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ROBOTICS
A.SAIKUMAR , Assistant professor , Department of Mechanical Engineering
ROBOT
 Definition of robot as per Robotics Industry
Association (RIA)
 a re-programmable, multifunctional manipulator
designed to move material, parts, tools or specialized
devices through variable programmed motion for a
variety of tasks
 possess certain anthropomorphic characteristics
 mechanical arm
 sensors to respond to input
 Intelligence to make decisions
Three Laws of Robotics
• Introduced by Isaac Asimov
 Law I (Zeroth law) : A robot may not injure a human being or,
through inaction, allow a human being to
come to harm.
 Law II (First Law) : A robot must obey orders given by humans
except when conflicts with First law.
 Law III (Second Law) : A robot must protect its own existence
unless that conflicts with the First and
Second Laws.
Robot Anatomy
The principal parts of industrial robot are
1)Manipulator(regional structure): it consist of
i)Base ii)Arm iii)Wrist assembly
2) End effector- (Orientational structure)-
it may be a gripper or tool.
3) Actuators-
i) Pneumatics
ii) Hydraulics
iii) Electrical - a) DC servomotor b) AC servo motor c) Stepper motor
4) Power transmitting element- i) Gear drive ii) linkage mechanism
iii) Belt drive iv) Chain drive
5
5) Sensors
6) Controller- The controller receives data from the computer,
 Controls the motions of the actuator
 Coordinates these motions with the sensory feedback information
internal
external
Position sensor
Velocity sensor
Analog type
Digital type
Potentiometer
resolver
Optical encoder
Tachometer
Tactile or touch sensor
Force or torque sensor
Proximity sensor
Range sensor
Automation
 In an industrial context, Automation can be explained as a
process to create, control and monitor the applications of
technology.
 It is the technology that is concerned with use of
mechanical, electronic and computer based systems in
operation and control of production.
 Includes the transfer lines, mechanized assembly machines,
feed back control systems, NC Machine tools and Robots
 Handling the operation of equipment such as processors,
machinery, stabilization of ships, aircraft, boilers and many
applications with minimum human efforts.
Types Of Automation
 Automation and robotics are two closely related
technologies.
There are Three Broad Classes of industrial
automation
1 fixed automation
2 programmable automation, and
3 flexible automation.
Fixed Automation
 Fixed automation is used when the volume of production
is very high.
 A good example of fixed automation can be found in the
automobile industry.
 The initial investment cost is high in fixed automation.
 If the volume of production turns out to be lower than
anticipated, then the unit cost becomes greater than
anticipated.
 Another problem with fixed automation is that the
equipment specially designed to produce the end product
and after the product’s life cycle is finished, the
equipment likely to become obsolete.
Programmable Automation
 Programmable automation is used when the volume
of production is relatively low.
 Variety of products to be made in programmable
automation.
 The production equipment is designed to be adaptable
to variation in product configuration.
 This adaptability feature is accomplished by operating
equipment under the control of "program" of
instructions which has been prepared especially for
the given product.
 In terms of economics, the cost of the programmable
equipment can be spread over a large number of products
even though the products are different.
 Because of the programming feature, and due to the
resulting adaptability of the equipment many different
and unique products can be economically produced in
batches.
 The robotics coincides most closely with programmable
automation.
Flexible Automation
 The third category between fixed automation and
programmable automation which is called flexible automation.
 Other terms used for flexible automation include "flexible
manufacturing system or FMS) and "computer-integrated
manufacturing systems”.
 Flexible automated system typically consist of a series of
workstations that are interconnected materials-handling
system and storage system.
 One of the features that distinguishes programmable
automation from flexible automation is that with
programmable automation, the products are made in batches.
 With flexible automation, different products can be made
at the same time on the same manufacturing system.
 The products can be produced on a flexible system in
batches that is desirable or several different product styles
can be mixed on the system.
13
Robot Classification
1) Classification based on the type of kinematic chain
i) Serial chain type robots (serial robots)
 Presently used industrial robots
