1 00:00:00,120 --> 00:00:04,920 We have enough knowledge on rotation mattresses and homogeneous transformation mattresses. 2 00:00:05,370 --> 00:00:12,030 We can find orientation or position of one frame with respect to another, and we can transform one 3 00:00:12,030 --> 00:00:13,290 frame to another. 4 00:00:13,770 --> 00:00:14,280 Perfect. 5 00:00:14,670 --> 00:00:21,030 Now it's time to put these theoretical concepts into practice and get much more interesting results. 6 00:00:21,570 --> 00:00:24,150 We will start with forward kinematics. 7 00:00:24,780 --> 00:00:32,370 Robot kinematics describes motion of robot manipulator without considering forces and talks that create 8 00:00:32,370 --> 00:00:33,120 this motion. 9 00:00:33,540 --> 00:00:35,940 So the conclusions are solid geometrical. 10 00:00:36,690 --> 00:00:42,990 If we can say the robot kinematics, we can split it as forward kinematics and inverse kinematics. 11 00:00:43,560 --> 00:00:52,320 Forward kinematics, which we are interested with for now, helps us to fund in the fact that the position 12 00:00:52,320 --> 00:00:58,500 and orientation in the workspace given joint angles of the robot manipulator. 13 00:00:59,220 --> 00:01:05,430 Indeed, by using forward kinematics, we don't only find position and orientation of the end effector 14 00:01:05,430 --> 00:01:10,050 of later, but also any point in the robot's structure. 15 00:01:10,770 --> 00:01:16,110 How can we calculate forward kinematics, surely using homogeneous transformation mattresses? 16 00:01:16,470 --> 00:01:22,470 Because by using homogeneous transformation mattresses, we can find position and orientation of one 17 00:01:22,470 --> 00:01:25,440 frame with respect to any desired frame. 18 00:01:26,110 --> 00:01:30,450 However, before going deep, we have to understand some basic concepts. 19 00:01:31,500 --> 00:01:37,170 First of all, as you may probably know, robot manipulators consists of joints and links. 20 00:01:37,590 --> 00:01:42,000 More generally, joints are connected with each other through joints. 21 00:01:43,770 --> 00:01:49,220 Excuse me, more generally, links are connected with each other through joints. 22 00:01:51,310 --> 00:01:55,630 Drones are used to provide motion to the links of the robot manipulator. 23 00:01:56,440 --> 00:02:02,230 Here are the joints indicated in this robot arm, which is called scalar robot by the creator. 24 00:02:02,950 --> 00:02:07,300 And here are the links of the robot arm connected through joints. 25 00:02:09,830 --> 00:02:17,060 Jones can be in different types because we want to give the robot as much flexibility as possible in 26 00:02:17,060 --> 00:02:24,530 order to provide a wide range of motions we want or in order to achieve wide range of motions. 27 00:02:25,040 --> 00:02:30,290 We want links to be able to rotate, not only rotate, but also translate. 28 00:02:30,680 --> 00:02:35,810 So let's see the alimentari joints that will provide all these alimentari motions. 29 00:02:36,350 --> 00:02:40,250 This is a joint which has one degree of freedom. 30 00:02:41,570 --> 00:02:45,470 As you know, object in space has six degrees of freedom. 31 00:02:45,980 --> 00:02:51,350 It can translate along x y z and rotate along x y z axis. 32 00:02:51,920 --> 00:02:58,250 But when we add rotational joined, it doesn't let leads to translate or any of the accesses. 33 00:02:58,700 --> 00:03:03,500 So we have lost three degrees of freedom already in terms of rotations. 34 00:03:03,830 --> 00:03:08,870 As you can see from the picture, it only lets rotation around one axis. 35 00:03:08,900 --> 00:03:15,650 This can be X. This can be why this can be depending on the orientation of rural joint. 36 00:03:16,070 --> 00:03:23,300 So we just have one degree of freedom with rotational joint, and this motion can be described by rotation 37 00:03:23,300 --> 00:03:26,140 angle to AI for each joint. 