1 00:00:00,120 --> 00:00:00,570 OK. 2 00:00:02,970 --> 00:00:09,540 In this video, we will learn how we will calculate forward kinematics for dramatic manipulator. 3 00:00:10,530 --> 00:00:20,980 Indeed, we can calculate forward kinematics using geometrical approach or by in a manual way, without 4 00:00:20,980 --> 00:00:25,260 any systematic way or without some specific method. 5 00:00:25,710 --> 00:00:27,120 But it would be very hard. 6 00:00:27,570 --> 00:00:34,340 What we can do, for example, we could do assign frames, the robotic manipulator, for example. 7 00:00:34,350 --> 00:00:35,530 Let's take this one. 8 00:00:35,550 --> 00:00:36,030 OK. 9 00:00:37,470 --> 00:00:44,930 We could assign for each joint coordinate system, OK, for example, for this one, for this one. 10 00:00:44,940 --> 00:00:47,010 OK, for this excuse me. 11 00:00:47,430 --> 00:00:52,080 And for this one, for each of the joint. 12 00:00:52,080 --> 00:00:55,740 OK, we could do assign Gordon Frames. 13 00:00:56,010 --> 00:01:05,820 And then we could find, therefore four homogeneous transformation metrics for each one. 14 00:01:05,820 --> 00:01:07,050 For example, this is joint. 15 00:01:08,310 --> 00:01:09,360 This is joint one. 16 00:01:09,360 --> 00:01:10,170 This is drawn to. 17 00:01:10,200 --> 00:01:12,060 This is three or let's do it. 18 00:01:12,060 --> 00:01:13,290 Not joint, but framed. 19 00:01:13,290 --> 00:01:14,480 This is frame zero. 20 00:01:14,490 --> 00:01:15,130 This is one. 21 00:01:15,150 --> 00:01:15,770 This is two. 22 00:01:15,780 --> 00:01:16,500 This is three. 23 00:01:16,800 --> 00:01:22,800 Then we could find, for example, h one zero, excuse me, eight zero one. 24 00:01:22,980 --> 00:01:26,370 OK, well, let me just h one zero. 25 00:01:26,700 --> 00:01:31,680 Then we could find that between this one h two one. 26 00:01:31,890 --> 00:01:32,430 OK. 27 00:01:32,670 --> 00:01:41,580 So from homogeneous transformation from two to one, then we could find for this one h three two OK. 28 00:01:41,610 --> 00:01:49,530 And for the end effector, we also assign the fourth coordinate system and we could run it for between 29 00:01:49,530 --> 00:01:53,700 h between the frame three and four eight four three. 30 00:01:54,090 --> 00:01:54,540 OK. 31 00:01:54,690 --> 00:01:57,930 We could conclude this in a manual way. 32 00:01:58,200 --> 00:02:00,290 OK, and then what we could? 33 00:02:00,600 --> 00:02:01,620 What could we do? 34 00:02:01,630 --> 00:02:04,560 We would mark multiply each of these. 35 00:02:04,740 --> 00:02:10,200 Excuse me, in each of these homogeneous transformations, mattresses with each other. 36 00:02:10,210 --> 00:02:18,780 And this is three two times h for three, and we could find the homogeneous transformation matrix of 37 00:02:18,780 --> 00:02:20,620 h four zero. 38 00:02:20,640 --> 00:02:21,030 OK. 39 00:02:21,060 --> 00:02:24,930 This would give the relation between the base frame and end effector frame. 40 00:02:25,260 --> 00:02:32,280 However, it would be very difficult to do that without in a systematic way, and it would also be very 41 00:02:32,280 --> 00:02:38,820 difficult when we would do it for a more difficult, more complex robotic manipulators. 42 00:02:39,030 --> 00:02:43,860 So what we will do, we will we will use almost the same logic. 43 00:02:44,070 --> 00:02:49,950 But instead of these assigning frames and calculating homogeneous transformation methods, this will 44 00:02:49,950 --> 00:02:52,850 be based on some method. 45 00:02:52,920 --> 00:02:53,370 OK. 46 00:02:53,580 --> 00:02:58,420 It's going to not be in some stochastic method. 47 00:02:58,440 --> 00:02:58,860 OK. 48 00:02:59,790 --> 00:03:06,720 So here is we will use the H Convention in order to calculate forward kinematics. 49 00:03:06,750 --> 00:03:07,140 OK. 50 00:03:07,500 --> 00:03:08,220 We will use. 51 00:03:12,820 --> 00:03:19,720 The convention and we have see, though, why we use the commission because it is systematic approach 52 00:03:19,720 --> 00:03:27,100 and it makes us easier to calculate the four kinematics, even for the difficult robot manipulators. 53 00:03:27,610 --> 00:03:36,630 OK, then what are the steps to calculate the age forward kinematics using the convention? 54 00:03:36,640 --> 00:03:42,280 The first what we have to do, we have to assign a frame to each of the joints. 55 00:03:42,310 --> 00:03:42,700 OK. 56 00:03:44,200 --> 00:03:49,330 As we have said before, we have to assign a frame fixed frame to each of the joints. 