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FRANCIS MOON: Again, my name is, formally, Francis Moon. I'm a professor of mechanical and aerospace engineering. And I've been at Cornell since 1975. And I did my doctoral work here in theoretical applied mechanics.
And my field of interest has been dynamics. And many of you are studying dynamics of particles and rigid bodies. But in the last 15, 20 years, I discovered that one of the areas of mechanical engineering that has not been covered very well is the area of kinematics of machines. And so although this is a lecture series on kinematics and kinematics of machines, it's also a lecture series on how to create a machine.
And today, we will talk about, mainly, planar mechanisms and also walking machines. So that's the beginning. That's the first part of this lecture.
And the topics you see here that we're going to cover is the introduction to the design of multi-body machines; the idea of links, joints, machine elements; the idea of degrees of freedom, Grubler's Criterion-- that's probably the only equation that we're going to put here; the types of mechanisms; the models that Professor Franz Reuleaux created and that were bought by the first president of Cornell, Andrew Dickson White, in 1880 and now, here, comprise one of the largest collections of these models in the world.
And then we'll talk about walking machines and how walking machines are related to kinematics. And in particular, we'll look at two different types of walking machines that have been in the news. One is on YouTube, the famous strandbeest, and another, a Chinese walking machine that has been reconstructed in Taiwan.
And we'll also talk about the difference between kinematic walking machines and dynamic walking machines-- in particular, the robotic walking machines of Professor [? Rowena ?] at Cornell, who has developed a unique laboratory for walking devices.
So that's the idea for today. And one of the things I want to emphasize in these lectures is that the creation of a new machine is an evolutionary process. There's a sense in engineering, when you're an engineering student, that you're going to create something for the first time. And there's also a sense, in the public description of invention, that somehow there's this lone inventor working in his or her basement. They've got this fantastic idea. And all they need is some money to make it happen.
The real truth is that it takes many, many people working together across all kinds of disciplines-- from economics to science to engineering-- to create a new machine. And it takes place over many decades, many generations. And I hope that you'll get that sense as we progress with these lectures.
Some of this material that I'm going to talk about is in my new book called-- a plug for The Machines of Leonardo da Vinci and Franz Reuleaux. And we'll talk about some of that as we go along. And we'll probably end on next week, in lecture number two or three, in talking about modern robotic machines. One of them, for example, is the so-called da Vinci surgical robot. Although Leonardo da Vinci didn't invent a surgical robot. They put his name on it.
But it does capture the idea that the idea of building machines out of links and joints goes back at least to the Renaissance, if not earlier before that. So in order to create a new machine, we must have a language to create a language of machines. And some of the elements of that language involves machine elements; kinematic pairs; kinematic chains, we'll talk about that in a minute; simple mechanisms; compound mechanisms; modules, such as a gear reducer or a transmission for a car.
And then you put them all together in some sort of a system. And you create a larger machine, such as an automobile or an aircraft. The president of Boeing once said about the 777, which came out a few years ago, that it was a collection of about a million parts flying in close formation, all right? And so basically, the idea of putting together a machine is they're putting together all of these parts so they'll accomplish some sort of goal, all right?
So besides the things like machine elements, we have the idea of a mechanism, a prime mover, automata. That gives the idea that somehow, there's a program that tells the machine what to do. Mechatronics-- some of you will take the course in mechatronics. And then the idea of micromachines-- the MEMS is micro electromechanical systems. And then the idea of the robot or the control machine.
So there's this whole hierarchy of ideas in, what does it mean to make a machine? And just to review for-- unfortunately, in modern devices that we buy, they're all packaged. You can't see them. In other words, the product designers have covered up the details.
But if you go inside, for example, an engine and you see a piston, and a connecting rod, and a part of the crankshaft, you see that they're important machine elements. And some of the issues that you have to deal with are lubrication, stresses, et cetera. And if you count up the number of elements in any particular machine, they go to the hundreds, if not thousands. And each one of those devices has to be designed and designed by people who are getting an education, like you, in mechanical engineering and related fields.
