what is an industrial robot?

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

CA

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1

An electronic system

A supervised and controlled system

OB

OTI

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

Y0

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

OB

OTI

C yor moves along rails

RO

The previous COMAU robot at LabRob


LabRob

PrerequisitesC

Y Read Chapter 2 of the textbook

02

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C

Reference systems

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DV

yVectorsMatrices

CA

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1

Rotations, translations, roto-translationsHomogeneous representation of vectors

OB

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C g pand matrices

RO


Reference Systems/FramesC

Y

Three unit vectors (versors) mutually orthogonal in 3D space

Right-hand reference frames (RHRF) obey right hand rule

02

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C

Color code RGBk

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DV

= ×k i jright hand rule

CA

–0

1 j

OB

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C i

RO

When the fingers go from i to j the thumb is aligned with k


Reference Systems/FramesC

Y

We call this the “cavatappi” (corkscrew) rule

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C

= ×k i j

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DV

j

CA

–0

1

iRj

OB

OTI

C

i

RO

This is also called a CARTESIAN FRAME


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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DV

All points in the rigid body are defined

CA

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1 All points in the rigid body are defined by suitable vectors in the body frame

OB

OTI

CR

O


Vectors and MatricesC

Y Introductory notes on vectors and matrices can be found here

02

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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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DV

http://www.ladispe.polito.it/Meccatronica/01CFI/2008-09/Slides/Vettori.pdfhttp://www.ladispe.polito.it/Meccatronica/download/Appunti_matrici_vettori.pdf

CA

–0

1

MATRICESMATRICES

OB

OTI

C MATRICESMATRICEShttp://www.ladispe.polito.it/Meccatronica/01CFI/2008-09/Slides/Matrici.pdf

RO


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)

02

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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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DV

it is necessary to define the concept of kinematic chain

A kinematic chain is a series of ideal arms connected by ideal joints

CA

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1O

BO

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]


Is the human arm a kinematic chain?C

Y

W i t

02

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C Wrist

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DV

Arm What is this?

CA

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1 The human arm + wrist has 7 dof

A redundant arm

OB

OTI

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.


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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DV

Joints (rigid and ideal)

It is defined only as a geometric entity (no mass, friction, etc.)

CA

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1

It has degrees of motion and degrees of freedom (DOF)

OB

OTI

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


Kinematic chainC

Y

A multi-body structure composed by ideal rigid arms/links (no mass and other dynamic properties), linked to other arms by

02

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C

ideal joints that allow a relative motion between two successive arms

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DV

Joints 4 5 6Link 3 Joints allow a single degree of motion

between connected links

CA

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1

Joint 3Joints 4, 5, 6

Arm 2

between connected links

Joints may beRotoidal or rotation or rotational joints

OB

OTI

C

Joint 2Arm 1

– Rotoidal or rotation or rotational jointsallow a relative rotation between arms

– Prismatic or translation joints allow a

RO

Joint 1relative translation between arms


Kinematic chain

shoulder

CY

shoulder

wrist

wristshoulder

02

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C wrist

CFI

DV

C

A –

01

OB

OTI

CR

O


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

CFI

DV

j

CA

–0

1

ij

OB

OTI

C

Rotation joints are draw in 2D as small circles or small hourglasses

RO

jik

axis is normal to the planepointing toward the observer


jk

ExampleC

Y0

2C

FIC

CFI

DV

C

A –

01

OB

OTI

CR

O


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

02

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CC

FID

V

CA

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1

Prismatic joints are draw in 2D as small squares

OB

OTI

C with a point in their centres or as small rectangles with a line showing the two successive links

RO

jik


i

ExampleC

Y0

2C

FIC

CFI

DV

C

A –

01

OB

OTI

CR

O


Another exampleC

Y0

2C

FIC

CFI

DV

C

A –

01

OB

OTI

CR

O


Kinematic chainC

Y The COMAU robot seen as an ideal kinematic chain

02

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CC

FID

V

CA

–0

1O

BO

TIC

RO


Kinematic representationC

Y q6

02

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C

q3q

q5

CFI

DV

q4

CA

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1

The joint motion produces a motion in

q2

OB

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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


Joint space and task spaceC

Y

Task Space (Cartesian)

02

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C

Joint space

Task Space (Cartesian)

z

CFI

DV

63qdirect

CA

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1

y

n

i

OB

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C x y

q2q

inverse

RO

1q

direct kinematics is easier than inverse kinematics


Task SpaceC

Y

Task Space Operational Space

WorkspaceAre synonymous

02

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C p

CFI

DV

C

A –

01

OB

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CR

O


Degrees of motion and degrees of freedomC

Y The degrees of motion (dom as they are called) count the

02

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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)

CFI

DV

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

OB

OTI

C can do with its center point, or to the task when measure what is required by the application

RO


Degrees of motion and degrees of freedomC

Y TCP Tool Center Point

Joint 3

02

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C

Joint 1

CFI

DV

Joint 4

Joint 2

CA

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1 Joint 2

Base

The KC has 4 degrees of motion since there are 4 rotating joints

OB

OTI

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


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

02

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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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DV

C

A –

01

OB

OTI

CR

O

E l f b t ith l t ti fi t


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

02

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CC

FID

V

CA

–0

1O

BO

TIC

RO

Robot with a translating base


Robot with a translating base

what is an industrial robot?

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