57 00:03:49,570 --> 00:03:57,820 Surely this assigning of frame will not be in an arbitrary way, but the age conventions specified method 58 00:03:57,820 --> 00:04:02,260 to assign frames to the joint of the robotic manipulators. 59 00:04:02,560 --> 00:04:10,630 Then what we will do, we will do calculate the age parameters or the age parameter table, which is 60 00:04:10,630 --> 00:04:14,530 four parameters four parameters OK for parameters. 61 00:04:15,940 --> 00:04:21,160 But then we will use by we will calculate this homogeneous transformation method. 62 00:04:21,160 --> 00:04:23,170 Is this using these four parameters? 63 00:04:23,440 --> 00:04:29,530 Then we will surely multiply these homogeneous transformation mattresses with each other in order to 64 00:04:29,530 --> 00:04:37,030 obtain relation between base frame and in the picture frame, or between base frame to some other and 65 00:04:37,030 --> 00:04:42,850 point on the robotic manipulator or between any point any frame of the robotic manipulator. 66 00:04:43,330 --> 00:04:50,650 So, OK, let's continue with how we will assign the rule of assigning frames to the robotic manipulator. 67 00:04:50,740 --> 00:04:51,160 OK. 68 00:04:51,810 --> 00:04:54,560 And this is the rule how we will do this. 69 00:04:54,580 --> 00:04:57,650 First, we will assign zit access. 70 00:04:57,670 --> 00:05:05,470 OK, here is it by axis because we will have more than one joint OK for each eye joint, we will assign 71 00:05:05,480 --> 00:05:08,440 Z I axis for real joins. 72 00:05:08,440 --> 00:05:09,070 Excuse me. 73 00:05:09,370 --> 00:05:11,340 This is not a trivial joint. 74 00:05:11,380 --> 00:05:17,900 We will assign the z axis in the direction of rotation, OK? 75 00:05:19,210 --> 00:05:26,230 Because as you know, the joints provide the rotation about some axis and we will choose this direction 76 00:05:26,230 --> 00:05:29,890 of rotation as a z axis. 77 00:05:30,160 --> 00:05:38,320 Then for prismatic joint, we will choose that axis as the translational motion direction. 78 00:05:38,350 --> 00:05:38,810 OK. 79 00:05:39,040 --> 00:05:46,110 So anyway, for z axis, it has to be in the joint direction of motion again. 80 00:05:46,450 --> 00:05:51,580 So let's see in in this example how we will assign z axis. 81 00:05:51,820 --> 00:05:59,740 So for the first joint, this joint, as you can see, is roll a joint and provide rotation about this 82 00:05:59,740 --> 00:06:00,260 axis. 83 00:06:00,280 --> 00:06:00,700 OK. 84 00:06:00,940 --> 00:06:03,400 It provides rotation about this axis. 85 00:06:03,910 --> 00:06:13,240 So as you let me just say, not about this, OK, this axis, it provides rotation about this active. 86 00:06:13,250 --> 00:06:17,590 So as we have said, so this joint rotates in this way. 87 00:06:17,620 --> 00:06:18,100 OK. 88 00:06:19,660 --> 00:06:22,960 So what we will choose then z axis. 89 00:06:23,980 --> 00:06:31,390 Surely it will be these taxes because they reveal that joined the direction of motion is about this 90 00:06:31,390 --> 00:06:31,750 axis. 91 00:06:31,750 --> 00:06:35,980 So this will be our rotation, our z axis. 92 00:06:35,980 --> 00:06:40,150 So this is four frames zero, this will be zero zero. 93 00:06:40,270 --> 00:06:49,150 OK, direction directional that zero, then what we will do, we will assign the the z axis for the 94 00:06:49,150 --> 00:06:49,960 second joint. 95 00:06:49,960 --> 00:06:57,110 As you can see, the second joint is also rotational joint and it will rotate all about this axis. 96 00:06:57,130 --> 00:06:57,760 OK. 97 00:06:57,790 --> 00:07:00,220 About this axis and what we can do. 98 00:07:00,550 --> 00:07:02,810 We can assign it in this way. 99 00:07:02,830 --> 00:07:07,350 OK, because this is the direction of motion. 100 00:07:07,360 --> 00:07:10,570 OK, the joint will rotate in this way. 101 00:07:10,720 --> 00:07:11,140 OK. 102 00:07:11,170 --> 00:07:12,780 This is theta zero. 103 00:07:13,060 --> 00:07:14,560 This is T to one. 104 00:07:14,590 --> 00:07:15,010 OK. 105 00:07:15,310 --> 00:07:17,050 This will provide this rotation. 106 00:07:17,410 --> 00:07:24,490 And as you can see, the third joint is prismatic joint. 107 00:07:24,520 --> 00:07:24,910 OK. 108 00:07:25,090 --> 00:07:28,740 So it moves in this direction upward and downward. 109 00:07:28,750 --> 00:07:29,110 OK? 110 00:07:29,140 --> 00:07:33,370 It it it provide translational motion like upward and downward. 