Fundamental of robotic manipulator

Mrs. S. N. Kale
Asst. Professor
PVPIT, Budhgaon
Fundamental of Robotic
Manipulator

In the first part of this unit we would be studying the
basics associated with the industrial robots,
like basic types,
Classifications:
the methods to specify the robots,
types of drive technologies used in robotic applications,
Motion control methods
the various applications of the robots.
specifications:
Example: RHINO XR-3
2 Fundamental of Robotic Manipulator

•Mankind has always strived to give life like qualities to its
artifacts.
•He tries to find substitute for himself to carry out his orders
and also work in hostile environment.
•Broadly robot is a machine that looks and work like a
human being.
•The industry is moving from automation to robotization , to
increase productivity and to deliver uniform quality.Robots are employed in hostile environment:
1. Atomic plant to handle radioactive material.
2. Construct and repair space station and satellites.
3. Nursing and aiding patient in medical field.
4. Heavy earth moving equipments.

reasons for using a robot but the central reason is to eliminate a human
operator.
The most obvious reason :
•To save labor and reduce cost.
Other classes of applications concern the product:
•Human is bad for the product: e.g. semiconductor handling,
food handling, pharmaceuticals, etc.
•Product is bad for the human : e.g. radioactive product.
robots can be used to replace human operators where the dangers are:
1.Repetitive strain syndrome.
2.Working with machinery that is dangerous for example presses, winders.
3.Working with materials which might be harmful in the short or long term(toxic
chemicals, radioactive material.

Here robot is considered as industrial robot called as
robotic manipulator or robotic arm.
This arm is roughly similar to human
arm.
It is modeled as chain of rigid links
interconnected by flexible joints.
Links corresponds to :chest, upper
arm, fore arm
Joints: shoulder, elbow, and wrist.
At end of arm is an end effector (
tool, gripper or hand).
Tool has two or more fingers that open
and closes.

Wrists connects end effector to forearm.
End effector may be a tool and its fixture or gripper or
any other device
1. Grippers: are generally used to grasp and hold an
object and place it at a desired location.
Grippers classified as mechanical grippers, vacuum or
suction cups, magnetic grippers, adhesive grippers,
hooks, scoops, and so forth.
2. Tools: a robot is required to manipulate a tool to perform
an operation on a work part. Here the tool acts as end-
effector.
Spot-welding tools, arc-welding tools, spray-painting
nozzles, and rotating spindles for drilling and grinding are
typical examples of tools used as end-effectors.7 Fundamental of Robotic Manipulator

Automation and robot:
Automation is technology which is concerned with the use of
mechanical ,electrical and computer based system in
operation and control of production.
e.g. Transfer lines,mechanized asembly
machines,feedback control system,numerically controlled
machine tools and robot
Two types:
Hardware automation and software automation

Hard automation, also called fixed automation, is built with
a specific production purpose.
This automation approach is best suited for mass
production of the same product with few alterations or
change-overs.
When volume of production is very high, special
equipment are designed to process product efficiently
and at high production rate.
When production cycle ends or new product is
introduced ,that m/c have to be shut down and h/w
retooled for next generation of models.
CNC machines are examples of hard automation

Soft automation, often referred to as flexible automation, is
reprogrammable and reconfigurable.
Now auto industry and other industries have introduced
more flexible forms of automation in manufacturing
cycle.
Programmable mechanical manipulator are now being
used to perform task as spot welding ,spray painting,
material handling etc.
Since computer controlled mechanical manipulators can
be converted through s/w to do variety of task they are
referred as soft automation.
Robots fall into this soft automation category. This method
is ideal for handling small batches of product and

Manual labor
Soft automation
hard automation
v1 v2
Product volume
Unit cost
Qualitative comparison of cost effectiveness of manual labor ,hard
automation and soft automation
Upto v1-manual labor is cost effective.
After v2 –hard automation is cost effective
V1 to v2-soft automation is cost effective

Robots, the industrial robots are the specialized, highly
automated mechanical manipulators which are controlled by
sophisticated electronic control systems and computer
systems
The robots can be programmed to do a variety of operations
by just changing the predetermined set of instructions
called program , through some compatible software.
This is also termed as soft automation.

What is an Industrial Robot?
 An industrial robot is a programmable, multi-
functional manipulator designed to move
materials, parts, tools, or special devices
through variable programmed motions to
perform a variety of tasks.
An industrial robot consists of a number of rigid
links connected by joints of different types,
controlled and monitored by a computer.

