what is an industrial robot?
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What is an industrial robot?C
Y
A kinematic chain
A robot is …
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C A kinematic chain
A multi-body dynamical system
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DV
A system with motors and drives
A system with digital and analogic sensors
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1
An electronic system
A supervised and controlled system
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C A supervised and controlled system
A software driven system
RO Therefore … a mechatronic system
Basilio Bona – DAUIN – Politecnico di Torino 002/1
Industrial roboticsC
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2C
FIC
Scope: object manipulation
Robots are often called
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DV
Robots are often called
Industrial Manipulators
CA
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1 Robots/robotic arms
Usually the robot base is fixed
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C yor moves along rails
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The previous COMAU robot at LabRob
Basilio Bona – DAUIN – Politecnico di Torino 002/2
LabRob
PrerequisitesC
Y Read Chapter 2 of the textbook
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C
Reference systems
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yVectorsMatrices
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Rotations, translations, roto-translationsHomogeneous representation of vectors
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C g pand matrices
RO
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Reference Systems/FramesC
Y
Three unit vectors (versors) mutually orthogonal in 3D space
Right-hand reference frames (RHRF) obey right hand rule
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C
Color code RGBk
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= ×k i jright hand rule
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1 j
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C i
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When the fingers go from i to j the thumb is aligned with k
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Reference Systems/FramesC
Y
We call this the “cavatappi” (corkscrew) rule
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C
= ×k i j
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j
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iRj
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C
i
RO
This is also called a CARTESIAN FRAME
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Reference frames and rigid bodiesC
Y
E i id b d i d fi d b RHRF
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C Every rigid body is defined by a RHRF, the so-called body frame (BF)
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All points in the rigid body are defined
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1 All points in the rigid body are defined by suitable vectors in the body frame
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CR
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Vectors and MatricesC
Y Introductory notes on vectors and matrices can be found here
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C
VECTORSVECTORShtt // l di lit it/M t i /01CFI/2008 09/Slid /V tt i df
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http://www.ladispe.polito.it/Meccatronica/01CFI/2008-09/Slides/Vettori.pdfhttp://www.ladispe.polito.it/Meccatronica/download/Appunti_matrici_vettori.pdf
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MATRICESMATRICES
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C MATRICESMATRICEShttp://www.ladispe.polito.it/Meccatronica/01CFI/2008-09/Slides/Matrici.pdf
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KinematicsC
Y
Kinematics allow to represent positions, velocities and accelerations of multibody points, independently from the causes that generate them (i e forces and torques)
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C them (i.e., forces and torques)
In order to describe the kinematics of manipulators or mobile robots,
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it is necessary to define the concept of kinematic chain
A kinematic chain is a series of ideal arms connected by ideal joints
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TIC Flexible Arm
M = 9.5 [g], J = 0.547 [Kgmm^2],L = 2.5 [cm]
RO
M = 102 [g], J = 530 [Kgmm^2],L = 25 [cm]
M = 192 [g], J = 3595 [Kgmm^2],L = 47.5 [cm]
Basilio Bona – DAUIN – Politecnico di Torino 003/8
Is the human arm a kinematic chain?C
Y
W i t
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C Wrist
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Arm What is this?
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1 The human arm + wrist has 7 dof
A redundant arm
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C
But it is not ideal, since it is composed by muscles, bones and other tissues is not a rigid body
RO other tissues, is not a rigid body,
the joint are elastic, etc.
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Kinematic chainC
Y A kinematic chain KC is composed
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C by a variable number ofArms/links (rigid and ideal)Joints (rigid and ideal)
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Joints (rigid and ideal)
It is defined only as a geometric entity (no mass, friction, etc.)