Now, when we talk about machines, often, we talk about a series of rigid bodies that are connected by joints. And the type of joints that we have here are-- let's-- I'll get over here. So we have a joint, for example, that restricts the rigid body to rotary motion. So we can have things like rotary motion.
We can also have joints that have sliding motion. So we have this rack and pinion, here, where this rack is [? on a ?] slider. We call that a prismatic joint. We also have joints which involve a screw, which involves rotation as well as translation. So we can classify different types of joints, different types of kinematic pairs.
The one is the revolute. The other is the prismatic cylindrical joint, a screw joint, and a ball joint. All of them involve surfaces, interacting with surfaces. So when we think of a prismatic joint for a piston, you see that the piston is constrained on a surface between the cylinder housing and the piston. So it's a surface constraint.
On the other hand, if we talk about gears-- so if we talk about a pair of gears, here, the contact between the two bodies, between this body here, is either on a line or a point, all right? So each of these points can be thought of, then, as a geometric constraint on the motion of one relative to the other, OK?
The other idea here is the idea of a kinematic chain. And that is the idea that in a mechanism-- I'll bring up this one here. So if we think of a so-called four-bar mechanism, we have one, two, three, four links. And we have one, two, three, four joints. And we can turn one of these. And one of them moves in a circle. And the other one moves in a oscillatory or rock-- so this is called a crank rocker.
So I'm turning, sort of, this particular link. And this one is oscillating this way. So then the question arises. If we couple up a whole bunch of links with joints, how many degrees of freedom will we get? In this particular one here, for example, we have four joints and four links. How many degrees of freedom do we have? Anybody?
Somebody said seven. No, that's not right.
AUDIENCE: [LAUGHS]
FRANCIS MOON: How many degrees of freedom do I have?
AUDIENCE: One.
FRANCIS MOON: I heard one. I heard two. Do I have three?
AUDIENCE: Three.
FRANCIS MOON: How many people think it's one? How many people think it's two? How many people think it's three? Between the ones and the twos, the twos win, but they're wrong.
AUDIENCE: [LAUGHS]
FRANCIS MOON: It's one degree of freedom. It can only move this way, here. On the other hand, if we look at this double pendulum here, if I fix this base here, I have two degrees of freedom. I can move this this way. And I can move this this way, all right?
Now, if I wanted to create a machine that was going to move objects in space, how many degrees of freedom would I need? Somebody says three. Somebody says six. How many people think it's three? How many people think it's six?
Six is correct, yes. You have three positions and three orientations. So if you're going to create a robotic machine that's going to move objects in space, let's say in manufacturing or some sort of surgical robot, you want to create a machine that has at least six degrees of freedom, all right? Now, you could do that with a series of individual mechanisms. Each one has a degree of freedom, all right?
But when you get done, you have to have six degrees of freedom, at least, if you're going to have created a robotic machine. So the idea of connecting the idea of connecting rigid bodies with joints then brings up the idea of how many degrees of freedom.
And one of the simple formulas here, and you should write this down, is Grubler's criteria. Some people thought there was an earlier mathematician, named Chebyshev, who thought of this, and that the numbers of degrees of freedom, F, is three times the number of links minus 1, and then minus 2 times the number of revolute joints or prismatic joints.
And the basic idea is this. The basic idea is that-- and we're talking about in a plane now. If I move in a plane, an object has-- without any constraints, how many degrees of freedom does an object have in the plane? Somebody said two. Somebody said three. If it was three, what would it be? I'd be able to move one point in two directions.
But I can also rotate the thing, right? So I have the position and orientation. So if we're going to create a robotic machine that's going to move things around, we have to be able to move a point in space as well as the orientation. In a plane, we have just two translational and one rotation. So that adds up to three.
If we're in three space, we have x, y, and z. But we also have rotation about different axes. We have rotation about this axis, this axis, or this axis here. So in general, we would have three rotations and three positions. But in a plane, we have three.