An industrial robot can be defined as :
Robot can also be defined as a software
controllable mechanical device that uses
actuators and sensors to guide one or more end
effectors through programmed motions in a
workspace in order to manipulate physical
objects.

What are the
parts of a robot?
• Manipulator
• Pedestal
• Controller
• End Effectors
• Power Source

Manipulator
(Mimics the human arm)
• Base
• Appendage
Shoulder
Arm
Grippers

Pedestal
•Supports the
manipulator.
•Acts as a
counterbalance.

Controller
(The brain)
• Issues instructions
to the robot.
• Controls peripheral
devices.
• Interfaces with
robot.
• Interfaces with
humans.18 Fundamental of Robotic Manipulator

End
Effectors(The hand)
• Spray paint
attachments
• Welding
attachments
• Vacuum heads
• Hands
• Grippers19 Fundamental of Robotic Manipulator

Power
Source
(The food)
• Electric
• Pneumatic
• Hydraulic

Classification :
based on drive technologies:
An important element: The drive system ,it supplies the power for
the actuation of various linkages and joints of a robot and
enabling the robot to move.
The dynamic performance depends on the type of power source.
three types of power sources for robots:
Electric drive:
Most of the industrial robots use electric drive system, in the form
of either DC stepper motor drive (open loop control), or, DC servo
motor drive (closed loop control).
Advantages: This drive system gives better positioning accuracy and
repeatability, and is suitable to keep cleaner environment around.22 Fundamental of Robotic Manipulator

Hydraulic drive:
at higher speeds and at substantial loads hydraulic drive
robot are preferred.
Disadvantage: it occupies large space area and there is a
danger of oil leak to the shop floor.
But it gives lower movement compare to the hydraulic robots and
the electric drive system is good for small and medium size robots
only.

Pneumatic drive:
used for high speed and/or high-load-carrying
capabilities. A pneumatic drive is clean and fast
but it is difficult to control because air is a compressible
fluid.
For both electrical and hydraulic drive robots most of the
time make use of the pneumatic tools or end effectors.
Pneumatic drives used especially when the gripping action
of the end effectors is simple open and close operation to
pick light objects.
the pneumatic drive system is preferred for smaller robots as
these are less expensive than electric or hydraulic robots and
suitable for relatively less degrees of freedom design for
simple pick and place application.

The Robotic Motions:
oThe industrial robots are designed to perform some
desirable work
o This can be performed by enabling the manipulator to
move the body, arm and wrist through a series of motions.
oIt helps the end effectors of the robot to achieve the
desirable position and orientation in the three dimensional
space surrounding the base of the robot.
Work envelop geometries:

Robot Joints
•A robot joint permits relative movement between parts of
a robot arm.
•The joints of a robot are designed to enable the robot to
move its end-effector along a path from one position to
another as desired. The end effector is mounted on a
flange or some plate secured to the wrist.
• It is the tool to perform some operation or some gripper for
pick and place operations.

The robot movements are broadly classified into two main
categories, namely
(i)arm and body motions
(ii) wrist motions.
The individual joint motions associated with these two
categories are also referred to as the degrees of freedom .
The first three axes of the robot are referred to as the
major axes.
The position of the end-effector of the robot is determined
by the position of the major axes.
Similarly three more axes associated with the wrist, are
called minor axes and are used to establish the
orientation of the tool or the gripper at wrist.

Degrees of Freedom
Degrees of freedom (DOF) is a term used to describe a
robot’s freedom of motion in three dimensional space
—specifically, the ability to move forward and backward,
up and down, and to the left and to the right.
For each degree of freedom, a joint is required.
A robot requires minimum six degrees of freedom to be
completely versatile.
Its movements are clumsier than those of a human hand,
which has 22 degrees of freedom

The number of degrees of freedom defines the robot’s configuration.
For example, many simple applications require movement along three axes: X, Y,
and Z.
See Figure 2-10. These tasks require three joints, or three degrees of freedom

The locus of the points in the three dimensional space that can
be reached by the wrist by the various combinations of the
movements of the robot joints from base up to wrist, is called the
gross work envelop of the robot.
The robot motions are accomplished by means of powered joints.
Thus a minimum of six axes are
required to achieve any desirable
position and orientation in the robot’s
work volume or work envelop or
workspace.

