870 this class property. 550 00:31:58,870 --> 00:32:09,220 OK, it's a private variable and belong to the class and of what will be its value will be will be the 551 00:32:09,220 --> 00:32:11,210 same throughout the class instance. 552 00:32:11,230 --> 00:32:11,770 OK. 553 00:32:12,070 --> 00:32:19,000 So that's why it's value as we multiply it with the homogeneous transformation matrix, it will be always 554 00:32:19,000 --> 00:32:21,160 updated and it will always increase. 555 00:32:21,340 --> 00:32:24,880 So we have to reset it at each iteration in order to avoid this. 556 00:32:25,630 --> 00:32:28,360 Then what we are doing again, we are starting. 557 00:32:28,360 --> 00:32:30,970 As we have said, the changes happen. 558 00:32:31,480 --> 00:32:42,220 If the endpoint is changed, the change must be done for the for the joints after the change. 559 00:32:42,220 --> 00:32:42,770 The joint. 560 00:32:42,790 --> 00:32:43,210 OK. 561 00:32:44,410 --> 00:32:48,350 So what we are doing first, we are calculating, uh, the H. 562 00:32:48,370 --> 00:32:50,440 For example, if the force joined is change. 563 00:32:50,440 --> 00:32:53,500 If we are calculating what is the transformation matrix h four zero? 564 00:32:53,740 --> 00:32:55,420 Well, OK with respect to the base frame. 565 00:32:55,600 --> 00:33:01,420 And then we apply this to our um point. 566 00:33:01,450 --> 00:33:02,020 OK. 567 00:33:02,680 --> 00:33:10,870 Because our transformation mattresses in mattresses, sheets of our all the uh, they are multiplication. 568 00:33:10,870 --> 00:33:12,100 We also change. 569 00:33:12,610 --> 00:33:22,060 Uh, so the so that we are, then we when we applied this homogeneous transformation matrix to the UM 570 00:33:23,230 --> 00:33:29,520 to the each point in order to obtain it to each of the joint centers in order to obtain new points. 571 00:33:29,530 --> 00:33:29,920 OK? 572 00:33:29,950 --> 00:33:36,540 After the angle has been changed, if you will get the updated values for the Joint Centers, OK, then 573 00:33:36,930 --> 00:33:38,140 this this. 574 00:33:38,380 --> 00:33:39,160 This is nothing. 575 00:33:39,160 --> 00:33:45,820 But this is for just in order to obtain the joint, um, central values. 576 00:33:45,820 --> 00:33:54,220 OK, because we will draw, uh, this is by this way, we are just obtaining the joint values, OK, 577 00:33:54,220 --> 00:33:56,080 because we will plot them in. 578 00:33:56,440 --> 00:33:57,880 You can do without this one. 579 00:33:57,880 --> 00:34:02,860 Also by making note making this x y z body, it is make life. 580 00:34:03,220 --> 00:34:08,860 It makes life easier during the plot using plot three function because plot summary function weights 581 00:34:08,860 --> 00:34:14,320 all the X in one vector, all the YS in one vector add all the assets in one vector. 582 00:34:14,330 --> 00:34:23,980 OK, and if you say that y we have started from two and seven because as you can see, I have we have 583 00:34:24,340 --> 00:34:28,180 six points, OK, including the in the affected. 584 00:34:28,330 --> 00:34:34,450 But in order to take into account the Bayes joint, OK? 585 00:34:34,480 --> 00:34:38,560 The base one, which is zero, which is always zero zero zero, doesn't change. 586 00:34:38,890 --> 00:34:49,180 I have made it the seven and I started to apply changes only after only, including second and the joints 587 00:34:49,180 --> 00:34:50,020 after the second. 588 00:34:50,020 --> 00:34:52,330 OK, because base preview will never change. 