Comprehensive Robotics and Automation Course Overview for Mechatronics Masters

hello everyone i hope that all of you are fine and enjoying good health

welcome to the lecture of robotics and automation my name is amir sharif

and i shall be teaching you this course so this course is designed for

masters in mechatronics it has three credit hours per week

and the course code is mct dash 551

so the suggested books that you can follow here are the five books

and because this course is already a combination of

robotics and automation and these two fields are not really

similar so that's why we need multiple books but these are only suggested books you

can follow any other any other books you like or any other material

from internet youtube whatever you like so this first book modern robotics

mechanics planning and control this in this book we shall we shall study some chapters

that are related to industrial robots and for the second book introduction to

robotics mechanics and control uh here we again we shall study some

chapters that are related to industrial robots their

configuration space and some concepts about

kinematics and inverse kinematics and the third book is elements of

robotics this also here we shall we shall

talk about a chapter that is focused about the transformation matrices

and and later we shall use these concepts for um from for kinematic modeling of

the robot so these three books they are

they will be used for carrots these three they will be used for

purely for robotics and especially industrial robots

and then the other two books industrial automation and robotics from this book we shall also

grab some concepts about automation especially the industrial automation and also

some basic concepts about robotics and the last book industrial

communication systems this will be about the communication standards that are being

used in the industry for example field bus profibus

so we shall take these concepts from these books again these are only suggested books you

are free to follow any material you want okay so um what is the objective of this

course what is the objective of this course robotics and automation of course robotics is already

a multi-field there are there are multiple fields merge in this form

and [Music] automation this is also again a broad

field so what is the objective of this course

this course is actually it is it is intended to give theoretical and industry related knowledge

about robotic manipulators and automation so

we got also theoretical knowledge as well as the industry related knowledge that is

useful for your future uh carrier so you you already know some stuff

before entering the practical world students are expected to learn kinematic modeling

and programming of industrial robots so this course is specifically designed for industrial robots

okay there are also other types of robots but this

robot is only focused on or mostly focused on industrial robots and we shall learn how to

model them and how we can program them for useful tasks

and you should also learn about programmable logic controllers so in the second phase in the second

part of this course which is automation you will be learn some basic concepts

and also some in-depth knowledge about programmable logic controllers and their industrial

applications at the end we shall also go through various industrial

communication methods so quickly just see

what are the course contents of this uh this course so clearly we have divided the course

into three parts the first one is the we they're about the industrial robots

where we shall cover about uh the concepts like introduction to robotics

and then we shall talk about in detail about the industrial robots

their types applications and then we shall talk about configuration space work and envelope

coordinate transformations manipulated kinematics like forward kinematics inverse

kinematics and i i hope that not if not all of you

some of you might have studied um

[Music] like or have introduction about these

concepts about forward and inward inverse kinematics if you did not already if you don't know

about these things then don't worry we shall try to explain it like

everyone can understand okay after that we shall we shall go through path planning

trajectory generation and following industrial robot programming

grippers and defectors robot commissioning and calibration and finally

safety and maintenance so this was the first pair part where we cover about the

robotics especially the industrial robots um

in the second part we have the industrial automation

so in this in this part we shall cover we shall

have an overview about industry automation and then

we shall go through basic architectures with some examples or case studies we shall talk about programmable logic

controllers and how to program them which languages we shall use and then some

[Music] input output interfacing visualization and control

and finally system development um in the third

part we shall cover the industrial communication so

in in the in the communication between different

automation devices we need to follow certain protocols or certain

methods for fast and robust communication so in this part we shall see how we can

how we can apply existing

technologies or methods of communication and which is better for example there are

methods like fieldbus profibus or industrial ethernet and we should go through them

