hello my name is Carlos Osorio I'm application engineer here at The
MathWorks and this is part one of a series of recording sessions that I am
doing for them how differential equation becomes a Robert seminar in this section
and then a focus on rigid body dynamics so we're going to talk about mechanisms
and how to build a differential equations for this mechanisms were gonna
be a little bit analytics then also show you how to interface with catcalls and
import the information directly from cattles to build full dynamic models of
you are three-dimensional Meccans so hopefully you watch the overview section
but just to recall the problem we're trying to build a moderate degree of
freedom mechanical manipulator in 27 degrees of freedom robotic manipulator
so the argument I was making is this idea to solve a complex problem we have
to be composted in simpler more manageable problem and soul within a
concentrate on the mechanics right now even though there's electrics and their
school controls and other things so let's just concentrate on the mechanics
for now so even when we look at the mechanics we want to look at the
simplest possible situation to try to understand and gain some insight into
the problem let me look at a single pendulums multi-link mickens so what are
their primary variables involved into sorry there's an angle of rotation
Anders
linked of the Macondo some ass that is pushing it down or bring it down I can
think of now when I want to have to establish I'm I went out grownups paper
to write some equations but the problem is like my new approaches are always
prone to error
written it here as an example but even writing this manner took me a little bit
so we have symbolic analysis tool that can be a very powerful symbolic analysis
system with this kind of task so let me go into MATLAB matlab in order to open
the symbolic analysis tool you can go on the Start menu toolboxes and look for
the symbolic math toolbox so if you have the symbolic math toolbox in your life
that you have this interface which is commuted by President notebook interface
that allows me to build my symbolic analysis or you can call it directly
from from the MATLAB environment here so this is a blank notebook it's a full
editing notebook so i can text for example I title diana doll and i can
answer
images for example if I wish I have a library somewhere here so I'm sure you
keep track of building if I'm going to use a first principle equations are I'm
trying to follow a paper or book in this case for the dynamics of opinion on that
first law then I'm going to use its Newton's law sodomy law says some of
torex sequel to The Times the angular acceleration so I'm going to define an
expression this is gonna be a symbolic expression not noticed that I'm using
the colony station and I'm gonna say this some thought to be the shower on
this easy access the rotational axis multiplied by the angular acceleration
so the angle is still down the angular acceleration will be the second Arab
leader so I can evaluate him directly
of course nothing very interesting company is happening here I haven't
defined any of the terms and this is a very simple problem because what I want
to do is just give you a sense for how this tool operates and so let's just
define some of the terms so let me find the moment of inertia of things wrong
for example around its center of mass you can look it up in any book you'll
find out that is supposed to be Mr square over 12 so demise multiplied by
the linked square Mr square over twelve so that's the moment of inertia around
the center of mass but the moment of inertia I want around as easy so I have
to use our alexis the urine so ICC will be actually that ICM translated by the
parallax mass times the distance in this case are over two squared times mass
transit square so not as even is simple things like this is actually doing all
their factoring and computing the whole operation for me so that starts at the
more complicated operations are becoming more helpful to speak on such a dork
historic will be produced by whatever for the gravity force in this case which
is empty
bad for that expression to talk so once perpendicular to the rotations oMG sign
of the US will be
miners G sign of the T minus because the forces opposing the direction of the
duck multiplied by the moment arm which is half the length of the wrought iron
over too so I am creating expressions right now they're all this is very
different than programming in MATLAB programming is equation 1 is a symbolic
expression that contains this file now so not is that now the equation looks a
little bit more like what we wanted to look although I still have filled out
there that is kind of bothering me so I can replace that limit defined as the
Greek symbol corresponding to see herself symbol of the ones you once you
get a little practice on this with annotation we can speed read
straightforward at first maybe the Armada programming might be a little bit
different so if I look at it again now now it looks more like let me get
cleared it up let me get this secondary very clear from this equation cause I
want equal to something so I can I can do things like this for example in the
final second equate a second expression there will be the first expression the
first symbolic expressions are equation 1 if I want a clear Mr square over 3 I'm