38 00:03:26,930 --> 00:03:32,900 Then we have translation joint, which provides translation and motion over just one axis. 39 00:03:33,170 --> 00:03:38,240 So again, we have one degree of freedom, and its motion can be described by variable. 40 00:03:38,240 --> 00:03:46,700 The eye for our joint and the AI is worrying length of the joint as it comes out or goes back inside. 41 00:03:47,660 --> 00:03:53,750 And that's vertical joint, which has three degrees of freedom because it allows on rotation along three 42 00:03:53,750 --> 00:03:54,400 axis. 43 00:03:54,650 --> 00:04:01,040 But the translation on Motion Spherical Joint can be described by three in the video rotation joints. 44 00:04:01,280 --> 00:04:07,940 So we will represent it always with three rotational joints because it's easier for us and the pictures 45 00:04:07,940 --> 00:04:13,760 inside the red boxes represents different joint tides in robotic pneumatic diagram. 46 00:04:14,240 --> 00:04:20,320 We will see now what is the robot's kinematics diagram, so don't worry, OK? 47 00:04:20,600 --> 00:04:24,260 We have seen different robot joint types and its limbs. 48 00:04:24,920 --> 00:04:30,410 However, we have to consider one another thing that will make our life a bit easier. 49 00:04:30,830 --> 00:04:37,640 We cannot do calculations or robots real image because there are too many unnecessary details on the 50 00:04:37,640 --> 00:04:38,360 real robot. 51 00:04:38,780 --> 00:04:41,060 This is like human and its skeleton. 52 00:04:41,390 --> 00:04:47,570 You can represent humans with only a skeleton, right, because it has the same shape as our body. 53 00:04:47,570 --> 00:04:54,440 But our bodies generally have many unnecessary things that will distract us from means of analyzing 54 00:04:54,440 --> 00:04:57,410 human or main aim of analyzing human. 55 00:04:57,800 --> 00:05:00,170 The same is with the robot manipulators. 56 00:05:00,530 --> 00:05:06,770 We want to draw the skeleton of it, and it can be done using robot kinematic diagram. 57 00:05:07,340 --> 00:05:11,270 You can immediately see how simple is the robot schematic diagram. 58 00:05:11,270 --> 00:05:14,000 It only consists of joints and links. 59 00:05:14,780 --> 00:05:16,430 That's all we can do. 60 00:05:16,430 --> 00:05:19,280 Calculations on that diagram much more easily. 61 00:05:19,820 --> 00:05:27,380 As you can see, we use joint designations that we have seen to represent the joints in the robot kinematics 62 00:05:27,380 --> 00:05:27,890 diagram. 63 00:05:28,280 --> 00:05:32,960 The first joint is rotary, so we use designation of rotational joint. 64 00:05:33,380 --> 00:05:36,200 The second one is also rotational joint. 65 00:05:36,500 --> 00:05:41,060 However, the third one is prismatic one, so its designation is different. 66 00:05:41,600 --> 00:05:49,450 And finally, we have again a rotary joint after we have seen these basic concepts basic concepts. 67 00:05:49,490 --> 00:05:52,130 Let's try to understand what we might explore. 68 00:05:52,300 --> 00:05:54,710 OK, now let's see. 69 00:05:56,120 --> 00:05:58,700 Let's try to understand the forward kinematics more clearly. 70 00:05:59,010 --> 00:06:05,900 OK, what we have see, for example, first of all, let's see what's the forward kinematics? 71 00:06:06,170 --> 00:06:12,350 What we have said in the lecture, we have said that if we are given for the robot manipulator at joint 72 00:06:12,350 --> 00:06:20,690 angles of the robots because this can be a prismatic also doing dito on Dito two, Dito three and four. 73 00:06:21,030 --> 00:06:30,680 So we are given let's throw that given Tito one, Tito two, Tito three Tito fourth. 74 00:06:31,100 --> 00:06:42,080 What's interesting for us output of the forward kinematics is the position and orientation orientation 75 00:06:42,440 --> 00:06:45,610 of either in the vector. 76 00:06:46,270 --> 00:06:46,790 Okay. 77 00:06:46,790 --> 00:06:50,170 And Victor, what is the in the sector in the fifth? 