111 00:07:33,790 --> 00:07:38,500 And so the direction of motion is this one? 112 00:07:38,500 --> 00:07:42,790 Yeah, it translates over this axis, it translates or this axis. 113 00:07:42,790 --> 00:07:50,770 So the z axis will be in this direction and we will choose the z axis for this one as this way. 114 00:07:50,800 --> 00:07:51,100 OK. 115 00:07:51,340 --> 00:07:56,930 This is the direction of the make it a bit shorter. 116 00:07:57,020 --> 00:07:57,220 OK. 117 00:07:57,430 --> 00:08:02,530 This is the direction of translation, so the direction of motion. 118 00:08:02,530 --> 00:08:05,260 So we will do this as z 119 00:08:07,930 --> 00:08:08,560 z to. 120 00:08:08,740 --> 00:08:09,310 OK. 121 00:08:09,370 --> 00:08:09,750 Yeah. 122 00:08:09,760 --> 00:08:11,290 The zeros, it's one and z. 123 00:08:12,150 --> 00:08:12,520 OK. 124 00:08:12,810 --> 00:08:20,670 This the fourth, the joint is also rotational joint, so we will assign and surely we have to find 125 00:08:20,700 --> 00:08:23,760 a full, first of all, what is the direction of rotation? 126 00:08:23,760 --> 00:08:28,660 And in this case, the rotation joint provides rotation in this way. 127 00:08:28,680 --> 00:08:29,130 OK. 128 00:08:30,660 --> 00:08:33,330 This is the rotation it provides. 129 00:08:33,630 --> 00:08:37,260 OK, and I hope you can find the direction of rotation. 130 00:08:37,980 --> 00:08:48,120 Just put your finger in, use your right hand and put your thumb in this way and the other cool other 131 00:08:48,570 --> 00:08:49,420 fingers. 132 00:08:49,470 --> 00:08:50,160 OK. 133 00:08:50,190 --> 00:08:58,020 I cannot draw in a good way, but curl your fingers in this way, and this finger will provide the axis 134 00:08:58,020 --> 00:08:59,580 of rotation and the curl. 135 00:08:59,580 --> 00:09:05,960 The fingers will provide you the the rotation. 136 00:09:05,970 --> 00:09:11,500 OK, so in this case, if you curl your fingers, it will be something like that. 137 00:09:11,550 --> 00:09:14,400 This will be your fingers because it is rotated in this way. 138 00:09:14,400 --> 00:09:17,730 Then if it is rotated, then your sum will be in this direction. 139 00:09:18,000 --> 00:09:23,160 So the direction of rotation is in the same direction, which is like that. 140 00:09:25,350 --> 00:09:38,190 OK, so this was the tool and this is the direction of rotation, and we can choose it in this way. 141 00:09:39,600 --> 00:09:40,050 OK? 142 00:09:40,410 --> 00:09:44,550 You can show that shows it in upward direction or downward direction. 143 00:09:44,910 --> 00:09:45,930 It doesn't differ. 144 00:09:46,140 --> 00:09:47,720 The only thing matters. 145 00:09:47,730 --> 00:09:55,470 It should be if it should be in this direction in this axis. 146 00:09:56,130 --> 00:09:56,580 OK. 147 00:09:56,640 --> 00:09:57,510 This is it. 148 00:09:57,780 --> 00:09:58,440 Three. 149 00:09:58,770 --> 00:10:04,700 And then we will assign one frame for also the end effector. 150 00:10:04,710 --> 00:10:05,130 OK? 151 00:10:05,370 --> 00:10:09,570 So let's take what will happen for the end effector end effector frame. 152 00:10:11,190 --> 00:10:20,250 We will choose the end effector as the same and the vector axis the same as the Z X is the same as the 153 00:10:20,250 --> 00:10:20,940 last drawing. 154 00:10:20,970 --> 00:10:23,280 OK, so it will be downward also. 155 00:10:24,780 --> 00:10:27,060 This is our Z Fold. 156 00:10:27,510 --> 00:10:27,960 OK. 157 00:10:29,130 --> 00:10:34,350 So after we have assigned our zip axis, now we can. 158 00:10:34,710 --> 00:10:37,260 Let's first write this well. 159 00:10:37,260 --> 00:10:43,590 So this will be the translation distance will be d, uh, two. 160 00:10:44,880 --> 00:10:51,400 This will be T to three because this is rotation and the rotation will be in this direction. 161 00:10:51,420 --> 00:10:51,810 OK. 162 00:10:52,620 --> 00:10:53,370 It will rotate. 163 00:10:53,370 --> 00:10:55,530 Excuse me, it will rotate in this way. 164 00:10:56,070 --> 00:10:58,470 Not in this direction, but in this direction. 165 00:11:01,540 --> 00:11:08,210 Because as we have chosen our it in this direction, our sample will be downward. 166 00:11:08,230 --> 00:11:08,860 OK. 167 00:11:09,280 --> 00:11:16,180 Some will be downward and surely there are others fingers will be colder in this direction. 168 00:11:16,220 --> 00:11:19,600 OK, in this direction, they will curve in this direction. 