Now, if we create a link between this body and another body, let's say my hand, then I'm going to reduce the number of degrees of freedom. The other thing is that when we create a mechanism, we often ground one of the links. So in this particular four-bar mechanism here, we've taken out three degrees of freedom by grounding this one link.
So this formula, if we didn't have any joints, the numbers of degrees of freedom would be 3 N minus 1. Because one of the links would be grounded. But because we're connecting one body with another with these revolute joints, we're taking out two degrees of freedom when we pin this, all right? We're taking out-- of the three degrees of freedom, we're only allowing, let's say, a relative rotation. We've taken out the relative x and y.
So that's the formula. And the important thing here is that this formula limits your choices. In other words, if you have four links and you want one degree of freedom, you have four joints. If you have six links, you have seven joints. If you have eight links, you have 10 joints.
Now, there's no reason why you have to stick to one degree of freedom. For example, I could say I'm going to create a planar robot arm that has three degrees of freedom, all right? Well, if I put F is equal to 3, if I have four links, I can have three joints. If I have six links, six joints, and eight links and nine joints.
So this is the idea that when you have connected rigid bodies, the geometry dictates the number of degrees of freedom. And this is one of the things which we don't emphasize in the age of calculus, especially where we're teaching pre-calculus earlier and earlier. We miss the idea that, in the creation of machines, geometry matters. Geometry rules.
And related to geometry is topology. And related to geometry is also kinematics, all right? Now, you can say, what's the characteristic structure if you were a civil engineer? What-- if you were-- and maybe there's some civil engineers in the audience. Are there any civil engineers in the audience? No civil engineers.
AUDIENCE: [LAUGHS]
FRANCIS MOON: But if you were a civil engineer, you like to create structures, right? And what's a classic structure for civil engineering?
AUDIENCE: A bridge.
FRANCIS MOON: A bridge. And what kind of a-- yeah, but what? A truss. OK. How many links does a truss have, the classic truss? Three. So it's three like this, all right? How many degrees of freedom does it have if I fix one of the links? None.
So if you put in N is equal to 3 and you put in three joints, you find that the numbers of degrees of freedom is zero. Whereas if you put in four full links and four joints, you get one degree of freedom. So the difference between a civil engineer and a mechanical engineer is one link and one joint. That's it, right?
And now, if you add extra links and extra joints, you get more degrees of freedom. And then the mechanical engineer becomes a robotic engineer. Because now you've enabled the machine to move in more than one degree of freedom. So again, geometry rules here.
And the other idea is that even if we have eight links-- and we'll see this later. Even if we just have eight links and joints and we end up with a mechanism that has one degree of freedom, there are many possibilities. The links don't have to have just the joints at the ends. The links could have many joints within the rigid body.
So here's a mechanism with four joints on one of the links. And over here is a mechanism with three joints on one link, right? So there are 12 possibilities for [? eight-link ?] mechanisms with one degree of freedom. That's the idea of topology.
And this was discovered in the late 19th century by people like Grubler and others. He lived in Germany. And one of the most famous kinematic circuits here is the so-called slider-crank mechanism. Now, here's an example of a slider-crank mechanism right here.
You see there's a crank. There's a connecting rod. And I can identify three elements here. I have the crank. I have the connecting rod. And here is the slider, here. But where's the fourth link? Where's the fourth one?
AUDIENCE: Is it the handles?
FRANCIS MOON: The handle is the crank.
AUDIENCE: [INAUDIBLE]
FRANCIS MOON: You guys don't look back on the Google professor here. Cornell students can't count. The fourth one is the base, all right? So this is-- again, instead of having a revolute joint, we have a prismatic joint. So we again have four joints and four links. But one of the joints is grounded, OK?
And the slider-crank mechanism, to take a phrase from an old Cornell professor named Carl Sagan, is probably one of the most ubiquitous mechanisms in the world. There's probably at least a billion of them, right? Maybe not billions and billions, but there's probably at least a billion sliding crank mechanisms.