going to divide this by far our square 2/3 so I am dividing both sides of the
expression by Mr square over 30 now is clearing out the double dots
daddy's a function of Science Theater a different issue a second order nonlinear
differential equation I can try to solve it analytically and by the way there are
some menus here
access to some functions directly without having to memorize everything so
they're solve this is the form of the equation force of the expression for
solving differential equations and so by the way this is all like MATLAB so bring
it up a little bit so if I put my cursor on top of one of the functions notice
how it will give me the form of the expression so they stole tells me all in
curly brackets I have to put the equation and the initial conditions to
solve the differential equation or you can also use the F one command to go
directly to the documentation same as you doing matter samples nation
everything so the equation I want us all again
curly bracket so just remember that the equation to solve this equation to the
initial conditions because it's a second order I have to give to initial
conditions I have to give initial condition for Steeda in order for our
pendulum to flip around we need to give it a little bit of an angle to start
moving otherwise you're not just going to hang their song when i activate are
over 12 and then I need the initial condition for their losses and here is
what viable and solving for which has seeped out so I seen any symbolic
analysis tool to solve differential equations this is gonna look for
patterns and this farm district this form of this equation this particular
form of this equation 3 double dog equal sign of feet doesn't have a closed form
solution so what this is telling me is that there's no closed form solution is
just back the equation and so if I want to solve this in this particular case
let me comment here I'm gonna use a small numerical trick so when you have
very small angles you can you can use what is called a small angle
approximation which means which says that for at small angles this the value
of the sign of the DA is the same as a value in radians and so and let me
create a third expression here I'm gonna create equation 3
three and that's gonna be where I'm going to do it I'm gonna use the comment
subs which substitutes substitutes in equation 2 substituting equation to what
is it that I want a substitute I want a subsidy to sign of the key
50 I wanna substitute that for just 50 so what I'm saying this with this
command is wherever in this expression equation to wherever you find sign of
feet up to just replace it based by Sedo or not is how it always has done it has
done that that situation now I have a second order linear differential
equation which hopefully I can solve analytically actually I will be able to
solve this is the same command only gonna
same initial conditions linear on it and is giving me a general solution of the
differential equation and symbolic analysis tool do this so it's given me
all the possible conditions but we have some physical insight into this we know
that gravity is not equal to serious or where I'm gonna do it I'm going to add a
little additional command here assuming solve it assuming that geez greater than
zero because I know that and also we can help in a little bit more even we can
say we know they're linked to the right is greeted us here so now it gives me a
better form so slightly prettier so I can replace the values of g for example
gee I know is 981 I know our let me to find some value limits a price on now
again I'll have a violation of the number numerics here
notice that is in curly brackets because he's giving me a vector of solutions
really so if I want and then a difference
redefine saw just their first element of that Victor and so now I'm extracting it
out that's the element i won
and once I have to solve that can actually just the law kinds of things I
can do
plotting for example I'm gonna plot saw and is a function of T so I need to tell
it I whant to vary from 0 to 5 seconds and that is going to evaluate the
expression 1401 1402 fight this analytic expression once I have this not only I
have a clean solution that I can change and modify incorrect or whatever but I
can also well first of all save it as a notebook that I can share with other
people don't have not slept under symbolic or I can export it I can
exported we're going to put it in my images directory business like my pain
and you can export things as PDFs HTML just text I'm gonna just the fault which
is PDF safe so what he has done is it has saved this notebook into a PDF
format
actually let me go back on here its images directory now so here I should
have some PDF outside of MATLAB and I have a fully documented version of the
analysis that I just did not uploading all the commands all the expressions and
it is a PDF file so I can email it to whoever I want they don't need to have
MATLAB the one thing that I wanted to show you to let me go back to the
directory where I was before so what I have here is a matlab script that shows
some of their interconnection between Newport and Madeline
a big part of the power of the stores affected it runs on MATLAB so you can
once you have your script you can call it from madeleine you can do it you can