The rigid members connected at the joints of the robot are called
links.
In the link-joint-link chain, the link closest to the base is referred to
as the input link .
The output link is the one which moves with respect to the input
link.
There are basically two types of
joints commonly used in industrial
robots, which are:
(i) prismatic or linear joints,(p)
which have sliding or linear
(translational) motion along an
axis.

(ii)Revolute ,(R) : which exhibits the rotary motion about an axis.
the links are aligned perpendicular to one another at this kind
of joint.
The rotation involves revolution of one link about another.

Based on the physical configuration or the combination of the
revolute or prismatic joints for the three major axes, a particular
geometry of the work envelop is achieved.
The table shows the some of the most common robot work envelops
based on the major axes:
robot Axis 1 Axis 2 Axis 3 Total
revolute
cartesian P P P 0
Cylindrical R P P 1
Spherical R R P 2
SCARA R R P 2
Articulated R R R 3

Cartesian Gantry Robot Arm

 robots with Cartesian configuration consist of links
connected by linear joints (p).
 Thus the resulting configuration is (PPP).
The three joints corresponds to the notation for the moving
the wrist up and down, in and out, and back and forth.
Thus the work envelop/ work volume generated by this
robot is a rectangular box.
example: the gantry robot
Cartesian Gantry Robot Arm
Uses 3 perpendicular slides
to construct x , y , z axes.
Hence called xyz/rectilinear
robot.
e.g. IBM RS-I robot

Cartesian Gantry Robot
Arm
commonly used :
•for pick and place work for
heavy loads
• assembly operations
• handling machine tools
• arc welding operations

work envelop/ work volume

The major advantages :
1.Ability to do straight line insertions into furnaces.
2.Easy computation and programming.
3.Most rigid structure for given length.
Disadvantages :
1.Requires large operating volume.
2.Exposed guiding surfaces require covering in corrosive or dusty
environments
3.Can only manipulate the objects in front of it.
4.Axes of robot are hard to seal

Changing the first prismatic joint of the Cartesian
coordinate robot by revolute joint, to have RPP configuration
we get the cylindrical coordinate robot.
The space in which this robot operates is cylindrical in
shape, hence the name cylindrical configuration.
Cylindrical Robot Arm
The revolute joint swings
the arm back and forth about
vertical base axis.
The prismatic joints then
move the wrist up and down
along vertical axis and in and
out along a radial axis.
R
P
P

Cylindrical Robot Arm

As there is
always some
minimum
radial
position, the
work envelop
is actually the
volume
between two
concentric
cylinders.

commonly used for: handling at die-casting machines,
assembly operations, handling machine tools, and spot
welding operations.
major advantages :
1.can reach all around itself
2.rotational axis easy to seal
3.relatively easy programming
4.rigid enough to handle heavy loads through large working
space.
5.good access into cavities and machine openings.
Disadvantages :
1.can't reach above itself.
2.linear axes is hard to seal.
3.won’t reach around obstacles.
4.exposed drives are difficult to cover from dust and liquids.

Spherical Robot Arm

If second joint of cylindrical coordinate robot is replaced with
revolute joint (RRP) this produces spherical coordinate robot.
•Here the first revolute joint
swings the arm back and forth
about a vertical base axis,
•the second revolute joint moves
the arm up and down about the
horizontal shoulder axis,
• the prismatic joint moves the
wrist radially in and out

The work
envelope is the
volume between
two concentric
spheres
e.g. UNIMATE
2000 series,
MAKER 110

commonly used for:
material handling at die casting
or fettling machines, handling
machine tools and for arc/spot
welding etc.
the advantages:
1.Large working envelope.
2.Two rotary drives are easily
sealed against liquids/dust.
The disadvantages are:
1.Complex coordinates more
difficult to visualize, control, and
program.
2.Exposed linear drive.
3.Low accuracy
Spherical: RRP

SCARA Robot Arm
Adept's SCARA robots

Like a spherical
coordinate robot, a
SCARA robot
(Selective
Compliance
Assembly Robot
Arm) is a robot with
at least two parallel
revolute joints (R)
and having one
linear joint for the
positioning of the
wrist.
But for a SCARA robot all three joint axes are vertical

The first revolute axis swings the
arm back and forth about base axis
i.e vertical shoulder axis.
The second revolute joint swings
the forearm back and forth about
the vertical elbow axis.
Thus two revolute joints control
motion in a horizontal plane.
The vertical component of motion is
provided by third joint, a prismatic
joint which slides the wrist up and
down.50 Fundamental of Robotic Manipulator

It gives
rigidity in
vertical
direction
and
complianc
e in
horizontal
axis
Work envelope

commonly used for:
pick and place work, and assembly operation with high working
speeds.
main advantages :
1.High speed.
2.Height axis is rigid.
3.Large work area for floor space.
4.Moderately easy to program.
The main disadvantages :
1.Limited applications.
2.Two ways to reach a point.
3.Difficult to program off-line.
4.Highly complex arm.