169 00:11:19,600 --> 00:11:22,990 So the rotation is this way, OK? 170 00:11:22,990 --> 00:11:29,050 Because our fingers, other fingers are curled in this way, but our sump is in this axis. 171 00:11:29,920 --> 00:11:33,200 OK, so. 172 00:11:34,750 --> 00:11:42,760 So this will be also the same way as the last joint so that the rotation angle will be offered only 173 00:11:42,760 --> 00:11:43,720 in this direction. 174 00:11:44,080 --> 00:11:50,440 No, let's assign the x axis how we will do for the x axis. 175 00:11:51,100 --> 00:12:01,140 The x axis for the Earth joint will be such that it will be perpendicular to the previous z axis and 176 00:12:01,140 --> 00:12:03,690 that intersect the previous z axis. 177 00:12:03,700 --> 00:12:09,850 OK, but for the first joined us, there is no previous joint before. 178 00:12:10,240 --> 00:12:12,670 There is no previous joint for the first joint. 179 00:12:12,910 --> 00:12:18,670 We will assign x axis as a suitable for us or as we design. 180 00:12:19,090 --> 00:12:20,440 So let's try to assign. 181 00:12:20,440 --> 00:12:21,730 Does it Axis Folsom? 182 00:12:22,990 --> 00:12:28,810 Excuse me, x x is also so for the first one, we have said that we can assign it in in any direction. 183 00:12:28,810 --> 00:12:30,910 So let me note one in here. 184 00:12:32,050 --> 00:12:42,670 During assigning the axis this, we can assign axis in the valid direction for the axis is upward or 185 00:12:42,670 --> 00:12:52,460 downward or, uh, right or left, OK, or inside the page. 186 00:12:52,480 --> 00:12:52,930 OK. 187 00:12:52,960 --> 00:12:56,110 This is this shows the inside the the page. 188 00:12:56,440 --> 00:12:58,400 This is the outside of the page. 189 00:12:58,420 --> 00:12:58,840 OK. 190 00:12:59,980 --> 00:13:04,510 You can assign the valid assign direction is are these one OK? 191 00:13:06,460 --> 00:13:10,030 So we can assign it how we can assign. 192 00:13:10,030 --> 00:13:13,140 Does it axis excuse an x axis? 193 00:13:13,150 --> 00:13:19,120 As we have said, we can assign arbitrarily, but we will choose for convenience in this way for the 194 00:13:19,120 --> 00:13:19,870 x axis. 195 00:13:19,880 --> 00:13:24,310 OK, in this direction, we will choose x axis. 196 00:13:24,310 --> 00:13:35,520 So this is our x zero, then what we will choose for the joint one, we will choose x axis in this way. 197 00:13:37,420 --> 00:13:45,880 Another in think I want to node is choosing the center of the frame, OK, choosing the center of frame 198 00:13:45,880 --> 00:13:51,400 if we can choose the central frame in this way, for example, while choosing the 199 00:13:54,610 --> 00:14:02,440 center of the frame for the joint, we will use this method again for this blue sync represents the 200 00:14:02,440 --> 00:14:02,920 plane. 201 00:14:03,070 --> 00:14:03,610 OK. 202 00:14:03,850 --> 00:14:11,140 So if the z axis previews that axis and the next axis are parallel to each other and they are on the 203 00:14:11,140 --> 00:14:14,060 same frame, then we will choose. 204 00:14:14,990 --> 00:14:19,740 We can choose the central frame for the Z Eye plus one joint. 205 00:14:19,750 --> 00:14:20,080 OK? 206 00:14:20,230 --> 00:14:28,120 Excuse me, I +1 joined over the Z +1 audacity +1 OK axis. 207 00:14:28,510 --> 00:14:34,750 So any point over this axis you can choose as the center of frame. 208 00:14:35,200 --> 00:14:43,690 If the Hollywood, when they are on the same frame, the previews and the next joints are on the same 209 00:14:43,690 --> 00:14:52,750 frame and the same plane and there is it accesses are cut each other or intersect. 210 00:14:52,780 --> 00:14:56,440 So if you make it longer, let's make it longer. 211 00:14:56,740 --> 00:15:00,940 If you make it longer, for example, this is just sync. 212 00:15:01,570 --> 00:15:05,650 And there are also additional note here seemed about 3D here. 213 00:15:05,680 --> 00:15:08,360 Everything is 3D is not in 2D. 214 00:15:08,380 --> 00:15:10,750 OK, so think about the planner. 215 00:15:11,020 --> 00:15:11,560 Everything. 216 00:15:11,800 --> 00:15:15,730 Excuse me, not planner, but in the space, in 3D, not in the 2D. 217 00:15:15,730 --> 00:15:17,080 This is very important. 218 00:15:17,140 --> 00:15:20,760 You have to have 3D visualization. 219 00:15:21,040 --> 00:15:24,490 OK, so you can also make it in this way. 220 00:15:24,490 --> 00:15:30,670 As you can see, these two accesses intersect here, so the center of the frame will be here. 221 00:15:31,360 --> 00:15:36,640 So but what happens if the accesses are skewed? 