and also we shall learn about the advantages and disadvantages of

each of the method okay so we have seen the course contents

and also the objective of this course so now let's see the introduction

so introduction to robotics so first we need to define what is a robot

the word robot was introduced in 1920 in a play by

carl capek called rosum's universal robots

so yeah you can see the word was actually introduced

long time before and this word comes from a czech word the word is robota

and the meaning of this word is force labor so in the previous times

yeah the the labor it was

forced labor was i think it was common because because of the slavery and because of

lack of human rights or labor rights so forced labor was common so

they came up with this machine and they came up with this idea about forced labor by a machine

and they use this word which is robota okay so how we define robot

in in a modern definitions so there are uh two definitions that i use here

the first one is a machine capable of carrying out a complex series of actions automatically

especially one programmable by a computer so

so notice that it's a machine and it it can perform complex actions

automatically so this is one part of a robot and

the important thing is it must be also program programmable by a computer so the computer must be there also

that means that without computer without a programmable computer

the machine the automatic machine is not really a robot so this is a one definition

the second definition is a robot is a computer controlled machine that is programmed to move

manipulate objects and accomplish work while interacting with its environment so this is

a little bit more um you can say a specific definition toward industrial robots or

robotic arms so here you can see that computer control machine there must be a computer

and if there should there should be a movement

and also a capability to manipulate objects to interact with the

with the bolt and accomplish work

so it should be also doing some useful work for humans so if it's not doing something useful so

i mean you can call it robot but it's not really

it doesn't make any sense if it's not doing any work for us because

it's it's uh for us it's a slave it's a cheap forced labor it's a robot

okay so we have seen the definition of robot and

so let's see here here we have a a picture of a robotic arm you can also call it a robotic

manipulator and what you can see here so the

the purpose of this robot is to draw something on the paper so here we have some

a microcontroller okay that's a you can call it a programmable computer

and then we have some electronic components power supply and the base of this robot

and then we have this arm and the arm has here joints so here this is a joint here

here is also joints and then here is one joint also then finally the end effector is here which is a pencil in this case

and then these are the links here that connects two joints um

so according to definition this

this robot can perform complex actions automatically if it's programmed by this

microcontroller or a tiny computer it can draw something by itself and it it's also it can do something

useful also for us for humans okay maybe it can draw our picture if it's properly

programmed it can manipulate objects for example it can hold this pencil and also

move it and draw something on the paper so this is this is a

example of a robot or specifically a robotic arm we have seen the robot now

now you're studying mechatronics you're doing masters in mechatronics so

i'm quite sure that you're familiar with the definition of mechatronics but

let's repeat it let's see what it says so what is mechatronics synergistic integration of mechanical

engineering electronics electrical engineering with intelligent computer control

in that design and manufacturing in the design and manufacture of

industrial products so so this you call mechatronics

it's a combination of of different fields mechanical electrical computer

and what you do you try you manufacture some industrial products

and also you design some industrial products using all using this integrated

knowledge so this we call mechatronics this field you call

mechatronic now we shall see what is robotics and how it is

related to mechatronics how it's what are the differences what are the similarities

so robotics is a branch of engineering that involves the design manufacture and operation of robots

so in robotics what we do we design manufacturer

and operate robots in the mechatronics we design manufacture industrial

products but here see that

you can clearly see that robotics is the subfield of mechatronics

how it is subfield because here it's more generalized it's industrial products or you can say just some

some items that you design and manufacture but robotics

is specifically related to robots the machines that have a computer controlled

controller and they can manipulate they can move and they can also do some useful

work so this is the difference between mechatronics and robotics

okay since our course is robotics and automation so we have to also we have to know what is automation

we will not go in depth here we shall only see its definition but in the second part we shall go in

detail about automation so what is industrial automation industrial automation is a use of

control systems such as computers robots and information technologies or handling

different processes in an industry to replace a human being

so what we do here in the automation we use control system we can use microcontrollers computers

robots plc's and what's the purpose of this is for

handling different processes for example if there is a packaging plant if there is a

milk packaging plant and we want to automate it we want to we want that

all the packaging or the processing should be done automatically without

the involvement of humans so so the use of all these technologies to automate some process is called