have all weighed all the functionality this is exactly the same script that at
the same
archive that just created before on you have a little party more comments but
the important thing is here at the end where the finding of our table so it's a
symbolic viable and I want you to notice let me go back to my script there's
commands like get var MATLAB functions like get fire and set the bar low you to
communicate back and forth either from them into MATLAB or vice versa I'm gonna
use that notebook that I create I want to bring up the variables and it's gonna
put it into a viable mice also when I run that if I look at MATLAB now I have
my soul viable we symbolic expression I can look at it here is the symbolic
expression of what I just calculated there this is still a symbolic
expression so if I wanna actually you sit there and take Matlab function that
allows you to convert that symbolic expression into one america expression
that can be evaluated by Madeline you can create function handles or you can
let me run this second one here so this is going to create actually a function
file for example so it just created here are my funk filed I am which is a fully
operational numerical model evaluation function so you can call it from your
mother scripts you can put it in a blocking Simulink there's out there
out of made it out of my ways of doing this now so if you look at the script
again here there's their command function block that allows you to
directly from the symbolic expression
create a a Simulink block that you can use for a dynamics let me go back to my
slides right now so I have shown you how you can use a symbolic interface to
analytically solve a problem
create equations dis symbolic analysis tool has multiple
animation commands is very powerful to the station and graphics so I will
recommend you guys take a look at it so once I have the differential equation I
can solve it if it has had an analytic solution I can solve it in her face or I
can solve it numerically
so you can also has an american soldiers that allow you to to solve nonlinear
differential equations for example or you can obviously bring it back to
MATLAB matlab has all kinds of bodies all very ordinary differential equation
solver second be called wants you to find a function that you want to solve
the set of differential equations are you want to solve you can call the OD
solver and that would that will give you the solution of the differential
equation in this case this example for example I'm here you notice that the
equation that I'm solving and I'm calling and Audis over to do it or I can
bring this up to Simulink go let me go back to my my script here and I'm now
open
Simulink implementation this is a Simulink implementation of that
differential equation calculator is satisfied all case of mathematical
capabilities to build any kind of linear nonlinear continues discontinuous
differential equation and Simulink already has the notion of time and all
the old and numerical solvers embedded in it so I don't have to worry about
calling the different than numerical integrators
I just killed by equations play and in this case it will be running it with a
naughty body runge-kutta 45 algorithm and its giving me the solution of that
differential equation the advantage of their graphical in nature of Simulink is
that you can component I think so star very quickly changing things if i were
now add additional nonlinearity 0 Council block download the situations
and backlash shares all lookup tables if you start if you start programming
systems are much bickering matter becomes very complicated to manage while
the other part of the power of this is the fact that singing US side showed you
in new Bruns on top of MATLAB so he can make use of the programming capability
of madeleine salami
close this and show you one more example where I have a matlab script there's no
matter where you have MATLAB commands allow you to talk between MATLAB and
Simulink so they're still communication here I'm opening a system it's just the
same equation they show you only added like a damping a damping element for a
full dynamic simulation environment so all the integration is happening
automatically
I am seen seen the behavior of the system in this case has damping sold-out
solution is coming down but the important part here is that because I
can run this from a script and outside of all this stuff that is a lot of
graphics when I went out while you I want you to pay attention to this line
in the script this send the same as a Matlab function that allows it to call a
dynamic simulation so simulated dynamic system so you tell us what model you
want her on and what are the parameters that you want to use for a particular
simulation and the cool thing is that you can put that inside a for loop for
example and very quickly run a parameter sweep or are multiple partners you can
see how you can have like nested for loops where you stretch many many
parameters and then automatically I can display here and this is gonna use of
simulation modeling the background is gonna run in many many times and he's
going to automatically capture all the resources and I'm putting them all in a
preneed matter plot for example so I big value of the environment is the fact