SCARA
PUMA
14
ii) Closed chain type robots ( Parallel robots)
Stewart platform Variax machining center
2) Classification based on Robot anatomy or robot
geometrical configuration
 Cartesian/Rectangular Robot(3P) : Examples of these types of robot are
the IBM RS-1 and 7565 white cloud or the SIGMA robot. They normally
consist of three linear orthogonal motions along their joint axex
16
 Advantages
 High resolution and great accuracy.
 Good obstacle avoidance and collision prevention
 Independency of gravity loading, that is ease of joint
motion control.
 Disadvantages
 Large structural framework.
 Confinement of workspace.
 More complex mechanical design for linear sliding
motions.
 Requirement of larger floor space.
Robot Configurations (cont’d)
 Cylindrical (R2P): Examples of these types of robot are Versatran Model
F600 of the Prab company or the Stanford. These robots normally consist
of two linear orthogonal motions and a rotary type motion.
Cylindrical Robot - Work Envelope
19
 Advantages
 Almost independent of gravity loadings.
 Collision free movement.
 Two linear axes make the mechanical design less
complex than the Cartesian robots.
 Disadvantages
 Large amount of structures.
 Restrictions on compatibility with other manipulators in
a common workspace.
 Less accuracy and resolution compared with
rectangular robot.
Robot Configurations (cont’d)
 Spherical joint (2RP): Example of these robots are the unimate 2000B
manufactured by Unimation Inc. These robots essentially consists of two
rotary motions and a single sliding motion.
Spherical Robot - Work Envelope
22
 Advantages
 Lowest weight and minimum structural complexity.
 Short joint travel for many motions.
 Compatibility with other robots and machinery in the
common work space.
 Good resolution because error in position is
perpendicular.
 Disadvantages
 Large and variable torque on second and third joint of
the arm, creating a counter balance problem.
 Limited ability to avoid collision with obstacles.
 Position error is large due to rotary motion and is
proportional to the radius.
Robot Configurations (cont’d)
 Articulated/anthropomorphic(3R) :These are humanoid type robot with
redundant degrees of freedom. Examples are the PUMA 500/600/250
series.
24
 Advantages
 Flexibility to reach over and under an object.
 Compatibility with other robots working in the same
common work space.
 Disadvantages
 Poor resolution and accuracy, that is, maximum period
error.
 Large and variable torque on joints, creating a
counterbalance problem.
 Limited ability to avoid obstacles.
 High moment of inertia, gravity effects and dynamic
instability.
Robot Configurations (cont’d)
 Selective Compliance Assembly Robot Arm (SCARA) (2R1P): They have
two revolute joints that are parallel and allow the Robot to move in a
horizontal plane, plus an additional prismatic joint that moves vertically
Robot Configurations
CONSIDER TYPICAL ROBOTS
What could a robot do without “end effectors”?
TYPES OF END EFFECTORS
Two types:
Grippers – to grasp and manipulate objects (e.g., parts)
during work cycle
Tools – to perform a process, e.g., spot welding, spray
painting
Grippers
End-effector that holds or grasp an object (in assembly, pick and
place operation and material handling) to perform some task.
Five MajorTypes of grippers
1.Mechanical
2.Suction or vaccum cups
3.Magnetised gripper
4.Adhesives
5.Hooks, Scoops, and other
devices
Mechanical Gripper
Two ways of constraining part in gripper
1. Physical construction of parts within finger. Finger encloses
the part to some extent and thereby designing the contact
surface of finger to be in approximate shape of part geometry.
2. Holding the part is by friction between fingers and workpart.
Finger must apply force that is sufficient for friction to retain
the part against gravity.
It is an end effector that uses mechanical fingers actuated
by a mechanism to grasp an object.
Mechanical Gripper
To resist the slippage, the gripper must be designed to exert
a force that depends on the weight of the part, coeff of
friction and acceleration of part.
Mechanical Gripper
Where g = the g factor
The g factor is supposed to take account of the
combined effect of gravity and acceleration.
If the acceleration force is applied in the same direction
as the gravity force, then the g value = 3.0. If the
acceleration is applied in the opposite direction, then the
g value = 1.0(2*the weight of the part due to acceleration
minus 1*the weight of the part due to gravity)
If the acceleration is applied in a horizontal direction,
then use g = 2.0
Types of Gripper Mechanism
Two ways of gripper mechanism based on finger movement
1.Pivoting movement – Eg. Link actuation
2.Linear or translational movement – Eg. Screw and
cylinder
Four ways of gripper mechanism based on kinematic devices