industrial automation so now i hope that you understood the

definitions and the differences between different terms that we use

let's see this figure here what you can say is this this a mechatronics device is this a

robot industrial robot what can you tell about this figure

okay so this is a mobile robot mobile robot because it has wheels here and also it has some sensors attached

for example this is the ir sensor for obstacle detection and on the top we have some

microcontrollers and power supply so you can you can call it as a

mechatronic system and that's basically you can you should call it a

a robotic system okay of course because robotics is a subfield of mechatronics

so this is our bot robot specifically a mobile robot

so it's a robotic system and also it's a mechatronic system but they're all

systems for example uh traffic light

have you seen our traffic light using uh using let's say um

microcontroller so this system that uses

some you that uses a predefined on off sequence of

lights after certain amount of time the the red light turns on and then

the green light turns on so what you say is this

what kind of system is this so is this a mechatronic system or robotic system

since we have for the we have defined for for the robot we have defined that a

robot is a machine so there is there should be some

movement involved some manipulation of objects in involved and

um so but here this in the and also here while interacting with its

environment so there is there also should be some interaction with the environment

but here if you see the traffic light traffic light has a let's say a microcontroller

and there is there is no sensor involved here

there is no movement involved here so we can we cannot call it a robotic system

so this is example of a mechatronic system but it's not a robotic system

okay so it means that uh every robotic system

is a mechatronic system but every mechatronic system is not necessarily a robotic system

you can come up with other examples also think about other examples that are the systems that

are mechatronic system but they are not robotic system okay so now you know about what is a

robot what is robotics and now it's time to

see what types of robots are there so generally speaking there are

two main categories of the robots the first one is the mobile robots as the name suggests a mobile robot is a

type of robot that has ability of locomotion so what is locomotion

locomotion is ability to move from one place to another place

literally the whole robot including the base so see here i didn't use a word movement

or motion okay locomotion is different than simple

motion for example i can move my arm

this is a motion of my arm but locomotion is actually moving my whole

body from one place to another place not moving my leg or my feet or my arm

so it means that a mobile robot must be capable of locomotion

displacement you can call it from position one to position two

or location one to location two so the here in this figure this is an example of a mobile robot

you can see it has four wheels and some electronic and computer system for

control and it can move around it can move around from positions to

position so this is a perfect example of a mobile robot now let's see the second type of the

robot which is industrial robot so industrial robots the name

says that it's industrial but it's not necessarily that they are only limited to industries you can use it

anywhere but the main

difference is that these robots can move are capable of motion

but they are not capable of locomotion so let's see the definition industrial robot is defined as a number of rigid

links connected by joints of different types

that are controlled and monitored by computer this is typical

definition of industrial robot so you will see some let's see this this figure you will see

here are some joints where it can move and also there are some links for example this is a link here this

again there is a joint here and it can rotate here and then again there is a link

and then also it can do motion here and then again link

and then motion here so it's a

it's a connection of links and joins and here we have the base you can call it

and it must be controlled by computer programmable computer so

the difference between mobile robot and industrial robot is that the industrial robot

can can have motion or move motion for example this arm can move there are of course there are

motors here the joints can move it can have any configurations like up and

down or it can rotate also so it can have motion but it cannot have locomotion

no no locomotion the base cannot move

cannot change its position in any access but for a mobile robot it's different okay

so our this course will be mostly related to industrial robots we shall go in depth of

industrial robots their their modeling and the terms related to this

but we we shall not go in depth of mobile robots because this is not the scope of this course

but you should have some basic idea

about the mobile robots and this is not the only type of mobile robot so you should see

a robot and you should be able to tell what kind of robot is this so certainly there are other types of

mobile robots let's let's pause this industrial robot here

and we shall now see what are other types of mobile robots so

so let's see this is the first this is a one of the type and this is the

one other type and finally this is third type

so this one is we call it omni-wheel omni-wheel robot so this is also a type of mobile robot