that oldest tools can talk to each other such a show now let's go back to our
original problem we have a full 360 recovery mechanism and I just started
with a single pendant so let me extend the approach to a double pendulum and
very quickly when you start doing this it becomes such becoming complicated
prev reason because now you have a relative motion and the inertia starring
so the equations from solving this armoire are much more complicated that
she does just using Newton's law created the exercise just a figure out how
complicated will be fine I'm not trying to excite Jerry here I'm just using oil
electrons equations calculating the end
the energies kinetic and potential energy to express the different
differential equations and notice that it took me seven or eight piece of paper
to write those questions for justice sink double pendulum of course you can
do this
still with me but not let me show you that weren't charging you let me go back
to my script here so this again is some new pad notebook but in this case I have
done all the analysis let me have done all the analysis for a double pendulum
in this case was dismissed solving it when I went to mention it again I am
trying to get inside into their problem that I'm trying to solve and that's why
I'm getting and I am trying to get an idea of the effects of the length of the
effects of the initial conditions may be and see what my range of motion but not
as here I have I met when this becomes a big advantage now I'm telling you from
doing it on paper which is super prone to error I cannot tell you how many
hours I spent jar writing a paper on my clean solution but getting I'm making a
mistake on a sign or a simple the river is ferries are so here I define
positions are some links thanks cosines of angles for example to calculate
velocities and accelerations I simply different shape positions different
shift allotted his I am using oil I grinded playgrounds equations of motion
to solve this problem
not because this stationary equation that solves that allows me to solve
multi decrease of freedom mechanisms I have to calculate graduation requirement
to calculate the kinetic energy and looking so even for a double pendant
this expression starting really really achey potential energy I can get a grand
jury which is the difference between those two then have to start taking
partial derivatives with respect to each one of the state's so this is this is
really cumbersome when you're doing it without the help of some kind of
symbolic analysis and eventually I will get
to the to the basic equations of motion to
connected second order nonlinear differential equations that you're
seeing them she wants to replace all the time now I can use this form a Simulink
model for example or I can solve them here I'm showing here the use of the
numerical solvers in Newport I am this is again this farm equation doesn't have
a closed form solution so I need to solve numerically
so this is doing the numerical solution and I'm sure I want to show a little bit
of the animation capabilities are you can create objects all kinds who access
what this animation showing you as animating the solution of that pair of
differential equations me to stop that of course I said once I get the
equations you can actually build them in seemingly so once I have those equations
I can do seem willing to build those expressions the more complicated the
problem the more complicated the models are gonna become so many many terms but
I can component sizes I can start adding elements are not his undoing integration
from Thida double dark defeated ought to feed up in this very simple form just by
adding integrator blocks and the solution that you're gonna see here is
exactly the same as the solution that you get if you do the analytics sorry
you're doing and americans but the problem that we're noticing is that the
more complicated the problem becomes a more complicated equations become so you
get to a point where does equations are not gonna give me very much insight and
so there are there's this saying about using the appropriate tool for the
appropriate program so if we went out to think of this problem this mechanic so
if I think of this problem in a slightly different way for example think of
mechanisms has just bodies rigid bodies that have inner shells and Mathis and
they have degrees of freedom that arguing but given by certain joints we
have a specific torkelson mechanics that is a part of Simulink that allows you to
model this in a very straight manner so let me go to the tool to show you how a
little bit of how cynical
works so first time in Matlab Simulink using Simulink icon or by type in
Simulink MATLAB command this is the basic Simulink Library Browser what
you're seeing here is the base Simulink product that has all the mathematical
blocks to do
integration systems of differential equations transfer functions you can do
all kinds of nonlinearities you have all kinds of mathematical operations are you
can implement and underneath here you see a list of I don't products so under
the same state heading here you'll find some mechanics sassou mechanics are
three-dimensional mechanical Marler an asshole based on rigid body dynamics Luc
libraries for bodies and joints and the way you model things here
islamic open up black campus here dragging a body and my body is defined