222 00:15:36,670 --> 00:15:37,930 OK, is it accesses? 223 00:15:37,930 --> 00:15:38,560 Are skill? 224 00:15:38,830 --> 00:15:40,430 What does it mean SKU? 225 00:15:40,450 --> 00:15:46,630 It means that they are not on the same plane, so they don't cut each other OK. 226 00:15:47,050 --> 00:15:49,420 They are not on the same plane as you can see. 227 00:15:49,630 --> 00:15:50,280 Does it eye? 228 00:15:50,290 --> 00:15:51,670 Plus one is a boot? 229 00:15:51,700 --> 00:15:52,770 This is it, I. 230 00:15:52,990 --> 00:15:53,310 OK. 231 00:15:53,380 --> 00:15:56,170 This is another plane and this is another plane. 232 00:15:56,740 --> 00:15:58,240 Think about 3D again. 233 00:15:58,380 --> 00:16:00,520 OK, then what we will do. 234 00:16:00,800 --> 00:16:06,100 We will just again, we will make them longer, OK? 235 00:16:06,140 --> 00:16:10,940 Make them longer this way, and we will also make it in this way. 236 00:16:11,360 --> 00:16:13,280 OK, longer. 237 00:16:13,280 --> 00:16:19,910 Okay, this passes here, but it doesn't cut because this is the length of zip as it is, it is passes 238 00:16:19,910 --> 00:16:22,380 under the plane of the eye plus one. 239 00:16:22,400 --> 00:16:22,790 OK. 240 00:16:23,060 --> 00:16:26,170 They don't cut each other at this, at this part. 241 00:16:26,180 --> 00:16:31,130 OK, because this is not 2D, but this is in 3D and we have different planes. 242 00:16:32,180 --> 00:16:39,310 So what we will do, we will choose the common normal to each of these planes. 243 00:16:39,320 --> 00:16:47,330 OK, what is the common normal is the minimum distance between these two planes and the common normal. 244 00:16:47,330 --> 00:16:55,530 And we will choose the point when this common normal intersects the zip by +1 axis. 245 00:16:55,550 --> 00:17:03,160 And this happens at one place only because there is unique common plane for these two accesses the and 246 00:17:03,170 --> 00:17:06,890 the common plane, excuse me, common normal to these accesses. 247 00:17:06,890 --> 00:17:13,880 And the common normal is the distance between these two axes is that is the minimal distance and perpendicular 248 00:17:13,880 --> 00:17:20,570 to both of them, so normal to both of these accesses and provides the minimum distance between them. 249 00:17:20,600 --> 00:17:26,360 This is the common normal and this is unique for each of these four for these two accesses. 250 00:17:26,700 --> 00:17:31,940 And the point where these common normal cuts that i +1 axis. 251 00:17:31,940 --> 00:17:40,580 This is, as you can see, this plane will be the center of the frame for the eye plus once joint. 252 00:17:40,790 --> 00:17:41,210 OK. 253 00:17:42,530 --> 00:17:46,670 So this is this can be seen know difficult in theory. 254 00:17:46,670 --> 00:17:50,660 But when we put in practice, I mean, in the robot manipulator, it would be easier. 255 00:17:50,960 --> 00:17:58,520 For example, in this way, as you can see, these and these are on the same plane, OK? 256 00:17:59,030 --> 00:18:05,570 At least in this, excuse me, in this picture, they are on the same plane. 257 00:18:05,600 --> 00:18:10,310 As you can see, overall, this robot is in the same plane because it doesn't start to. 258 00:18:11,120 --> 00:18:12,410 Then it will rotate. 259 00:18:12,410 --> 00:18:16,610 For example, when the first George will rotate, then they will not be in the same plane. 260 00:18:16,610 --> 00:18:19,350 But for now they are on the same plane. 261 00:18:19,440 --> 00:18:21,110 OK, robot is straight. 262 00:18:22,460 --> 00:18:33,980 So as you can see, if they are on the same plane, then zero zero and zero one will be what parallel 263 00:18:33,980 --> 00:18:35,180 to each other. 264 00:18:35,190 --> 00:18:35,810 So what? 265 00:18:35,810 --> 00:18:39,950 We can take the center of the center for the second frame. 266 00:18:40,220 --> 00:18:41,810 Any point here, OK? 267 00:18:42,230 --> 00:18:43,520 Or go to the axis, OK? 268 00:18:43,730 --> 00:18:48,650 We can take it over here, here, here and here. 269 00:18:48,770 --> 00:18:49,310 OK. 270 00:18:49,580 --> 00:18:53,230 For example, what I mean this one, for example, you can assign X here. 271 00:18:53,240 --> 00:18:57,200 OK, that is so and there y here, OK? 272 00:18:57,380 --> 00:19:02,480 Or you can assign x axis to here. 273 00:19:02,660 --> 00:19:03,230 OK. 274 00:19:03,500 --> 00:19:04,100 Excuse me. 275 00:19:04,360 --> 00:19:08,590 For example, you can assign x axis to here and y axis like that. 276 00:19:08,600 --> 00:19:09,010 OK? 277 00:19:09,050 --> 00:19:13,670 This is and this is the opposite axis, but it is not convenient for us. 278 00:19:13,700 --> 00:19:21,680 OK, why we have to do it in this way, right in the center of frame has to be has to have an offset 279 00:19:21,680 --> 00:19:24,710 to the center of the joint. 