it has wheels four wheels just like a car and

actually not a car but it has four wheels that that have motors attached to it

so the difference is that between between uh this robot this mobile robot and this here this

omni-wheel robot is that this omni-v robot can instantaneously change the direction of motion

but this one here it cannot let's say if it's moving in forward here and suddenly you want to move it in this

direction let's say this was the x-axis and this is the y-axis and you want your robot to move along y-axis while it was

already moving here along the x-axis it cannot it needs some time so first you can do

the robot will stop it will rotate in this direction and then it will start

moving here or it will slowly it will take some time to change that

direction if it's if it don't stop completely but in case of omnibus robots this is

not the case it can instantaneously change its direction of motion if it's moving forward

along x-axis and what you want to do you you want to now move it along

y-axis so it can do it instantaneously just need to change the

speed of the or the direction of motion of the wheels and it will

move like in any direction along x and y axis okay then we have

here the differential drive robot this is another type of mobile robot

so so how it turns is that when

it's moving forward now it wants to turn along the y axis here

so what it will do it will change the relative speeds of the two wheels this is the wheel here

and what it does that this wheel will start moving slower than

the other wheel and then it slowly turns in this direction and

it will change in its direction and start moving along y axis so you can call it it's

similar like this is also a differential drive robot this is also

a differential drive robot but the difference is that this one has four wheels and this one has only two wheels

and one passive view for support maybe on the back side or in the front side here it has a

passive view to support because the robot cannot be stable on two wheels

okay unless it's it's a self-balancing kind of robot

so normally if it's not a self-balancing robot then it cannot be

stable on two wheels it must need a third wheel for support for stability

okay let's see now the third type of configuration of the wheels that we can

have in a mobile robot which is a car-like robot so this is again an example of

a mobile robot it's a car-like robot the weeds are arranged like a car the wheels of the car

so this steering the turning mechanism which is attached

to the front wheels it's called ackermann steering

okay and and the

the rear wheels they have the differential drive okay

so the advantage of this thing is that um during turning

during turning there will be no there will be less slipping okay

but the other kinds of robots for example this differential drive they

they might face some slipping problems especially at high speed turning this is not really a good idea

differential drive so that's why most of the cars they have this

ackermann steering and differential drive so that they can turn

at high speeds without slipping or without getting unstable

so this is we call it car like robot and this is again example of mobile robot huh so

the mobile robots are not only limited to wheels nowadays you will find some

drones and this is also a type of mobile robot the drones how they work they

they have four propellers powered by motors and

they they produce a thrust downward

and which in turn lift the robot upward okay

and how this when the robot want to move forward

so what it does it decreases the speed of the it increases the speed of the the rear

two propellers and in this way it will start moving forward

and similarly it can change directions it can move in any direction just by changing the relative speed of the

propellers nowadays as the sensors are becoming cheaper and

lightweight and power efficient so these drones are becoming more and more autonomous

so they have gps sensors they have obstacle detection capability also

different types of gyroscopes and accelerometers so they are getting more and more

autonomous so this is also a good example of a mobile robot then we have some mobile robots that

look like they have legs

and they are inspired from animals for example in this picture we have a robot with four legs

and this is used for some kind of

transportation of goods but i guess it's for military purposes and

yeah so this is also an example of a mobile robot now so finally we have two more

categories of robots that they are not mobile robots actually um

you can you they actually they can they have a capability of locomotion

but we call it humanoid robots we don't call it like industrial robots or mobile robots we

name them humanoid so this for example this one is from honda

and it has it's a self-balancing robot just like humans it can balance on

on two legs and also they are making it more intelligent

and especially they are these kinds of robots they are being designed for the

for social interaction and for personal use for assistance

okay they're not suitable for really suitable for industry

um but they're more suitable for social

interactions where close interaction with humans is desired

so one more type of robot these are called soft robots so

of course they are not mobile robot okay this is also another different category of robots