589 00:34:52,330 --> 00:34:54,940 It will be always position will be zero zero zero. 590 00:34:55,180 --> 00:34:58,420 OK, so it will be the first one will be always zero zero zero. 591 00:34:58,720 --> 00:34:59,050 So. 592 00:34:59,760 --> 00:35:06,210 When we applaud, the robots will be corrected, never will be plotted correctly, then we are doing 593 00:35:06,210 --> 00:35:08,490 the joint positions as a circle. 594 00:35:08,730 --> 00:35:13,080 We are throwing for the first joint, OK, which is zero zero zero b's joint. 595 00:35:13,080 --> 00:35:16,440 OK, and we are then dropping the other joints also. 596 00:35:16,710 --> 00:35:17,190 OK. 597 00:35:18,480 --> 00:35:27,660 Here, as the last joint is as the last frame is not joint, but in the fact that I have stopped at 598 00:35:27,660 --> 00:35:28,610 51, OK? 599 00:35:29,570 --> 00:35:30,220 And doesn't. 600 00:35:30,240 --> 00:35:32,570 They didn't throw a circle in the last joint. 601 00:35:32,580 --> 00:35:36,660 OK, because it is not a joint, it's in the filter and then we throw gripper. 602 00:35:36,900 --> 00:35:39,500 And this is our true gripper function. 603 00:35:39,510 --> 00:35:40,020 OK? 604 00:35:40,050 --> 00:35:41,340 Here is the gripper. 605 00:35:41,580 --> 00:35:43,170 We choose our offset. 606 00:35:43,380 --> 00:35:47,290 Then we calculated again, as I have said, H6 zero. 607 00:35:47,310 --> 00:35:53,340 OK, then what we are doing, we just apply transformation to our point. 608 00:35:53,520 --> 00:35:55,470 This is our homogeneous transformation matrix. 609 00:35:55,710 --> 00:35:57,650 This is our offset values. 610 00:35:57,660 --> 00:36:01,830 OK, what is a b c d in its own frame? 611 00:36:01,830 --> 00:36:08,200 But we are converted to them using this h matrix to base frame? 612 00:36:08,250 --> 00:36:10,380 OK, and then we just plotted them. 613 00:36:11,700 --> 00:36:12,090 OK. 614 00:36:13,500 --> 00:36:13,810 OK. 615 00:36:13,830 --> 00:36:15,410 This is transfer point function. 616 00:36:15,420 --> 00:36:19,470 It is nothing but takes the transformation matrix. 617 00:36:19,470 --> 00:36:21,990 This homogeneous transformation metric takes point. 618 00:36:22,020 --> 00:36:22,470 OK. 619 00:36:22,500 --> 00:36:23,540 The coordinates point. 620 00:36:23,550 --> 00:36:23,900 OK. 621 00:36:24,150 --> 00:36:26,790 This is three by one x y z. 622 00:36:26,970 --> 00:36:30,140 But we have to make it in homogeneous coordinates point. 623 00:36:30,150 --> 00:36:34,650 OK, so we add one in order to transform it using a homogeneous transformation matrix. 624 00:36:34,650 --> 00:36:40,530 Because homogeneous transformation matrix is four by four, but petty when it's four, it was given 625 00:36:40,530 --> 00:36:41,340 is three by one. 626 00:36:41,340 --> 00:36:44,760 So we add one in order to make it homogeneous. 627 00:36:44,760 --> 00:36:46,030 OK, coordinate. 628 00:36:46,030 --> 00:36:47,490 Then we multiply it v. 629 00:36:47,910 --> 00:36:52,560 So by this way, we are transforming it, and then we take the first three ones. 630 00:36:52,560 --> 00:36:56,600 OK, because this is x y z and the last one was one v. 631 00:36:57,660 --> 00:37:04,170 We threw out the one convert a homogeneous corner to the normal coordinates and sent them back. 632 00:37:04,860 --> 00:37:06,660 OK, perfect. 633 00:37:06,660 --> 00:37:08,250 You know the plot in MATLAB. 634 00:37:09,000 --> 00:37:13,530 So let's run this after so much time. 635 00:37:13,560 --> 00:37:22,200 OK, now first of all, let me say to you that when I make this go like this meager, I don't know why 636 00:37:22,200 --> 00:37:24,570 I couldn't figure go to how it has been done. 637 00:37:25,830 --> 00:37:32,820 But the last one, this fifth one is separated from these others and I don't care about it too much 638 00:37:33,120 --> 00:37:36,600 because the robot is working as intended as a robot. 