1.Linkage actuation
2.Gear and rack actuation
3.Cam actuation
4.Screw actuation
Mechanical Gripper Mechanism
1. Linkage actuation
Mechanical Gripper Mechanism
2. Gear and rack actuation
Mechanical Gripper Mechanism
3. Cam actuation
Mechanical Gripper Mechanism
4. Screw actuation
Gripper force analysis
The purpose of the gripper mechanism is to convert
input power into the required motion and force to grasp
and hold an object
VACUUM CUPS
Vacuum cups also called as Suction Cups can be used
as gripper devices for handling certain types of objects
These are required flat, smooth, and clean conditions
necessary to form a satisfactory vacuum between the
object and suction cup.
The suction cups used in this are typically made of
elastic material such as rubber or soft plastic.
MAGNETIC GRIPPERS
magnetic grippers are very feasible means of handling
ferrous materials however stainless steel plate would not be
handled.
These are divided into two categories,
1. Using Electro Magnets
2. Using Permanent Magnets
Adhesive Gripper
Used to handle fabrics and light weight materials
Adhesive substance can be used for grasping action.
One contact surface is needed.
The reliability is diminished with successive operation.
It is used to lift light weight object.
 Hooks and scoops are the simplest type of end effectors
that can be classes as grippers.
 A scoop or ladle is commonly used to scoop up molten
metal and transfer it to the mould.
 A hook may be all that is needed to lift a part especially if
precise positioning in not required and if it is only to be
dipped into a liquid.
HOOKS and SCOOPS
A tool is equipped in the robot for carrying out several
operations on the work parts instead of grasping it.
A tool acts as an end effectors when it is attached directly
to the robot’s wrist.
In some applications, there will be a need fro multi-tool
task, and changing the tool all the time from the robot wrist
will be highly difficult.
In robot applications, the most commonly used three tools
as end effectors are listed below;
1. Spot welding tools
2. Spray painting nozzle
3. Arc welding torch
Tools as End Effectors
44
 Classification Based on control system
1. Limited sequence robots
2. Playback robots with point-to-point control
3. Playback robots with continuous path control
4. Intelligent robots
45
LIMITED-SEQUENCE ROBOTS
 Limited-sequence robots do not use servo-control to
indicate relative position of the joints.
 They are controlled by setting limit switches and/or
mechanical stops to establish the endpoints of travel
for each of their joints.
 The sequence in which the motion cycle is played out is
defined by pegboard or stepping switch or other
sequencing device.
 Any of the three drive systems can be used with this
type of control system; however. pneumatic drive
seems to be the type most commonly employed.
46
PLAYBACK ROBOTS WITH POINT-TO-POINT
CONTROL
 Playback robots use a more sophisticated control unit in
which a series of positions or motions are taught to the
robot, recorded into memory, and then repeated by the
robot under its own control.
 Point-to-point robots are capable of performing motion
cycles that consist of a series of desired point locations
and related actions.
 Point-to-point robots do not control the path taken by the
robot to get from one point to the next.
 Control of the sequence of positions is quite adequate for
many kinds of applications, including loading and
unloading machines and spot welding.
47
Playback robots with continuous path control
 Continuous path robots are capable of performing motion
cycles in which the path followed by the robot is
controlled.
 The individual points are defined by the control unit
rather than the programmer.
 The programmer specifies the starting point and the end
point of the path, and the control unit calculates the
sequence of individual points that permit the robot to
follow a straight line trajectory.
 CP control is required for certain types of industrial
applications such as spray coating and arc welding.
48
Intelligent robots
 Intelligent robots constitute a growing class of industrial
robot that possess the capability not only to play back a
programmed motion cycle but to also interact with its
environment in a way that s
 Intelligent robots can alter their programmed cycle in
response to conditions that occur in the workplace.
 The robots in this class have the capacity to communicate
during the work cycle with humans or computer-based
systems.
 Intelligent robots are usually programmed using an English-
like and symbolic language not unlike a computer
programming language.
49
BASIC ROTATION MATRICES
 Rotation about x- axis
03/25/2025
50
 Rotation about y- axis
51
 Rotation about z-axis
EULER ANGLES
Fixed Axis System (XYZ)
RPY system







