Lecture Notes for Introduction to Robotics

Chapter 1 Intro duution


c. / Mathematical Modeling of Robots
1. 1 /
.

Symbolic Representation of Manipulators (Robots)
Manipulators have links that are connected to joints to form a kinematic chain
Joints →
usually rotary or linear
" "


Revolute Joint → Allows relative rotation between two links (R)
"
Prismatic Joint → Allows a linear relative motion between two links (P)
"




A 3- link arm with 3
rotary joints would be RRB
Joint Variables → ④ for Revolute Joint (d) for Prismatic Joint

I. 1.2 Configuration Space of Manipulator
configuration → the location of
point on the manipulator
every
configuration Space → set of all possible configurations
A configuration is denoted by 9i where joint Variables can be set to % % % , ,
. . .
.
In

qi=⊖i for revolute joint Ii =D ± for Prismatic Joint where each % is a vector



1. 1.3 State Space
State of a
manipulator →
contains a set of Variables that describes the manipulator 's dynamics and
"


Important for determine future state !
'

input .




state space → the set of all possible states I=(9 IF I
,
contains joint velocities .




Dimension of the state
space
is Zn it
system has a D0F


1. 1.4 The Workspace
Workspace
→ Max space or dimensions of Motion of a manipulator 's end effector
Points that can be reached by the end effector .




Workspace ( w ) PEW Piseud effector Position

Joint space
Joint space → set of all Possible postures


of C- Q 9 is individual postures (9,4 %) . . .




•



Joint space ! Workspace
Forward
kinematics B→
Joint Space Workspace
9. c- Q PEW
%

Inverse kinematics
" "

For g. there is up → I→ P PLAY £ ) C- w Forward kinematics
every ,




be[o◦r•]q" →
"
For any P there
may p→q

, I. 1 Extra Info on Workspaces and Joint spaces

Voids

Voids are areas or dimensions that are unreachable by the end effector
☆ Unreachable by the end effector in any pose -




Dexterous workspace
" "

that be reached with all
possible orientations
set of all positions can



☐
Workspaces of Different configurations

THPP → cylindrical Arm RRP →
Spherical Arm PPP → Cartesian




widely used for

printers



Factors influencing shape and size of Workspace
1) # of 1) of
2) Type of Joints
3) Order of Arrange Joint
4) Link Lengths
5) Constrained Joints 1? )

, 1. 2 Robots as Mechanical Devices
I. 2.1 Classification of Robotic Manipulators
criteria of a manipulator → Power source geometry application
, ,
area
,
method of control
.




Method of Control : Servo → closed to determine their motion
°



loop
-




comp control .




Non -

servo → The earliest robots and are
open
-

loop .




No sensor to determine movement
Geometry →
articulated (RRR ) , Spherical (RRP) ,
SCARA (RRP ) , cylindrical (RPP ), Cartesian (PPP


articulated →
9=[0,0-203]