Where do you think we'd find slider-crack mechanisms? All the cars and engines in the world, right? So you guys are working. You guys are studying mechanisms and machines that there are at least a billion of them around, huh? There's like six or seven billion people. And there's like a billion slider-crank mechanisms around, right? And they're all hidden. People can't see them, right?
By the way, I should say that there's a wonderful exhibit in the Johnson Museum on the so-called Nano car. And it's the world's cheapest car and designed by a company that's a Cornell graduate, named Mr. Tata. So please go over to the Johnson Museum. Or go online and see it.
And it tells-- it takes a vehicle and explodes it. So it's exploded physically in the different parts. And you can identify-- and one of the exploded views is an engine. And in that engine, you can see the slider-crank.
So if we looked out-- and this was Reuleaux's idea. Reuleaux's idea-- and Reuleaux lived and practiced in the late 19th century. And that was the age of the so-called Industrial Revolution. And people were inventing all kinds of things. And he was on the German patent board. And they were coming up with all kinds of different combinations.
And he asked the question, what constitutes a unique machine? And he had this idea, which came from earlier work, that any machine can be broken down, deconstructed into basic machine elements, and more important, basic mechanisms. So this particular-- but if you-- this is a five-axis Eshed robot machine that we use in our robotics class. And you see there's a gripper here. There's a belt drive here. There's a differential gear mechanism there.
So if you look at this machine, you see at least four. There's four different mechanisms in this machine. And so we can think of that if we learn the names and the functions of different mechanisms, then we're building a language. So each one of these mechanisms, you think of as a word. And if you put different words together, you get a sentence, OK?
The sentence then becomes sort of a smaller machine. You put the sentences together into paragraphs, and you get a larger machine. So that's the idea. It is to learn the language of mechanisms so that you can put them together and create all kinds of interesting machines.
Now, this is a sketch from my book on The Machines of Leonardo da Vinci. And this was a machine, for example, for spinning. And often, you see pictures of Leonardo with military machines throwing all kinds of heavy objects. But he also lived in Florence and Milan. And both of those places were places which dealt in textiles-- wools, silk.
And he created machines that would spin. He has a spindle right here. And not only did it have to spin, but it had to distribute the yarn. And he created a machine. And if you look at the devices-- if you deconstruct this, you'll find a belt drive, a worm gear, an alternating mechanism, and a double slider, OK?
So we can take any machine, going back to the Renaissance or to the present day, and we can deconstruct it. Now, just as a commentary here, many people think of Leonardo as an artist, right? How many paintings do you think Leonardo painted in his lifetime?
AUDIENCE: Four.
FRANCIS MOON: Four, that's close. Anybody else?
AUDIENCE: Five.
FRANCIS MOON: It was about, maybe, 10 or 12, you can think of. Whereas if you read his Codex Madrid, which is digitized online by the Cornell Library, he has about 1,200 pages of drawings of machine elements, OK? And he loved gears. This is all the different gears you can find in Leonardo.
So Leonardo was not an artist, but he was also an engineer. In fact he was hired by the Duke of Milan as an engineer, the royal engineer. And another one, of course, is James Watt. And this is a picture of his steam engine here.
But I want to call for your attention to the idea-- we use the word mechanical engineer. But in Germany, they use the word maschinenbauer. Now, how many know a little bit of German? What does maschinenbauer mean? Machine builders! It's up there.
AUDIENCE: [LAUGHS]
FRANCIS MOON: What does he think, we're stupid?
AUDIENCE: [LAUGHS]
FRANCIS MOON: Yeah. So mechanical engineers build machines. If civil engineers build trusses and structures that don't move, you're going to build machines that move, change energy from one form to the other, right? And the kinds of things that go into creating machines is, one, kinematics, which we're talking about in these lectures, also materials, control, energy, fabrication, and, of course, marketing. But the first-- before you begin, you have to know how they're going to move or how you want them to move.