0
0
X
1 0
Q  0 C   S 

S 
C 
Fixed-axes Rotations …




C 


 
S 
0

0
 C  0
S  
1
0
Y
Q

1




 0
0

Z
C   S
 0 
Q   S  C 
0
Fixed-axes Rotations …
Q = QZQYQX






C C

 S

S C  C   S
 S 
S C  S   S
 C 
C C

S S  C   C
 S 
S S  S   C
 C 
C S

Q   C
S 
Euler Angles
Representation
(ZYZ)

1




 0
0

Z
C   S
 0 
Q   S  C 
0
Euler Angles Representation …



0

 C  0 S
 
0 1

  S 0 C
 
Y'
Q




1


0
0

Z'
'
C   S
 0 
Q   S  C 
0
Euler Angles Representation …






Q = QZQY’QZ’’
 C C C 
 S S 
 S C

 S C  C
S 
 C C  S
S 
C 
 C C
S 
 S C
S 
S S 
Q   S C C   C
S 
03/25/2025
61

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Robot unit 1 2022 about the robotics in the environment

  • 1. 1 ROBOTICS A.SAIKUMAR , Assistant professor , Department of Mechanical Engineering
  • 2. ROBOT  Definition of robot as per Robotics Industry Association (RIA)  a re-programmable, multifunctional manipulator designed to move material, parts, tools or specialized devices through variable programmed motion for a variety of tasks  possess certain anthropomorphic characteristics  mechanical arm  sensors to respond to input  Intelligence to make decisions
  • 3. Three Laws of Robotics • Introduced by Isaac Asimov  Law I (Zeroth law) : A robot may not injure a human being or, through inaction, allow a human being to come to harm.  Law II (First Law) : A robot must obey orders given by humans except when conflicts with First law.  Law III (Second Law) : A robot must protect its own existence unless that conflicts with the First and Second Laws.
  • 4. Robot Anatomy The principal parts of industrial robot are 1)Manipulator(regional structure): it consist of i)Base ii)Arm iii)Wrist assembly 2) End effector- (Orientational structure)- it may be a gripper or tool. 3) Actuators- i) Pneumatics ii) Hydraulics iii) Electrical - a) DC servomotor b) AC servo motor c) Stepper motor 4) Power transmitting element- i) Gear drive ii) linkage mechanism iii) Belt drive iv) Chain drive
  • 5. 5 5) Sensors 6) Controller- The controller receives data from the computer,  Controls the motions of the actuator  Coordinates these motions with the sensory feedback information internal external Position sensor Velocity sensor Analog type Digital type Potentiometer resolver Optical encoder Tachometer Tactile or touch sensor Force or torque sensor Proximity sensor Range sensor
  • 6. Automation  In an industrial context, Automation can be explained as a process to create, control and monitor the applications of technology.  It is the technology that is concerned with use of mechanical, electronic and computer based systems in operation and control of production.  Includes the transfer lines, mechanized assembly machines, feed back control systems, NC Machine tools and Robots  Handling the operation of equipment such as processors, machinery, stabilization of ships, aircraft, boilers and many applications with minimum human efforts.
  • 7. Types Of Automation  Automation and robotics are two closely related technologies. There are Three Broad Classes of industrial automation 1 fixed automation 2 programmable automation, and 3 flexible automation.
  • 8. Fixed Automation  Fixed automation is used when the volume of production is very high.  A good example of fixed automation can be found in the automobile industry.  The initial investment cost is high in fixed automation.  If the volume of production turns out to be lower than anticipated, then the unit cost becomes greater than anticipated.  Another problem with fixed automation is that the equipment specially designed to produce the end product and after the product’s life cycle is finished, the equipment likely to become obsolete.
  • 9. Programmable Automation  Programmable automation is used when the volume of production is relatively low.  Variety of products to be made in programmable automation.  The production equipment is designed to be adaptable to variation in product configuration.  This adaptability feature is accomplished by operating equipment under the control of "program" of instructions which has been prepared especially for the given product.
  • 10.  In terms of economics, the cost of the programmable equipment can be spread over a large number of products even though the products are different.  Because of the programming feature, and due to the resulting adaptability of the equipment many different and unique products can be economically produced in batches.  The robotics coincides most closely with programmable automation.
  • 11. Flexible Automation  The third category between fixed automation and programmable automation which is called flexible automation.  Other terms used for flexible automation include "flexible manufacturing system or FMS) and "computer-integrated manufacturing systems”.  Flexible automated system typically consist of a series of workstations that are interconnected materials-handling system and storage system.  One of the features that distinguishes programmable automation from flexible automation is that with programmable automation, the products are made in batches.
  • 12.  With flexible automation, different products can be made at the same time on the same manufacturing system.  The products can be produced on a flexible system in batches that is desirable or several different product styles can be mixed on the system.