280 00:19:25,220 --> 00:19:25,640 OK. 281 00:19:26,750 --> 00:19:30,190 Why we make the life difficult for ourselves. 282 00:19:30,410 --> 00:19:35,580 Let's make the as we can choose in the axis. 283 00:19:35,900 --> 00:19:42,440 This was our z axis, so let's see if we can choose the center of frame anywhere on the z axis. 284 00:19:42,450 --> 00:19:43,590 Let's choose it here. 285 00:19:43,610 --> 00:19:46,130 OK, so our lives will be easier. 286 00:19:46,420 --> 00:19:54,200 And what we have said for X, we have said that the X one axis has to be in the way, for example, 287 00:19:54,470 --> 00:19:57,320 four in it, it can be in this weight. 288 00:19:57,320 --> 00:20:05,420 Yeah, if we consider the permissible directions, it can be to the page. 289 00:20:05,600 --> 00:20:09,680 It can be out of the page and it can be in this direction again. 290 00:20:10,070 --> 00:20:15,320 So but let's check which are which of these directions are 291 00:20:17,900 --> 00:20:19,720 suitable for the D.H method. 292 00:20:19,730 --> 00:20:27,620 We have said that, as you can see here for the X Axis A has to be perpendicular and intersect. 293 00:20:27,650 --> 00:20:29,600 This is it I minus one axis. 294 00:20:29,870 --> 00:20:36,800 If we choose x by axis in this way, for example into the page, will it intersect the X? 295 00:20:36,820 --> 00:20:39,200 Is it a z zero axis? 296 00:20:39,200 --> 00:20:40,820 So is it a minus one axis? 297 00:20:40,820 --> 00:20:45,640 Surely not because of line, because it think about in 3D. 298 00:20:45,650 --> 00:20:50,150 If you make it longer, as you can see, it will not cut it. 299 00:20:50,570 --> 00:20:50,970 OK? 300 00:20:51,020 --> 00:20:56,540 You can see that it will cut it here, but it it will happen in 2D. 301 00:20:56,570 --> 00:20:57,080 OK. 302 00:20:57,260 --> 00:21:00,020 But if we are in 3D, it will not. 303 00:21:00,890 --> 00:21:04,700 Got it, but it will pass over the pass. 304 00:21:05,380 --> 00:21:05,770 OK. 305 00:21:07,100 --> 00:21:10,710 There will be distance between this access and success in 3-D. 306 00:21:10,760 --> 00:21:15,830 OK, so they will not intersect with each each other, so we cannot choose. 307 00:21:17,000 --> 00:21:20,300 We cannot choose this direction as our X can. 308 00:21:21,000 --> 00:21:25,700 So as our X one direction, the vehicle can be triggered by the same logic. 309 00:21:25,710 --> 00:21:31,020 We cannot choose out of the page because if we make it in this way, OK. 310 00:21:31,040 --> 00:21:34,720 And in this way, it will not intersect the z zero axis. 311 00:21:34,730 --> 00:21:40,550 OK, because we are in 3D again and you have to have 3D imagination for this one. 312 00:21:40,940 --> 00:21:44,270 OK, let admit this one goes to that. 313 00:21:44,330 --> 00:21:44,930 OK. 314 00:21:45,770 --> 00:21:48,200 Make it in this way again. 315 00:21:49,010 --> 00:21:49,780 OK. 316 00:21:51,830 --> 00:21:52,190 OK. 317 00:21:53,930 --> 00:21:55,070 In this way, yeah. 318 00:21:56,750 --> 00:21:58,910 So we have two directions. 319 00:21:58,910 --> 00:22:02,450 We can either choose it in the left or in the right. 320 00:22:02,750 --> 00:22:11,060 And then in order to make our life easier during the calculation of the age parameter table, we need 321 00:22:11,060 --> 00:22:11,360 to. 322 00:22:13,190 --> 00:22:16,800 It would be better if we choose the axis in the same direction. 323 00:22:16,820 --> 00:22:17,120 OK. 324 00:22:17,870 --> 00:22:19,700 Making minimal changes. 325 00:22:19,700 --> 00:22:20,060 OK? 326 00:22:20,270 --> 00:22:23,150 We would like we want every time. 327 00:22:23,150 --> 00:22:27,110 The optimal thing is that for us, it will make the calculations easier. 328 00:22:27,350 --> 00:22:29,270 If these accesses don't change. 329 00:22:29,270 --> 00:22:31,310 OK, so that zero is in the direction of Z. 330 00:22:31,310 --> 00:22:35,660 One x zero is in the direction of X one y zero is in the direction of one. 331 00:22:35,840 --> 00:22:44,030 And for this one also, they are as much similar as possible to each other, then it would be easier 332 00:22:44,030 --> 00:22:48,140 for us to make their calculations so we will choose X. 333 00:22:48,290 --> 00:22:55,740 In order to minimize the changes, we will choose our X One Direction as in the same direction of X0. 