our bodies defined by mass and it's inertia tensor and what you see on this
table here are the court in a location so points so where those CES wanna see
us to see a stands for coordinate systems so I am going to find CES wanna
Siro Siro Siro with respect to an adjoining reference what that means is
that this Court in a system is going to fall on top of whatever it is he's
connected to and what I am gonna do is I am gonna differing the CG I'm gonna very
simple Creek simply create a bar for example when I say the CDs 1 meter on
the x direction with respect to that serious one and that seems to the second
hooker point is gonna be two metres to the right of that serious one point for
example so I am just doing a relative location for example in this case and
creating a two metre long Bauer the CT is in the middle and there in 10 the
other extremists 24
for the sake of argument here what we're doing is we're let's let's imagine that
X is horizontal axis here and why is a vertical axis here
sold and that means that C would be easy access we'll be coming out of the
screen essentially so I have a buddy I can bring in I'm going to bring our
growing our reference cuz that's what this is connected all these measurements
are gonna be references some kind of ground to suggest a corner location of
that ground I need an environment port because every time you have you create a
money machine in some mechanics you have to bring one of this solver point what
the winner of this solver blocks let me flip it around and disempowerment
machine is going to control how the solution of the equations of motion for
the mechanism are happening so here you define your constraints and tolerances
for that solver and also you define that direction of gravity by the fall
gravities negative in the y direction so his vertical here so we're happy with
that but we can input it from the outside if I connect us to nothing's
gonna happen because I'm connecting my bar to ground so the way you give motion
to fix it by adding degrees of freedom and the way degrees of freedom are added
this by using this library staff joint and so notice that the library of joint
at all kinds of combinations Europe bushings one degree of freedom revolute
or prismatic joint up to 60 we saw freedom in this case what I want this I
revelatory revolution how you will think of her husband at door for example a
handgun authorities also on one side of the frame of the door on the other side
a half underway joints are defined as by a taxes action so noted that the axis of
action for this revolute joint is seriously what is around it's a
rotational degree of freedom around the sea access so around an axis coming out
of the screen which is what I want so I have a bar that is going to rotate are
on that point so once I have said all dat I can because this is a
three-dimensional mechanical modeling tool he has his release Asian so I'm
gonna just said it so it starts when I run the simulation shearson mechanics
their show animation and
play machines when we updated our rooms to turn on the animation and when i
press play here what you're going to see is the animation is going to start the
animation is going to start I have a bar that is really royalty
here so this is a single pendulum rotating back and forth this is desirous
0 where the ground location is my CG and at Sears stores over here but notice
that this doesn't look very realistic cuz I'm just wrote an ideal keep on
retaining no matter how long and simulating it because they joined there
have to find an idealised joint there's no one no friction damping no losses so
this will keep on rotating forever so the way I can affect joint for example
is by opening additional ports so I can open however many parts I want notice
that a couple of extra ears appear on this and when I go in the library
there's a section for sensors and actuators so you can activate embody
send massive thinks our bodies are you can activate on joints and measure
things from joins Anthony bring a joint activator and I joined sensor so I can
activate on this with any kind of Simulink calculation and I can measure
things for example so these actuators allow me to activate with either Torx
our forces or I can do motion profiles for example if I wanna send the motion a
specific motion prefer I can say that like this if I wanna fly out damping
force for example to make this more realistic a damping forces cannot be
proportional to the velocity in with at which this is retaining so in my
measurement side I can select notice that it recognizes it's a revolute so
kiss me all the possible measurements are my one from a revolute I can measure
angle never lost city Torx for example everlasting this case that is gonna come
out as a Simulink signal and I can actually feedback if I want to force is
going to be fed back as a force proportional to the velocity in this
case I wanted proportional to their losses so let me let me go to my senior
math operators
and bringing a game here so it's gonna be proportional to the velocity and he's
gonna be opposing the motion so I went again that missus minus 4.2 whatever
either I'm not even sure where protests random parameters and putting in what
will be correct there is also actually that is a little bit too much dumping me