Articulated Robot Arm

In articulated coordinate robot all joints are revolute
joint (RRR).
It closely resembles the anatomy of human arm.
First revolute joint swings robot
back and forth about vertical
base axis.
Second joint pitches the arm
up and down about horizontal
shoulder axis.
Third joint pitches the forearm
up and down about horizontal
elbow axis.54 Fundamental of Robotic Manipulator

Work envelope

commonly used for:
assembly operations, welding, weld sealing, spray painting, and
handling at die casting or fettling machines.
main advantages :
1.All rotary joints allows for
maximum flexibility
2.All joints can be sealed from the
environment.
The main disadvantages are:
1.Extremely difficult to visualize,
control, and program these robots.
2.Restricted volume coverage.
3.Low accuracy.56 Fundamental of Robotic Manipulator

Manipulators
57
 Robot Configuration:
Cartesian: PPP Cylindrical: RPP Spherical: RRP
SCARA: RRP
(Selective Compliance
Assembly Robot Arm)
Articulated: RRR
Hand coordinate:
n: normal vector; s: sliding vector;
a: approach vector, normal to the
tool mounting plateFundamental of Robotic Manipulator

Classification based on motion control methods:
It is based on method used to control the movement of end effec
There are two types of motions:
1. Point to point motion:
• Tool moves to sequence of discrete points in a workspac
• The path between points is not explicitly controlled by user
• It is useful for operation which is discrete in nature.
e.g. Spot welding , pick and place , loading and unloading
Continuous motion:
•End effector follows a prescribed path in three
dimensional space.
•The speed of motion may vary along the path.
e.g. arc welding , spray painting

What Can Robots
Do?
Industrial Robots
Material Handling
Manipulator
Assembly
Manipulator
Spot Welding
•Material handling
•Material transfer
•Machine loading
and/or unloading
•Spot welding
•Continuous arc
welding
•Spray coating
•Assembly
•Inspection59 Fundamental of Robotic Manipulator

1.12.1 Loading/unloading parts to/from the machines
(i)Unloading parts from die-casting machines
(ii)Loading a raw hot billet into a die, holding it during forging and
unloading it from the forging die
(iii)Loading sheet blanks into automatic presses
(iv)Unloading molded parts formed in injection molding machines
(v)Loading raw blanks into NC machine tools and unloading the finished
parts from the machines

Single machine robotic cell applications include:
(i)The incoming conveyor delivers the parts to the fixed position
(ii)The robot picks up a part from the conveyor and moves to the
machine
(iii)The robot loads the part onto the machine
(iv)The part is processed on the machine
(v)The robot unloads the part from the machine
(vi)The robot puts the part on the outgoing conveyor
(vii)The robot moves from the output conveyor to the input
conveyor
Multi-machine robotic cell application: Two or three CNC machines
are served by a robot. The cell layout is normally circular.

Assembly Operations:
Electronic component assemblies and machine assemblies are
two areas of application.
Inspection:
Industrial robots are used for inspection applications, in which
the robot end effector is special inspection probe.

Palletizing and Depalletizing:
Many products are packaged in
boxes of regular shape and
stacked on standard pallets for
shipping.
Robots are commonly used to
palletize and depalletize boxes
because they can be programmed
to move through the array of box
positions layer after layer.

Drilling
Hole drilling is a precision
machining process.
Drilling robots use special
drilling end effectors which
locate and dock onto the work
piece or a fixture.

Spot Welding Spot welding is the most
common welding application
found in the manufacturing field.

Fastening
Robots are commonly
used for applying
threaded fasteners in the
automobile industry for
fastening wheels,
in the electronics
industry for screwing
components to circuit
boards and circuit
boards into chassis.

Paint and Compound
Spraying
Robots provide a consistency
in paint quality and widely
used in automobile industry
for medium batch
production.
Painting booths are
hazardous because the
paint material is often
toxic, and flammable.