639 00:37:36,660 --> 00:37:43,070 It seems very small because you can correct it by changing these limits. 640 00:37:43,080 --> 00:37:43,620 OK? 641 00:37:44,580 --> 00:37:46,260 I will not do that, but you can. 642 00:37:47,100 --> 00:37:48,030 Maybe let's do that. 643 00:37:49,020 --> 00:37:49,770 Let me just. 644 00:37:50,550 --> 00:37:53,490 No, let me just to run. 645 00:37:53,880 --> 00:37:56,940 OK, go one. 646 00:37:57,180 --> 00:37:58,120 Okay. 647 00:37:58,150 --> 00:38:01,740 Uh, one and one. 648 00:38:01,890 --> 00:38:03,120 Let me see what will happen. 649 00:38:03,120 --> 00:38:03,840 No. 650 00:38:04,320 --> 00:38:06,480 It should show it a bit bigger. 651 00:38:06,990 --> 00:38:07,530 No. 652 00:38:09,630 --> 00:38:10,200 Yeah. 653 00:38:10,410 --> 00:38:18,210 As our robot is small, it again shows it like that. 654 00:38:18,210 --> 00:38:20,220 But you can see it's a bit bigger. 655 00:38:20,490 --> 00:38:24,480 Yeah, you can buy a, uh, your mouse. 656 00:38:24,480 --> 00:38:26,730 You can make it closer and I will use this one. 657 00:38:26,760 --> 00:38:31,920 No need to make it to change the limits, but you can change a game to 0.5. 658 00:38:31,920 --> 00:38:33,930 It will, I think, show much better way. 659 00:38:34,200 --> 00:38:34,530 OK. 660 00:38:34,650 --> 00:38:39,570 Let's now, as you can see, these these are our joints. 661 00:38:39,600 --> 00:38:40,020 OK. 662 00:38:40,320 --> 00:38:44,610 These are our joints, these circles and this are in the sector at the end. 663 00:38:45,060 --> 00:38:46,930 And these are all realistic robots. 664 00:38:46,930 --> 00:38:49,560 So let's change the first journal and see what's happening. 665 00:38:49,560 --> 00:38:51,090 As you can see, it rotates. 666 00:38:51,330 --> 00:38:52,200 Oh, OK. 667 00:38:52,740 --> 00:38:54,330 It rotates as expected. 668 00:38:54,900 --> 00:38:57,870 Let's change this joint, OK? 669 00:38:57,960 --> 00:39:02,160 This is the same way it goes out because of this one. 670 00:39:02,160 --> 00:39:03,720 If you make it like that, OK? 671 00:39:03,900 --> 00:39:05,840 Zoom out, we will see the robot again. 672 00:39:05,850 --> 00:39:07,560 OK, it moves as expected. 673 00:39:07,560 --> 00:39:08,040 Perfect. 674 00:39:08,370 --> 00:39:10,220 Then let's change this joint. 675 00:39:10,260 --> 00:39:10,740 OK? 676 00:39:11,130 --> 00:39:13,330 This also moves as expected. 677 00:39:13,350 --> 00:39:15,830 OK, then let's change this. 678 00:39:15,840 --> 00:39:19,390 As you can see, look at the end effector see and the factor is rotating. 679 00:39:19,410 --> 00:39:20,220 OK. 680 00:39:20,670 --> 00:39:23,310 This is also working correctly. 681 00:39:23,490 --> 00:39:23,940 OK. 682 00:39:24,270 --> 00:39:25,920 Let's change this one. 683 00:39:25,920 --> 00:39:30,720 Also, OK, if this works correctly, and let's change this one. 684 00:39:30,720 --> 00:39:34,530 Also, as you can see the amount of play that rotates again and the factor? 685 00:39:35,100 --> 00:39:35,560 OK. 686 00:39:36,600 --> 00:39:44,580 I think we have finished with our robot manipulator and you can see how you can create your robot manipulator. 687 00:39:44,820 --> 00:39:46,350 Uh, OK. 688 00:39:47,490 --> 00:39:48,340 In 3D. 689 00:39:48,360 --> 00:39:50,700 Here is your 3D robot manipulator. 690 00:39:51,330 --> 00:39:52,160 That's perfect.