to play and now this is a pendulum that is rotating and there's friction so it's
losing energy and the rotation is coming down so that the nice thing about having
this in Simulink in a graphical environment now is that what I just did
can be very easily represents let me get myself a little bit morse piece a little
bit more space so once you have components in Simulink you can actually
grab grab and group them all together in what are called subsistence so what I am
doing is I'm just putting what I just created let me instead of subsystem let
me call this link link 11 insight here I have that element that I just created
that revolute joint with the body connected to it and a damping element
for example what I can do is I can very easily copy and paste this and all of a
time when I have dealt is why I have converted my diagram from a single
pendulum to now have two elements connected to each other and remember
this now make make a little more sense I i define DCS one coordinate system I
said not joining reference so that means that is gonna located relative to
whatever is connected to automatically when I do this connection this CBS won
the second element Matt maps to see us doing the first element and I showed you
how complicated haha more complicated their questions for us to link pendulum
marinol I have done it's just that simple copy and paste here actually I
can get even a little more dramatic and start combining this
exciting area and let me make up an eighth victim and I just want you to
imagine how complicated or how convoluted the equations of motion for
it that would be so now I have all I've done is I'm copy and paste on in two
seconds I have a multi link element all of their differential equations of
motion are being implemented by the tool automatically for me so is combining all
this individual leaner meaner shower body in her chest with their degrees of
freedom and its building dole's
differential equations dynamic differential equations and so this is
essentially the basis the basics of house in mechanics works close that and
let me go back here so you can come you can start combining this into a very
very much any kind of mechanism that you wish and click for a particular Robert
go to my to my script here actually I have three Inc percent so I kinda did
the same thing that I just showed only I each element has a different different
in a shower and a relations then I'm doing anything they nurture calculations
are functions of the masses under links everything so you can do analytics here
and then let me add up to the calculations this is gonna set up the
inertia I have the first element this turntable the turntable for my robots
old standoff rotating around errands heed the only thing that have changes
that this rotator y axis if I actually felt this turn on the haitian hear what
you see is you have like I have four elements that turntable element that is
gonna rock around the y axis which is the vertical axis and when i press play
here I have initial condition of the initial conditions and I have also we
have because damping and stiffness are such common plus we have blocked that
allow you to feed that directly but I can monitor all the angles for example
in this case that while I'm looking at their table that is not rotating at all
in this case but I can see the patience of their their the angle of rotation for
the base airport for the forearm for the rest for example so of course this is a
mechanical modeling tool and i'm looking up by the way I'm looking at dinner she
opens her so you can view this line diagrams like I showed you before just
stick the realization or you can do equivalent sensors which is what you're
seeing here so now it looks a little bit more based on the shape of the parts it
looks more like that that's that young that's not the exact geometry of the
part by it looks like that and we have connection gimme gimme actually close
this we have a connection to CAD tools so what I'm gonna show you now is how
you can bring all that information from a definition in a cut or I am gonna be
using SolidWorks for this example but we have connections not only to SolidWorks
we have direct connections to engineer and the advantage of using a catalyst
not only that you despite the sign the final the graphic of geometric
characteristics in a cattle but once you define that geometric characteristics
you for example it also if you put into material properties you get all the
answers and all the masses automatic so what was the translator the same
mechanics translator is gonna do is from the cat definition capture all the
senior ship enters its gonna capture the location of all the coordinate systems
of all them makes all the joints in this case and got his gun interpret the mates
from the cad and convert them into equivalency mechanic joints and so was
that translate once you have some mechanics installed this up with this
would appear as an add-on to SolidWorks assisi earned their specific context
link but the way this operation on the File menu if you go save us besides all
the normal performance that you have from SolidWorks you will have a specific
form that while the normal format that you have for many cattle you have this
XML format so what I'm gonna do as I'm gonna save a file called Robert one XML
this XML for Maurice a text format that is gonna just replaces going to capture