Arc Welding
Ship building, aerospace,
construction industries are
among the many areas of
application

Robot specification
But in addition to classification, there are several additional
characteristics :
(i)Number of axes
(ii)Load carrying capacity (kg)
(iii)Maximum speed (mm/sec)
(iv)Reach and stroke (mm)
(v)Tool orientation (deg)
(vi)Precision, accuracy and Repeatability of movement (mm)
(viii) Operating environment

Number of Axes
The industrial robots have got a number of axes about which
its various links rotate or translate.
the first three axes of the robot called major axes are used to
establish the position of the wrist.
The remaining axes of the robot are used to establish the
orientation of the robots wrist, called minor axes .
Thus a six axes robot is a general manipulator which can move
its end effector to both an arbitrary location and an arbitrary
orientation with in its work volume.

Some industrial robots have more than six axes, termed as
the redundant axes , which are generally used to avoid
certain obstacle in the robots work volume.
The mechanism to activate the robot tool (end effector), or
the opening and closing of the robots gripper, is not
considered as the independent robot axis, as this
mechanism (axis) do not contribute to acquire either the
position or the orientation of the end effector in robots
working space.

Load Carrying Capacity:
The load carrying capacity is mainly determined by various factors
: robot’s size, configuration, type of drive system and the type
of application for which it is designed.
A very wide range: from few grams to several thousand of
kilograms.
The maximum load carrying capacity should be specified for the
condition that it is in its weakest position.
It is the position when the robots arm is at maximum horizontal
extension.

The specification provided by manipulator manufacturers is
actually the gross weight capacity that can be put at the
robotic wrist.
Thus to use this specification the user must know weight of
the end effector.
E.g., if the gross load carrying capacity of a robot is 10.0 kg
and it’s end effector weigh 3.0 kg, then the net load carrying
capacity of the robot would be only 7.0 kg.

The maximum tool tip speed of the robots is from a few mm per
second to several meters per second.
The speed of the robot is measured at robot’s wrist.
Thus the highest speeds can be achieved with maximum
horizontal extension of arm away from the base of the robot.
Also the type of the drive system affects the joint speeds,
e.g. the hydraulic robots are having faster joint motions than the
electrical drive robots.
Maximum Speed of Motion

A meaningful measure of the robot speed is the cycle time,
which is the time required to perform several periodic
motions of robot.
As it is desirable for any production operation to minimize
the cycle time of task, most of robots have the provision to
regulate or adjust the speed.

Reach and Stroke:
Reach and stroke of the robot are the measure of the work volume of
the robot.
The horizontal reach: it is the maximum radial distance at which the
robotic wrist can be positioned away from the vertical axis about which
the robot rotates, or the base of the robot.
The horizontal stroke: it is the total radial distance the wrist can move.
There is always a certain minimum distance the robot’s wrist will
remain away from the base axis.

Thus, the horizontal stroke is always less than equal to the horizontal
reach.
For a cylindrical coordinate robot the horizontal reach is the outer
cylinder of the workspace, while the horizontal stroke is the difference
between the radii of the concentric outer cylinder and the inner
cylinder, as shown in figure 1.10

The vertical reach:
is the maximum vertical distance above the working surface
that can be reached by the robot’s wrist.
The vertical stroke:
is the total vertical distance that the wrist can move.
the vertical stroke is also always less than equal to the
vertical reach.
articulated robot have full work envelope means stroke equal to
reach
But necessary to program to avoid collision with itself or work
surface.

Tool Orientation
The three major axes of the robot determine the work
volume, while remaining additional axes of the robot
determine the orientation of the robot’s end effector.
If three independent minor axes are present then the end
effector will able to achieve any arbitrary orientation in the
three dimensional work volume of the robot.
the three axes associated with the wrist are called as yaw-
pitch and roll which are used to define the orientation of end
effector of robot.

Degrees of Freedom
Degrees of freedom (DOF) is a term used to describe a
robot’s freedom of motion in three dimensional space
—specifically, the ability to move forward and backward, up
and down, and to the left and to the right.
For each degree of freedom, a joint is required.
A robot requires six degrees of freedom to be completely
versatile.
Its movements are clumsier than those of a human hand,
which has 22 degrees of freedom

For applications that require more freedom, additional
degrees can be obtained from the wrist, which gives the
end effector its flexibility.
The three degrees of freedom in the wrist have names:
pitch, yaw,and roll.
See Figure 2-11. The pitch, or bend, is the up-and-
down movement of the wrist. The yaw is the side-to-
side movement, and the roll, or swivel, involves
rotation.