so they are they have some soft materials for example silicon or some

some other type of plastic or rubber and but they are not made of some

some stiff or metallic material so

you can compare this thing this for example this [Music]

gripper you can call it with an elephant trunk so the elephant trunk it's soft

it's not really hard there is no born bone inside it okay and meanwhile it can

do tasks for example picking placing and also it can manipulate objects

but there is no bone inside it so there is no bone inside it it means it's less stiff it's not that hard so it means

that it can be used in places where

less risk is required less you can say accidental risk is required

so the elephant trunk will damage less for example if a human is get struck by

an elephant trunk there will be less damage as compared to

if the human is struck by some kind of metallic

kuka robot so there is there is more damage because

it's hard it's tough so this field is a newly

soft robotics it's a new field they're working on it to develop some different

mechanisms of actuation using some pressurized air

and or fluid to expand contract these uh these kind of

uh actuators you can see in this figure

so they are pressurizing it with air or some kind of fluid and you can see various movements

they can control it so i've seen also some of these soft robots

where it can pick and place some objects or manipulate some objects okay so this was a brief introduction

about different types of robots we have seen mobile robots and

two other categories and one category which is industrial

robots that we will continue in detail so what are some some

some terms that we shall use in this course you must know that i hope that you're

familiar with most of these definitions

but it's it's good you just revise them okay so links and joints

links are the solid structural members of a robot and joints are the

movable couplings between them so this is a base of a robot let's say and then you have here a joint

and then you have here a link this is a joint here and the link here

and then you have again one joint and one more link here so you can call it link one

link two and this is joint one and this is joint two

so these are the links and joints if we combine them together we can make a robotic arm or

you can call it also robotic manipulator the second is degrees of freedom degrees of freedom is the number of

independent movements a robot can realize with respect to its base so independent movements for example if

there is two links are connected by one joint

so let's say this is a fixed fixed link then here is a joint and this is link

one and this is link two so here because this is if this is a joint that allows

rotation about one x's okay

so it means that this link which is l2 the link l2

can have one independent motion about um

let's see this is the z-axis here so about z-axis the link to can have a circular motion

okay circle movement so you can call it

it has one degree of freedom because it cannot move there is no translation involved it

cannot move along x y axis it cannot move it cannot rotate also about x y axis it

can only have one motion which is the rotation about the z axis so this is the degree of freedom of this

specific arrangement of the links second thing is the third thing is the

accuracy accuracy describes

how close the arm will be when it moves to the desired point so let's say your robotic arm

your robot the end effector of your robot and defector means the the tool that you have attached here for

example this was a your two link robot and here you have attached uh let's say a paint brush

for painting okay let's say this is a paint brush uh

so this paint brush is a end effector okay so you want your paint brush to be at

position let's say uh at x axis it's uh

two and at y axis it's let's say also two but

in reality it goes in the x-axis like two

but in the y-axis it goes like one so it means that it's not really

accurate so this is the draw it here with the different color

so actually it's here somewhere let's say here so the green one is your desired

position and red one is your actual position of your end effector so it means that your

the [Music] your robot is not accurate it has a low

accuracy now comes precision cn is defined as how accurately

a specified point can be reached this is a function of resolution of the actuator

as well as its feedback devices so for the for the precision we mean that

how close are the if for example in let's take the same example

this is your desired point but let's say your robot

first time it reaches here very accurately near to the your desired point but second time it's not really

good third time it's somewhere here full time here so

so it means that your the it means that different

every each time it has error

and the output is not consistent okay every time it has different

uh position it reaches different position sometimes it's accurate sometimes it's

not okay so it means that this robot is

you can call it it's precise within the uh

with a specific error sorry uh it's accurate within a specific error but it's not precise

okay then comes the work envelope a robot can only work in the area in

which it can move this area is called the work envelope so

every robot it can reach a specific region of the space near around it and we call it work

envelope the work envelope is determined by how for the robot's arm can reach and how