  • 13. 13 Robot Classification 1) Classification based on the type of kinematic chain i) Serial chain type robots (serial robots)  Presently used industrial robots SCARA PUMA
  • 14. 14 ii) Closed chain type robots ( Parallel robots) Stewart platform Variax machining center
  • 15. 2) Classification based on Robot anatomy or robot geometrical configuration  Cartesian/Rectangular Robot(3P) : Examples of these types of robot are the IBM RS-1 and 7565 white cloud or the SIGMA robot. They normally consist of three linear orthogonal motions along their joint axex
  • 16. 16  Advantages  High resolution and great accuracy.  Good obstacle avoidance and collision prevention  Independency of gravity loading, that is ease of joint motion control.  Disadvantages  Large structural framework.  Confinement of workspace.  More complex mechanical design for linear sliding motions.  Requirement of larger floor space.
  • 17. Robot Configurations (cont’d)  Cylindrical (R2P): Examples of these types of robot are Versatran Model F600 of the Prab company or the Stanford. These robots normally consist of two linear orthogonal motions and a rotary type motion.
  • 18. Cylindrical Robot - Work Envelope
  • 19. 19  Advantages  Almost independent of gravity loadings.  Collision free movement.  Two linear axes make the mechanical design less complex than the Cartesian robots.  Disadvantages  Large amount of structures.  Restrictions on compatibility with other manipulators in a common workspace.  Less accuracy and resolution compared with rectangular robot.
  • 20. Robot Configurations (cont’d)  Spherical joint (2RP): Example of these robots are the unimate 2000B manufactured by Unimation Inc. These robots essentially consists of two rotary motions and a single sliding motion.
  • 21. Spherical Robot - Work Envelope
  • 22. 22  Advantages  Lowest weight and minimum structural complexity.  Short joint travel for many motions.  Compatibility with other robots and machinery in the common work space.  Good resolution because error in position is perpendicular.  Disadvantages  Large and variable torque on second and third joint of the arm, creating a counter balance problem.  Limited ability to avoid collision with obstacles.  Position error is large due to rotary motion and is proportional to the radius.
  • 23. Robot Configurations (cont’d)  Articulated/anthropomorphic(3R) :These are humanoid type robot with redundant degrees of freedom. Examples are the PUMA 500/600/250 series.
  • 24. 24  Advantages  Flexibility to reach over and under an object.  Compatibility with other robots working in the same common work space.  Disadvantages  Poor resolution and accuracy, that is, maximum period error.  Large and variable torque on joints, creating a counterbalance problem.  Limited ability to avoid obstacles.  High moment of inertia, gravity effects and dynamic instability.
  • 25. Robot Configurations (cont’d)  Selective Compliance Assembly Robot Arm (SCARA) (2R1P): They have two revolute joints that are parallel and allow the Robot to move in a horizontal plane, plus an additional prismatic joint that moves vertically
  • 27. CONSIDER TYPICAL ROBOTS What could a robot do without “end effectors”?
  • 28. TYPES OF END EFFECTORS Two types: Grippers – to grasp and manipulate objects (e.g., parts) during work cycle Tools – to perform a process, e.g., spot welding, spray painting
  • 29. Grippers End-effector that holds or grasp an object (in assembly, pick and place operation and material handling) to perform some task. Five MajorTypes of grippers 1.Mechanical 2.Suction or vaccum cups 3.Magnetised gripper 4.Adhesives 5.Hooks, Scoops, and other devices
  • 30. Mechanical Gripper Two ways of constraining part in gripper 1. Physical construction of parts within finger. Finger encloses the part to some extent and thereby designing the contact surface of finger to be in approximate shape of part geometry. 2. Holding the part is by friction between fingers and workpart. Finger must apply force that is sufficient for friction to retain the part against gravity. It is an end effector that uses mechanical fingers actuated by a mechanism to grasp an object.
  • 31. Mechanical Gripper To resist the slippage, the gripper must be designed to exert a force that depends on the weight of the part, coeff of friction and acceleration of part.
  • 32. Mechanical Gripper Where g = the g factor The g factor is supposed to take account of the combined effect of gravity and acceleration. If the acceleration force is applied in the same direction as the gravity force, then the g value = 3.0. If the acceleration is applied in the opposite direction, then the g value = 1.0(2*the weight of the part due to acceleration minus 1*the weight of the part due to gravity) If the acceleration is applied in a horizontal direction, then use g = 2.0
  • 33. Types of Gripper Mechanism Two ways of gripper mechanism based on finger movement 1.Pivoting movement – Eg. Link actuation 2.Linear or translational movement – Eg. Screw and cylinder Four ways of gripper mechanism based on kinematic devices 1.Linkage actuation 2.Gear and rack actuation 3.Cam actuation 4.Screw actuation