Now, the other idea here, that has changed in the creation of new machines since when I was a student here at Cornell and when you you're here now, is the idea of mechatronics. So now the creation of new machines is bringing in different disciplines, OK? You not only have mechanical sciences, but you have electrical sciences, and you have information sciences.
And later in your curriculum, you'll take a course which tries to integrate all of those subjects. But one of the key things to creating a machine that's going to work-- and not a virtual machine, but a machine that's going to work in the real world-- is the idea of motion and description of motion, kinematics. And that's the-- this is, by the way, a landing gear of an Airbus jet.
But we don't get to see those anymore because you have jetways. You're hidden. In fact, now, you go on the plane, they have all the shades drawn. You can't even look out. But underneath, there's a wonderful mechanism here for the landing gear.
And mechanisms then can go from the very large to the very small. And we've already said here that all machines are constructed from a basic set of kinematic mechanisms. And Reuleaux proposed a dictionary of invention by looking at all of these different mechanisms. Now, what do mechanisms do? They change the motion from one form to the other.
So for example, if we talk about the slider-crank mechanism here, we can either think of this as converting rotary motion into linear motion, or, of course, in the the real engine, the engine is producing the linear motion. And the linear motion turns it into rotary motion, which eventually ends up to rotary motion of your wheels, which eventually ends up to linear motion in the car. So we're all about converting motion from one form to another.
If we look at an endless screw mechanism here, we're rotating about this axis here. And we're creating motion about an axis that doesn't intersect. And it's not colinear. So this is called an endless screw. And if you look at that slide of Leonardo, the endless screw was around at the time of Leonardo and other Renaissance engineers, OK?
We can also have rotary motion that creates intermittent motion. We'll talk about that on the next lecture. So kinematic mechanisms change motion from one form to another. And we can concatenate each of these different mechanisms.
Now, perhaps-- and maybe we'll distribute this. There's a list of basic kinematic mechanisms. In the Cornell collection, we have about 230 Reuleaux models. But in the original German collection in Berlin, which was which was eventually destroyed in World War II, Reuleaux had 800 different models of different mechanisms. And there's a Russian book by a man named [INAUDIBLE], who, in the early '50s and '60s, published a book with 5,000 different mechanisms. So there's many, many mechanisms.
But the dozen or so I have here-- first of all, the basic linkage is the four-bar, of the slider-crank, belt and chain drives. Here's a simple belt right here, where we have motion about here. And it's creating a motion about this, here. So we're transmitting motion from here to here. And you could do that with chains. There's some of that in your automobile.
And we have screw mechanisms. Here's a kind of screw mechanism here, in which you see there's a screw in this cylinder here. And as I turn this, here, I convert this into rotary motion here. Or I can have rotary motion convert into linear motion here. These types of mechanisms are in ball-screw devices. in the vertical stabilizer for a jet aircraft, often, there will be ball-screw mechanisms.
In fact, one of the failures of a-- probably in the '90s, there was a plane, Air Alaska, that went down because of a failure of a ball-screw mechanism to control the vertical stabilizer. So many of these mechanisms-- and maybe you've already been taught this by your TAs. But for those who might be away from Cornell, many of these mechanisms can be found on the website KMODDL, which stands for Kinematic Models for Design Digital Library.
And the URL is here. But I think if you just Google KMODDL, it will come up. And we have put models not only from the Cornell collection, but also collections from Germany and the Boston Museum of Science, and also from other collections. So we probably have about 400 different mechanisms. We also have various references there and lots of videos that were developed. So look at this site here. And just play with it. And we'll look at that tomorrow.
Now, one of the ideas here is the idea of inversion. And that's the idea that even though you have a certain kinematic chain here-- so here, we have four links and four joints-- the types of motion that you can get out of this depends on which one you ground. And it doesn't matter-- in this particular one, we just ground this one here. And when we grounded this one, here, we had this so-called crank-rocker here.
But we could decide to ground one of the other links. So if we ground one of the other links, you see, now, we have both of the links can go around. And the first one will be grounded. And we turned the crank, and we got a rocking motion. Here, we get both of them. This is called a [? lag ?] mechanism.