334 00:22:55,910 --> 00:23:01,070 Because if it does excellent in this direction, it will be perpendicular and will cut the zero zero 335 00:23:01,070 --> 00:23:06,440 axis, which is, um, which we require for the H conversion. 336 00:23:06,500 --> 00:23:06,860 OK. 337 00:23:08,060 --> 00:23:15,050 So for this axis, for this prismatic joint, for joint to what we will do or joint three with what 338 00:23:15,050 --> 00:23:20,630 we will do, we will choose the first of all central frame how it will be the central frame. 339 00:23:20,840 --> 00:23:23,750 Again, they are in the same plane. 340 00:23:23,750 --> 00:23:33,370 So as you can see, is it two and Z are parallel to each other so we can choose the center of the frame, 341 00:23:33,380 --> 00:23:37,610 OK, as any point over the Z to access. 342 00:23:37,880 --> 00:23:42,350 And in order to make our life easier again, we will choose it here. 343 00:23:42,740 --> 00:23:43,130 OK? 344 00:23:43,460 --> 00:23:47,810 At this point, as the joint center as the central frame. 345 00:23:48,110 --> 00:23:50,960 OK, we will choose the x axis. 346 00:23:50,960 --> 00:23:58,070 As we have said x two axis has to be perpendicular and it intersected z one axis. 347 00:23:58,400 --> 00:24:03,810 So we have as in the previous case, we have two possible direction. 348 00:24:03,830 --> 00:24:10,190 Either this way, OK, or either this way, in order to minimize the changes, we will not choose this 349 00:24:10,190 --> 00:24:14,970 direction, OK, because divide to choose it opposite to the X1 axis. 350 00:24:14,990 --> 00:24:15,320 OK. 351 00:24:15,560 --> 00:24:23,300 If we can choose the same as x one axis, choose it as the X1 axis the same direction as X1 because 352 00:24:23,300 --> 00:24:26,610 it will make our the edge parameter calculation easier. 353 00:24:26,630 --> 00:24:30,890 OK, so we will choose our X two direction in this way. 354 00:24:30,920 --> 00:24:32,950 OK, perfect. 355 00:24:33,590 --> 00:24:35,090 Because in this way it will. 356 00:24:35,420 --> 00:24:43,260 If you make it longer, it will come and cut it that one axis, OK, which we require. 357 00:24:43,670 --> 00:24:46,460 Let's think about this three axis, OK? 358 00:24:46,640 --> 00:24:52,250 As you can see, in this case, also Z two and Z three are parallel to each other because they are on 359 00:24:52,250 --> 00:24:59,960 the same plane so we can choose the central frame as at the center of the joint. 360 00:24:59,990 --> 00:25:00,390 OK. 361 00:25:01,400 --> 00:25:08,260 So let's try to make the here also to choose X reduction again. 362 00:25:08,270 --> 00:25:13,640 We can choose in this case, we can choose X Three Direction as part of the page. 363 00:25:13,670 --> 00:25:14,300 OK. 364 00:25:14,750 --> 00:25:17,620 As right as left. 365 00:25:17,630 --> 00:25:18,180 OK? 366 00:25:18,200 --> 00:25:20,960 And excuse me, this is inside to the page. 367 00:25:21,020 --> 00:25:22,280 This is inside to the page. 368 00:25:22,280 --> 00:25:25,130 But and then also to the page. 369 00:25:25,370 --> 00:25:26,900 We can choose all of these. 370 00:25:27,170 --> 00:25:27,640 Why? 371 00:25:27,830 --> 00:25:34,910 Because in each of these cases, if we make it longer and this one is longer as they are on the same 372 00:25:34,910 --> 00:25:36,720 plane, they will cut each other. 373 00:25:36,740 --> 00:25:37,090 OK? 374 00:25:37,730 --> 00:25:40,220 Let's, for example, in order to make it clear. 375 00:25:41,960 --> 00:25:47,660 Let me first, for example, choose inside the page, OK, inside the page. 376 00:25:47,660 --> 00:25:52,730 Let's choose it as the axis as im inside to the page. 377 00:25:53,090 --> 00:25:53,600 OK. 378 00:25:53,660 --> 00:26:00,230 For example, in this way, as we have said there, if you make it longer this and make it this longer. 379 00:26:00,360 --> 00:26:04,180 And they take also into account that these are on the same plane. 380 00:26:04,200 --> 00:26:04,770 OK. 381 00:26:04,860 --> 00:26:06,150 These are on the same plane. 382 00:26:06,450 --> 00:26:11,890 If you make it longer the z axis, it will cut this x axis at this point. 383 00:26:11,910 --> 00:26:15,570 OK, so we can choose our X in this direction also. 384 00:26:16,020 --> 00:26:16,470 OK. 385 00:26:16,500 --> 00:26:20,360 By the same logic, we can choose our x axis. 386 00:26:20,370 --> 00:26:25,080 Let me make it by the same logic we can choose. 