1.Wrist roll: it involves the rotation of the wrist mechanism about
the arm axis. Wrist roll is also referred to as wrist swivel.
2. Wrist pitch: if the wrist roll is in its center position, the wrist pitch
is the up or down rotation of the wrist. also called wrist bend.
3.Wrist yaw: if the wrist roll is in center position of its range, wrist
yaw is the right or the left rotation of the wrist.
The wrist yaw and pitch definitions are specified w.r.t.the central
position of the wrist roll,
the rotation of the wrist about the arm axis will change the
orientation of the pitch and yaw movements.
The robot would have a spherical wrist if the axes used to orient
the tool intersect at a common point.

F3,m3
F2,m2
F1,m1
wrist
Roll
Pitch
Yaw

To specify tool orientation a mobile tool coordinate
frame M={m1,m2,m3} is attached to tool and moves
with tool.
M3 is aligned with principal axis of tool and pts
away from wrist
M2 is parallel to line followed by fingertips of tool as
it opens or closes.
M1 completes right handed tool coordinate frame
MBy convention, yaw pitch and roll motions are performed in
specific order about set of fixed axis
Initially mobile tool frame is coincide with wrist coordinate
frame F= {f1,f2,f3} attached at fore arm
1) Yaw motion is performed by rotating tool about wrist axis
f1
2) Pitch motion by rotating tool about wrist axis f2
3) Roll motion rotating tool about wrist axis f3

Precision, Accuracy and Repeatability of movement
The precision of movement is basically a function of three features:
special resolution, accuracy, And repeatability
These terms are defined for:
• the robot's wrist end without any tool attached
• for the conditions under which the robot's precision will be at
its worst.
the robot has least precision of movement with the robot's
arm is fully extended

The control resolution for a robot is determined by the
position control system and the feedback measurement
system.
It is the controller's ability to divide the total range
of movement for the particular joint into individual
increments that can be addressed in the controller.
(i) Spatial Resolution
It is defined as the smallest increment of movement into
which the robot can divide its work volume.
depends on the system’s control resolution and the
robot's mechanical in accuracies.

Accuracy is an absolute concept, repeatability is relative.
Accuracy relates to the robot's capacity to be
programmed to achieve a given target point.
The actual programmed point will probably be different from
the target point due to limitations of control resolution.92 Fundamental of Robotic Manipulator

It is measure of ability of robot to place tool tip at
arbitrarily prescribed location in work envelope.
Error is half of spatial resolution.
Error is worst in outer range of its work volume and
better when arm is closer to base.

Repeatability:
Repeatability is the measure of the ability of the robot to
position the tool tip at same position repeatedly.
There is always some repeatability error associated because
of backlash in gears, flexibility of the mechanical linkages
and drive systems.
The repeatability errors are very small in magnitude for well
designed robotic manipulators.
Repeatability and accuracy refer to two different aspects.

Repeatability errors form a random variable and constitute a
statistical distribution.95 Fundamental of Robotic Manipulator

A robot that is repeatable may not be very accurate, and visa versa.
Let T be the desired target point to where the robot is commanded
to move ,
but due to limitations on its accuracy, the programmed position
becomes point P.
The distance between points T and P is robot's accuracy.
When, the robot wrist is commanded to the programmed point P
again , it does not return to the exact same position.
Instead, it returns to position R.
The difference between P and R is limitations on the robot's
repeatability.
The robot will not always return to the same position R on
subsequent repetitions of the motion cycle.
Instead, it will form a cluster of points on both sides of the position
P

Precision :
It is closely related to repeatability.
It is measure of spatial resolution with which tool can be
positioned within work envelope.
A B
If tool tip is positioned at A then next closest position that it
moves is B
Then distance bet. A and B is precision.
Tool tip might be positioned anywhere on 3 dimensional grid of
pts within work space.
Overall precision is max. distance between neighboring pts in
grid97 Fundamental of Robotic Manipulator

Cartesian robot: interior grid pt have 8 neighbors in
horizontal plane + 9 neighbors in plane above and below
For Cartesian
robot, Precision
is uniform
throughout
work envelop

Robot type Horizontal
precision
Vertical
precision
Cartesian Uniform Uniform
Cylindrical Decreases
radially
Uniform
Spherical Decreases
radially
Decreases
radially
SCARA varies Uniform
articulated varies varies

cartesian
Cylindrical robot

a
b
c
d
∆r
r∆ф
Grid
elemen
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Fundamental of robotic manipulator

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Fundamental of robotic manipulator