78 00:06:50,180 --> 00:06:54,810 Or is this what you saw with forward given that you're interested? 79 00:06:54,890 --> 00:07:00,740 This one, we are given Tito one, Tito to Tito, three, and Tito for what will be the position and 80 00:07:00,740 --> 00:07:08,240 orientation of in the victor in the past space or work workspace by workspace, we mean this one to 81 00:07:08,240 --> 00:07:08,540 be able to. 82 00:07:08,650 --> 00:07:10,610 About it later moves. 83 00:07:10,630 --> 00:07:14,530 OK, so this is interesting for us. 84 00:07:14,650 --> 00:07:20,560 So, for example, we are given 15 degrees for this one, 30, 20 and, for example, 10 degrees. 85 00:07:20,740 --> 00:07:27,310 What will be the position and orientation, for example, it will be five, six and one in X Y Z. 86 00:07:27,640 --> 00:07:33,130 And for example, with respect to the base frame, surely we get it with respect to the base frame. 87 00:07:33,310 --> 00:07:37,610 For example, 30 degrees for two degrees and then minus 10 degrees. 88 00:07:37,630 --> 00:07:39,910 Okay, why this? 89 00:07:39,960 --> 00:07:41,860 Why this is interesting for us? 90 00:07:42,070 --> 00:07:44,260 For example, we want to get. 91 00:07:46,150 --> 00:07:52,420 For example, we want robot manipulators in the vector to come to the object in order to grab it. 92 00:07:52,450 --> 00:07:52,960 Okay. 93 00:07:53,410 --> 00:08:01,480 So this is interesting for us in if we give, for example, this is certainly 2010 and five degrees. 94 00:08:02,110 --> 00:08:04,290 OK, excuse me for this 10. 95 00:08:04,300 --> 00:08:09,910 OK and five degrees will be end effector near the object. 96 00:08:10,030 --> 00:08:12,550 Or it's far from the object, OK? 97 00:08:12,970 --> 00:08:19,450 Because from the joint angles, we can conclude what will be the end of the position and orientation, 98 00:08:19,450 --> 00:08:24,970 the tusk space or workspace, and we can know that whether it is near the object or not. 99 00:08:25,360 --> 00:08:35,410 And the second we can know the position and orientation of any point, any point in the robot, any 100 00:08:35,410 --> 00:08:42,840 point in the robot, okay, robot structure, for example, we can know the what will be the position 101 00:08:42,850 --> 00:08:47,500 and orientation of this point, what will be the position and orientation of this point or this point 102 00:08:47,500 --> 00:08:51,190 or this point or this point, any point in the robot manipulator? 103 00:08:51,200 --> 00:08:51,610 OK. 104 00:08:51,940 --> 00:08:53,530 Why this is interesting for us. 105 00:08:53,740 --> 00:09:01,120 For example, we we want to grab this object, OK, we want to grab this object, but we have an obstacle 106 00:09:01,390 --> 00:09:07,270 in the workspace and we don't want robot any point to touch to that obstacle. 107 00:09:07,270 --> 00:09:14,790 OK, so we can calculate each of robot manipulators for points. 108 00:09:14,800 --> 00:09:22,600 OK, these points and check that whether they are collided with their coordinate is the same with the 109 00:09:25,000 --> 00:09:29,770 coordinate of the obstacle or it is near the obstacle. 110 00:09:29,770 --> 00:09:36,190 We can calculate this one and we can predict whether it will collide or it has already collided and 111 00:09:36,430 --> 00:09:38,680 try to avoid from the obstacle. 112 00:09:38,810 --> 00:09:45,850 OK, so you can see that the forward kinematics is pretty interesting for us per team. 113 00:09:46,840 --> 00:09:49,480 And this is the let's summarize again. 114 00:09:49,630 --> 00:09:50,170 Excuse me. 115 00:09:50,200 --> 00:09:51,700 Let's summarize again why. 116 00:09:52,420 --> 00:09:53,800 What is the forward kinematics? 117 00:09:53,800 --> 00:09:56,980 So the purpose of everything makes be able to give them joint angles. 118 00:09:57,250 --> 00:10:05,170 We want to calculate position and orientation of either in the vector or any point in the robot manipulator.