flexible the robot is the more reach and flexibility a robot has the larger

the work envelope will be so if a robot if your robot is like

let's say a one link robot attach this is a one link robot we have here

there is one joint and one link so so its work envelope will be something

like this here so the robot can

reach in this region of space um now we not not the end it will be limited

let's say within this region the robot can reach and it can perform

some tasks for example painting welding but within this region so this is just work envelope

it cannot move in the other direction because we assume that it's not allowed here

because of the fixed joint okay so

another thing is we call it stability stability refers to robot motion with the least amount of oscillation

now this is very important for example most of time we are concerned about the position control of the end effector

whenever we have a robot we are doing something like for example welding let's say we are doing welding with this robot

here and what we are doing is we are we want actual

sorry accurate position control we want the position to be accurate here okay

but if the position control is not stable and the robot is shaking and

uh not really maintaining its position and there are

some oscillations then there there are some stability problems so

if the robot is stable okay it means that it's

position control is very good and there are no oscillations so as we call it the robot is very stable

and it's a good quality of our robot next thing is speed speed refers either to the maximum velocity

that is achievable by the tool center point or by individual joints so the speed is

how fast the joints or the the tool

center point is moving and this is also very useful property

because sometimes we need we need this

desired speed especially when your your uh

your object is moving and the robot must move with the object then you need

accurate speed control so yeah

another thing is payload payload is the weight a robot can carry and still remains

within its specifications reach is the maximum okay this is

reach is the okay payload is the weight of a robot can carry and still remain within its

specifications so um here you see that um

within its specification when a robot lifts a payload payload means a weight so whenever a robot lifts a weight for

example a car okay or some some part of your of a car and

so robot should be should able to carry this weight and

also it should maintain the specification of position control

like it should maintain its uh position

with a good within within a good uh [Music] you can say

range of position it should not become unstable you know while not starting to oscillate or shake

so this maximum load although this maximum weight

we call it a payload that the robot can carry

and this is also very important especially when we are we want to select the robot later you

will see that this is also important for example when your owner says that find a robot that can

do this this and this and it must have also a payload capacity of let's say

uh 100 kilograms so then you have to either design a robot

or you have to purchase a robot that can carry 100 kilograms without shaking

or without consuming extra power i mean extra means without uh extra

means the power that can overload your circuit okay

one more definition is the reach which is the maximum distance a robot can reach within its work envelope

so in this case uh you can say

when there is a let's say two this is a joint

this is a robot and so this is a link one of the robot and this is a link to

and this is here we there's a end effector here some kind of tool that's a drilling a drill

so what is the reach of this this robot here so the maximum distance that it can

reach starting from your base this is the base the fixed one

the maximum distance is when this uh

this link will move like here it will get straight like this

and this will be true you can call it this maximum distance is the reach of

your robot so of course when this link will turn from here to here

okay so but this is the maximum distance this is the radius you can call it

this is the reach okay the last concept is a settling time

so what is the settling time i hope that some of you have already studied it in

your control system during a movement the robot moves fast

but as the robot approaches the final position it slows down

and slowly approaches at final position the settling time is a time required for

the robot to be within a given distance from the final position

so so what happens at the robot when it it moves to position one let's

say position one to position two so what happens is that

it uh it moves fast and then when it reaches near the position two

it started to slow down okay um so it

it's not like instantaneous break otherwise if you if you uh stop it like very

quickly it will be a cause a jerk and then the the load the

object that is carry that is attached to the robot there is a chance

that it may get damaged so what it does it try to slows down and then finally stop at the final

position so the time it takes to slow down

okay we we we call it settling time and if you remember from

control system let's say this was a position this is a final position

and it was something like there were some oscillations and finally the oscillation is gone

and then your there was some steady state error but your robot was finally at your