387 00:26:28,330 --> 00:26:31,490 The x axis as part of the page, OK? 388 00:26:31,510 --> 00:26:35,680 Yes, because in this case, also it will cut there's a two axis. 389 00:26:35,950 --> 00:26:44,480 OK, so then what we can do, we can choose also the x axis, um, to the left or to the right. 390 00:26:44,500 --> 00:26:52,030 OK, because all of these kids, it's the z two axis and the two axis will intersect each other. 391 00:26:52,240 --> 00:26:56,740 But as we have said before, what we want to make the changes minimum. 392 00:26:56,880 --> 00:26:57,430 OK. 393 00:26:57,670 --> 00:27:05,960 So then the changes will be minimum because as X2 is to the right, we will choose it to the right. 394 00:27:05,980 --> 00:27:10,690 OK, in order to make changes minimum with respect to the previous joint. 395 00:27:10,780 --> 00:27:11,500 OK. 396 00:27:11,900 --> 00:27:17,530 Um, so we will choose this direction because it is a volatile action. 397 00:27:17,800 --> 00:27:19,750 This is our X3 axis. 398 00:27:20,020 --> 00:27:24,540 Then what we will choose, we will choose and we we what we have said, we will. 399 00:27:24,540 --> 00:27:33,100 We have said that we will almost in every case we will just copy the last frame for the end effector 400 00:27:33,100 --> 00:27:41,500 because if we choose it in this way again, we will make the changes minimum with respect to the last 401 00:27:41,500 --> 00:27:41,890 frame. 402 00:27:41,920 --> 00:27:42,430 OK. 403 00:27:42,700 --> 00:27:50,470 And also, this will cut the Z three axis, which is required for the H m convention. 404 00:27:50,810 --> 00:27:53,860 Now what happens with the Y axis? 405 00:27:54,430 --> 00:27:59,230 We can assign y axis or we cannot assign if what we get? 406 00:27:59,460 --> 00:28:00,530 We cannot assign. 407 00:28:01,260 --> 00:28:07,480 It's possible that not assign the y axis because during the calculation of h parameters, we will not 408 00:28:07,480 --> 00:28:09,160 require the y axis. 409 00:28:09,190 --> 00:28:15,040 However, if you want to know how we will assign the y axis, you probably assume this. 410 00:28:15,290 --> 00:28:22,960 You probably know we will choose just as we know that axis x axis of evil, use the right hand convention 411 00:28:22,960 --> 00:28:24,640 for choosing y axis. 412 00:28:24,970 --> 00:28:26,560 OK, what is the right hand role? 413 00:28:26,740 --> 00:28:29,710 You will make your sub impact. 414 00:28:29,710 --> 00:28:32,020 Started showing you all this. 415 00:28:32,140 --> 00:28:38,200 I think this is the middle finger in the Z direction and this finger, OK, this finger will be in the 416 00:28:38,200 --> 00:28:39,860 right direction automatically. 417 00:28:39,880 --> 00:28:40,270 OK? 418 00:28:40,300 --> 00:28:42,100 It will show you right direction. 419 00:28:42,100 --> 00:28:44,920 So based on the right hand rule. 420 00:28:45,610 --> 00:28:53,890 So in this case, if you put a middle finger in z axis, OK, middle finger in the direction of z axis 421 00:28:53,890 --> 00:28:57,790 and your sum in extraction, OK? 422 00:28:58,300 --> 00:29:05,530 So the extraction and the your y will be in this direction. 423 00:29:05,530 --> 00:29:09,950 So like that it will be the y axis will be in this way. 424 00:29:09,970 --> 00:29:10,620 This is why. 425 00:29:10,640 --> 00:29:11,080 Zero? 426 00:29:11,170 --> 00:29:15,040 Yeah, this will be the same for y one. 427 00:29:15,460 --> 00:29:17,950 And what will happen in this case? 428 00:29:18,670 --> 00:29:24,700 The two middle finger in the Z two direction somewhere in the X two direction. 429 00:29:24,700 --> 00:29:29,680 Yes, extradition and Y will be out of the page to us toward us. 430 00:29:29,950 --> 00:29:31,890 This will be y two. 431 00:29:31,930 --> 00:29:32,330 Yes. 432 00:29:32,710 --> 00:29:38,110 And let me do the same and it will be the same for y three. 433 00:29:38,110 --> 00:29:42,090 And it will be the same for Y for. 434 00:29:42,400 --> 00:29:46,600 And here is how we assign the coordinate frames for the. 435 00:29:47,660 --> 00:29:47,840 Yeah. 436 00:29:48,280 --> 00:29:52,800 As in the D.H convention, OK, we will do some examples also again. 437 00:29:53,110 --> 00:29:56,500 And so it will be easy for us. 438 00:29:56,800 --> 00:30:02,410 And now what we have to do in the next lesson, we will calculate the H parameters.