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It has degrees of motion and degrees of freedom (DOF)
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C
One must be able to fix on each arm a RF -> DH conventions
b bl d bRO One must be able to describe every
possible point in a given RF
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Kinematic chainC
Y
A multi-body structure composed by ideal rigid arms/links (no mass and other dynamic properties), linked to other arms by
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C
ideal joints that allow a relative motion between two successive arms
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Joints 4 5 6Link 3 Joints allow a single degree of motion
between connected links
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Joint 3Joints 4, 5, 6
Arm 2
between connected links
Joints may beRotoidal or rotation or rotational joints
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C
Joint 2Arm 1
– Rotoidal or rotation or rotational jointsallow a relative rotation between arms
– Prismatic or translation joints allow a
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Joint 1relative translation between arms
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Kinematic chain
shoulder
CY
shoulder
wrist
wristshoulder
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C wrist
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C
A –
01
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CR
O
Basilio Bona – DAUIN – Politecnico di Torino 003/12
Rotation Joints
How we draw joints and links?How we draw joints and links?
CY Rotation joints are draw in 3D perspective as
small cylinders with axes aligned along each
How we draw joints and links?How we draw joints and links?
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C small cylinders with axes aligned along each rotation axis k
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j
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ij
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C
Rotation joints are draw in 2D as small circles or small hourglasses
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jik
axis is normal to the planepointing toward the observer
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jk
Prismatic Joints
Prismatic joints are draw in 3D perspective as
CY
Prismatic joints are draw in 3D perspective as small boxes with each axis aligned along the translation axis
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CC
FID
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Prismatic joints are draw in 2D as small squares
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C with a point in their centres or as small rectangles with a line showing the two successive links
RO
jik
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i
Another exampleC
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2C
FIC
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C
A –
01
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Kinematic chainC
Y The COMAU robot seen as an ideal kinematic chain
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CC
FID
V
CA
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1O
BO
TIC
RO
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Kinematic representationC
Y q6
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C
q3q
q5
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q4
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The joint motion produces a motion in
q2
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C j pCartesian 3D space.
One must be able to describe the relation between the two representations
q1
RO between the two representations
Joint space vs Task space
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Joint space and task spaceC
Y
Task Space (Cartesian)
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C
Joint space
Task Space (Cartesian)
z
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63qdirect
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y
n
i
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C x y
q2q
inverse
RO
1q
direct kinematics is easier than inverse kinematics
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Task SpaceC
Y
Task Space Operational Space
WorkspaceAre synonymous
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C p
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C
A –
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CR
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Degrees of motion and degrees of freedomC
Y The degrees of motion (dom as they are called) count the
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C The degrees of motion (dom, as they are called) count the number of prismatic/rotation joints (active, i.e., motor-driven or passive)
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The degrees of freedom (dof, as they are called) count the number of free parameters of the considered body
CA
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1 number of free parameters of the considered body
Dofs may be referred to manipulator, when they count what it can do with its center point or to the task when measure what
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C can do with its center point, or to the task when measure what is required by the application
RO
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Degrees of motion and degrees of freedomC
Y TCP Tool Center Point
Joint 3
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C
Joint 1
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Joint 4
Joint 2
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1 Joint 2
Base
The KC has 4 degrees of motion since there are 4 rotating joints
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C The KC has 4 degrees of motion since there are 4 rotating joints
An object in a plane has only 3 dof (two positions + one angle)
Therefore this KC is redundant (redundancy 4-3 = 1).
RO Therefore this KC is redundant (redundancy 4 3 1).
If the task requires only the object positioning, with no particular constraint on i t ti th d f ill d t 2 d th d d i t 4 2 2
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orientation, the dof will reduce to 2 and the redundancy increases to 4-2=2
Often one reads that a robot control is able to manage, e.g., 8 dof.
This sentence should be correctly understood, since it means that the robot is able
CY
to control 8 degrees of motion.
In the example below the robot has 5 dof and 5 dom, and the additional 3 dom on
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C
the rotating fixture are useful only for part machining.
The task on parts on the rotating fixtures requires 5 or 6 dof.
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C
A –
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CR
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E l f b t ith l t ti fi t
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Example of a robot with a slave rotating fixture with additional degrees of motion
In this example the robot has 5 dom, + 1 of the translating base + 2 of the two
rotating fixtures.
CY
otat g tu es
In total 5+1+2=8 dom, and the task maybe 5 or 6 dof
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CC
FID
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TIC
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Robot with a translating base
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Robot with a translating base
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