final uh position position which is the position two

so this time in which the the robot still uh

still trying to stop and getting closer to the final position

this we call it settling time okay so now i

we are we are familiar with the basic concepts and basic terms used in robotics

so let's move and see what else

what else things we need for for robotics to start with

so now uh we are from here we are specifically talking about the robotic manipulator or you can call it

robotic sorry the industrial robots so here we shall talk about

types of joints of the industrial robots a robot joint is a mechanism that permits relative movement between parts

of the robot arm again when there are two links

one is fixed and then here we have a joint that can that

allows rotation and then there is a second joint so this is link one this is link two

this is joint so what is the joint is the joint allows a relative motion

between movement between link one and link two in this case it's a

circular motion so we call it a robot joint

j is a robot joint there are basically uh

five types of five major types of robotic joints

actually there are more but here we are discussing only the uh

commonly used or the important ones so the first one is prismatic joint prismatic joints are also known as

sliding as well as linear joints they are called prismatic because the

cross section of the joint is considered as a generalized

prism they permit link links to make a linear displacement along fixed axis

in other words one link slides on the other along the straight line

these joints are used in gantry cylindrical or similar joint configurations

so what is uh imagine uh so a prismatic joint imagine you can say uh

some kind of a rod okay a rod

that is square shaped but hollow from inside so this is here here is a material

it's a metallic rod let's say okay but from inside it's hollow and then now imagine one more

rod that's also a square shaped okay

but it can slide inside this red color rod okay

so this rod this square shape rod one it can enter in

this red color hollow rod two

so the movement will be the movement movement will be like in this direction okay let me change the color

so the movement of this rod will be either in this direction or in this direction so let's say this is x axis

so it means that the rod this green rod can enter in this

this red color hollow [Music] link you can call it

and it can also come out but it cannot rotate in any because it's a square shape okay

it's fixed within this within this red color rod so it cannot rotate it cannot move in

any other axis the only axis it can move is along x axis

so we call it prismatic joint this joint is a prismatic joint and it's

it allows only linear displacement okay let me they permit links to make a linear

displacement along fixed axis yeah so that's we have already explained here

and they say that these kinds of joints are used in uh

gantry or cylindrical so later when we study the different types of

of the industrial robot then we shall see what where we use these prismatic joints

so how many degrees of freedom this this kind of joint has only one let me write down here degrees of

freedom one for prismatic joints

and only linear motion then we have revolute joints the second type of joint is a revolute

joint where a pair of links rotates about a fixed axis

so we have already given the example here

so the revolute joints let's see can we

move it from here to here or let's draw in better draw one here

okay so for our level let's draw the revolute

joint we have here a fixed link

and then i cannot hear and then a joint that allows

rotation and then we have one more link here attached with this so this link

this link to can rotate

because here we have a joint that allows circular motion it cannot have any linear motion because

the joint is revolute joint it only allows rotation along z axis or any axis

so it means that this type of joint which is a revolute joint it has a degree of freedom of

one degree of freedom because there is only rotation along one axis there is no displacement

so degree of freedom is one i think this is the most common type of joints

for for robots okay the third types of joints are cylindrical joints

uh cylindrical joints they are they look like similar to the to the prismatic joints but the

difference is that here we have the so here here we have instead of our

square rod we have a circular rod hollow circular hollow robot

okay it doesn't look like proper rod maybe i should

so this is this rod is hollow from inside

okay and let's assume another link which is a rod which is not a hollow road but a rod

that enters that can enter inside this rod here

so in this case we have two rods rod one is a solid rod and rod two is the hollow rod

but they are circular they look like you can imagine same like here prismatic

joints case and here we have a square shaped okay both the rod one and draw two but here

for cylindrical joints as the name suggests here the cases both are circular

okay so in this case there will be one motion will be along so that this rod green rod

can move along x-axis like in and

out this rod can go inside and then come out so one motion will be along x-axis and the second motion that it can also

rotate about one axis so let's say the the rotation is about also x-axis

so it means this kind of robot this kind of joint it has degrees of freedom

too because it can have two independent motion