all the information from from each one of the parts of the tools so you'll see
it in a second start and what it's doing right now is going piece-by-piece
throughout the mechanism and is capturing all the mass and inertia
princess said before and also the cornea locations of all the hook up points and
eventually once it finishes is gonna shave all this information into that XML
file
just finished so save the XML file into Robert def SolidWorks CAD files Robert
one XML so let me get ok here and gonna close my SolidWorks and if I go back to
my MATLAB now underneath here I have this robot 101 XML this is the file
their West just automatically generated so the way I can bring an end is with
the command called me in Matlab function that campus in mechanics that allows you
to select the file that you wanna import so there is one XML file that I have
noticed that it also has the options to update so if you go back to the category
for something and want to bring it again and that lose your previous work you can
just update existing models but all I'm gonna do here is it ok and this is going
to read that XML file for me is gonna be the location of all the blocks are
automatically putting them all together this is a whole series of cinema conduct
blocks and is robert has many many pieces and so you see the forearms and
biceps
joint that connected the gripper for example there is great for subsistence
here where you have all the components of the gripper and notice this old
bodies and joint on most of those joint because it's a relatively simple modest
has it their all rotational revolute joints and so when i press play here
this is a full fully functional dynamic model helping the simulator enemies stop
the second bigger so whether when I want you to notice what I want you to notice
it has not only turned on its not only brought in mass information inertia
information and cordial ok has also saved
STL versions of each one of them got parts so it's broadening that graphics
with it and now I have probably it looks like an actual road when I press play
all the dynamic equations are gonna be constructed on this one is being solved
now this looks kinda weird because what is happening is the only force acting on
my robot right now is gravity and so when i press play what you're seeing is
the only thing i acting on this is to wait because of the way this is going to
fall down fall off or on top of itself I went I went out to a couple comments 0
this that you're seeing is incorrect
obviously because all the joint the cat doesn't have information dynamic
information about the journey to all those joints are ideal there's no
friction there's no damping there's no notion of loss of this will keep on
flipping around forever so in that sense this is not a correct solution right now
but what I want to point out is that the equations are being solved right now are
the full set of differential equations that represent the dynamics of this so
that step
the following step when you brought it in is for example let me see I cannot
click on that part that's the forum let me open the block and you when I see the
populated data here is all being brought in from you see the inertia tensor hamas
says all the Corning at the quarry locations of all those points so that
has been automatically populated by the translator now when there is deformed
this one is that by six years so between the farm on the bicep have a revolute
joint which is where this mortar will be police said the adl will be in this
joint I would actually like open an additional port here and I can feed that
torque the idea will be to feeding the tour that will be coming from my
electric motor that is driving this so I can have a mathematical model or some
kind of control system that he's feeding back into disjoint whatever it is
supposed to be doing whatever tortoise receiving oral motion profits actually
when I have many close this
what I have got here to my script I have I have worked on this is exactly the
same model that I just showed you the translator Mohammad I have put some
callers on it so we can differentiate the pieces so when we look at them and I
have added actuators to each one of the joint actuators where what I'm doing a
meeting in a smooth polynomial trajectory so I'm giving it a motion
profile so now when I press play instead of you seen the think fallen itself know
what you're going to see is the rob the robot manipulator following a prescribed
rejected so I feel I can I decrease for the turntable 45 degrees for the buySAFE
30 degrees for the forum etcetera etcetera making it open and closed so
I'm exercising on my degrees of freedom to make sure that my mechanism is
properly defined in an automated way I have brought in all these dynamics are
now have a fully functional mechanical model of the system that I am gonna used
to the controls are used to do
simulations of different events are different trajectories for example so
let me go back to my slides and this is the final part so I just show you how to
bring him a translator bringing the information directly from a cattle and
we're going to continue in part two which we've talked about how do we do
the electric motors and how would we do the activation for this mechanism
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