And so we're getting-- so from the same kinematic chain, chain being the sequence of links and joints, we get different mechanisms. And we can see this in the slider-crank, I think, in the next slide here. And so these are videos from the Cornell website. And you can see that up in the upper left-hand corner, you have the traditional one in an automobile engine, where you sort of fix the cylinder case. And the cylinder just has pure translational motion.
On the other hand, you can have these others where you fix the connecting rod or one of the other links. And you get a different realization of the mechanism depending on which of these you ground. So not only do you have the idea that you can create different mechanisms with certain numbers of links and joints, but you also create mechanisms by which one new ground and which one you move, OK?
So this is the four-bar kinematic chain in the so-called crank-rocker. This is the so-called slider-crank here. Again, this is a cutaway engine. And we do have a number of these cutaway engines that were-- I think this is the GM Chevrolet engine. We acquired these in the 1950s. And they almost were thrown out. People said, these are old, we don't teach this anymore. But we still have these. And they're brought into the class for, maybe, a class in combustion.
So there, you can see that there's at least two slider-cranks. And if this is an eight cylinder, there's eight of these slider-cranks. This is the so-called endless screw, in which you turn motion about one axis, and it moves around a perpendicular axis. And then we have these various planetary gears.
Now, here's one here, which-- this is a so-called planetary gear here. And you can see here that it's called planetary because the gear in the middle is called a sun gear. This is called a planet gear here. This outside, here, is called a ring gear. And you can have the input this way, here. Or you can-- the connecting link, here, is called the spider. Because often, there'd be three or four of these.
But you can also lock the spider. And now you can have the ring gear move, OK? And so these are so-called differential-- they're sometimes called differential gears. They can either be one-input devices. Or if I unlock both of them, they can be two-input devices.
And these are sometimes used in mechanisms to design a risk mechanism in robotics. But they may be in the shape of more bevel gears. So you can have the same type of idea. But now, instead of the planet here, facing out like this, I could have a series of bevel gears with the same type of sun gear and various planet gears.
And there are also gears here. So this is a special planetary gear in which the pinion is half the diameter of the large gear. And what that produces is that the motion on the outside of the pinion will produce an exact straight line of motion. In the next lecture, we'll talk about, how can you produce particular mathematical motions with mechanisms?
This is a double-slider mechanism here. And I have one right here. The double slider has two-- if you look at the back, there'll be a prismatic joint this way, a prismatic joint this way. And as I move this up and down, I have sliding both this way and this way. So that's a double slider.
And this is a ratchet. I didn't bring a ratchet. Maybe tomorrow, I'll bring a-- Monday, we'll bring a ratchet. And this is kind of a mechanical diode. In other words, it moves in one direction and not in other directions. And this is a cam mechanism. And in this particular cam, mechanism there's a dwell at each end of the cycle.
So in fact, the shape of that cam is called a Reuleaux triangle. And we'll talk about that in the next lecture, on how we can create a device that has a pause. In other words, at this end, here, it's pausing. At that end, there, it's pausing. And where would you use that pause? You might use that pause in a manufacturing operation. During the pause, you may want to drill something or paint something and then to have the thing moving on.
So you can do things like have almost digital-like behavior with these kinematic elements. Of course, the screw mechanism is very famous. And there's another one here, which I didn't bring. We'll bring it the next time. It's the so-called universal joint, where we can create motion about one axis and have it produce rotary motion about a non-parallel axis. So here, you see a so-called universal joint, all right?
So I'm going to skip here, to-- I want to talk a little bit before. We have about five minutes left. I want to introduce the idea of walking machines and robots. And there are two or three different types of walking machines. One is kinematic, and one is dynamic. And I want to talk about-- and again, we [? somehow ?] thinks that we're only creating robots in the 21st century. Well, there were a lot of robots created in the 20th century.