  • 34. Mechanical Gripper Mechanism 1. Linkage actuation
  • 35. Mechanical Gripper Mechanism 2. Gear and rack actuation
  • 38. Gripper force analysis The purpose of the gripper mechanism is to convert input power into the required motion and force to grasp and hold an object
  • 39. VACUUM CUPS Vacuum cups also called as Suction Cups can be used as gripper devices for handling certain types of objects These are required flat, smooth, and clean conditions necessary to form a satisfactory vacuum between the object and suction cup. The suction cups used in this are typically made of elastic material such as rubber or soft plastic.
  • 40. MAGNETIC GRIPPERS magnetic grippers are very feasible means of handling ferrous materials however stainless steel plate would not be handled. These are divided into two categories, 1. Using Electro Magnets 2. Using Permanent Magnets
  • 41. Adhesive Gripper Used to handle fabrics and light weight materials Adhesive substance can be used for grasping action. One contact surface is needed. The reliability is diminished with successive operation. It is used to lift light weight object.
  • 42.  Hooks and scoops are the simplest type of end effectors that can be classes as grippers.  A scoop or ladle is commonly used to scoop up molten metal and transfer it to the mould.  A hook may be all that is needed to lift a part especially if precise positioning in not required and if it is only to be dipped into a liquid. HOOKS and SCOOPS
  • 43. A tool is equipped in the robot for carrying out several operations on the work parts instead of grasping it. A tool acts as an end effectors when it is attached directly to the robot’s wrist. In some applications, there will be a need fro multi-tool task, and changing the tool all the time from the robot wrist will be highly difficult. In robot applications, the most commonly used three tools as end effectors are listed below; 1. Spot welding tools 2. Spray painting nozzle 3. Arc welding torch Tools as End Effectors
  • 44. 44  Classification Based on control system 1. Limited sequence robots 2. Playback robots with point-to-point control 3. Playback robots with continuous path control 4. Intelligent robots
  • 45. 45 LIMITED-SEQUENCE ROBOTS  Limited-sequence robots do not use servo-control to indicate relative position of the joints.  They are controlled by setting limit switches and/or mechanical stops to establish the endpoints of travel for each of their joints.  The sequence in which the motion cycle is played out is defined by pegboard or stepping switch or other sequencing device.  Any of the three drive systems can be used with this type of control system; however. pneumatic drive seems to be the type most commonly employed.
  • 46. 46 PLAYBACK ROBOTS WITH POINT-TO-POINT CONTROL  Playback robots use a more sophisticated control unit in which a series of positions or motions are taught to the robot, recorded into memory, and then repeated by the robot under its own control.  Point-to-point robots are capable of performing motion cycles that consist of a series of desired point locations and related actions.  Point-to-point robots do not control the path taken by the robot to get from one point to the next.  Control of the sequence of positions is quite adequate for many kinds of applications, including loading and unloading machines and spot welding.
  • 47. 47 Playback robots with continuous path control  Continuous path robots are capable of performing motion cycles in which the path followed by the robot is controlled.  The individual points are defined by the control unit rather than the programmer.  The programmer specifies the starting point and the end point of the path, and the control unit calculates the sequence of individual points that permit the robot to follow a straight line trajectory.  CP control is required for certain types of industrial applications such as spray coating and arc welding.
  • 48. 48 Intelligent robots  Intelligent robots constitute a growing class of industrial robot that possess the capability not only to play back a programmed motion cycle but to also interact with its environment in a way that s  Intelligent robots can alter their programmed cycle in response to conditions that occur in the workplace.  The robots in this class have the capacity to communicate during the work cycle with humans or computer-based systems.  Intelligent robots are usually programmed using an English- like and symbolic language not unlike a computer programming language.
  • 49. 49 BASIC ROTATION MATRICES  Rotation about x- axis
  • 53. Fixed Axis System (XYZ) RPY system        0 0 X 1 0 Q  0 C   S   S  C 
  • 54. Fixed-axes Rotations …     C      S  0  0  C  0 S   1 0 Y Q
  • 55.  1      0 0  Z C   S  0  Q   S  C  0 Fixed-axes Rotations …
  • 56. Q = QZQYQX       C C   S  S C  C   S  S  S C  S   S  C  C C  S S  C   C  S  S S  S   C  C  C S  Q   C S 
  • 58. Euler Angles Representation …    0   C  0 S   0 1    S 0 C   Y' Q
  • 59.     1   0 0  Z' ' C   S  0  Q   S  C  0 Euler Angles Representation …
  • 60.       Q = QZQY’QZ’’  C C C   S S   S C   S C  C S   C C  S S  C   C C S   S C S  S S  Q   S C C   C S 