But there were robots created, at least, in the Renaissance. And there's thought that Leonardo da Vinci had created some sort of automaton. One of the more popular ones that you'll see-- this was created by an artist. This is a walking machine called a strandbeest. And in Dutch, that would mean beach animal. Strand means beach in German or Dutch. And this artist, Theo Jansen, created this.
And each one of these leg gears, leg mechanisms is an eight-link mechanism. So here's an-- and you see he can pull this. And as he pulls this, each one of the legs moves in a certain pattern. And I didn't have the video. Maybe the next one, we'll look at the video. But this system, here, can move in the wind.
And each one of these leg systems, here, can be thought of as a planar eight-link mechanism. So in fact, this is the eight-link mechanism here. In fact, there's two of them. There's one here. There's one here. They're both sharing a couple of links there.
And as you turn the crank there, then this particular leg then walks. And in fact, we can create a little toy walking mechanism here. So this is-- you can see, now, the two legs here. And the eight links involved-- first of all, the base is one. Then there's the crank here. That's two, three, four, five, six, seven eight, all right?
And some of these links have more than one joint. For example, this one, here, has one, two, three joints. So the idea here is that I can create a leg. And what I want the leg to do is to move in a straight line for part of the triggers and then lift the leg up and another part of the triggers. Of course, when it lifts up, you want another leg to come down.
So in using eight linkages here, you can change the lengths of the links here with these wires or whatever. Of course, you can do it on the computer. And you can create, now, different walking patterns, OK? And so this is the mechanism that he uses.
And there's a similar mechanism-- and I'll end with this, a similar mechanism from a group in Taiwan, by Professor Yan. And this is their eight-link. It's a different eight-link, right? And it was used to create a model of a Chinese walking horse. There's evidence in Chinese literature, going back at least 1,000 years, that they had walking machines that would carry goods up a mountain, which was-- they couldn't use wheels because they didn't have paved roads.
But they created these machines that would walk. And we have one of them right here. Professor Yan has given me one right here. And it's operated by a little battery here. But you could also push it if you wanted. So now you see the little Chinese walking horse here. And if we put it here, you'll-- whoops, it's going the wrong way. I'll turn the motor the other way. [INAUDIBLE]
All right. So this, each one of these legs is a an eight-link mechanism, right? Each one of these is an eight-link mechanism. So let me end this particular lecture with, and summarize that one of the things that mechanical engineers do is build machines. And it takes many different disciplines. But one of the disciplines to create a new machine is looking at how groups of solid bodies can be connected to produce a certain type of motion.
And the subject of that is called kinematics or kinematics of machines. And the design of, let's say, robotic machines in the 21st century depends on having certain knowledge of how you can connect all these links and joints to produce a certain type of motion. So in the next lecture, we'll go further into using kinematics of machines to produce various robotics.
And here, you have one here. It may be a nice toy, Robosapien. And this particular robot will say goodbye to you if I can turn him on.
[ROBOTIC NOISES]
AUDIENCE: [LAUGHS]
FRANCIS MOON: And you can see that-- I have two grandsons, who are about 7 and 8. And you can see that this machine was designed for the language of eight-year-old boys. But other than that, you can see that, also, it's a collection of links and joints--
[ROBOTIC NOISE]
AUDIENCE: [LAUGHS]
FRANCIS MOON: Links and joints--
[ROBOTIC NOISE]
AUDIENCE: [LAUGHS]
FRANCIS MOON: I've got to shut it off.
AUDIENCE: [LAUGHS]
FRANCIS MOON: All right. We'll continue this subject on Monday. Thank you.
AUDIENCE: [APPLAUDS]
This three-part lecture series was given by legendary retiring Joseph C. Ford Professor of Mechanical Engineering Francis Moon on the topic of kinetics as it relates to robotics on June 10, 2011, at Cornell University.
In this lecture, Professor Moon covers his investigations into the kinematics of machines with a focus on planar mechanisms and walking machines. He also discusses the history of the Reuleaux collection at Cornell, purchased by A.D. White in 1880, which now comprise the largest collection of these kinematic models in the world.
