Introduction to Robot Arm Kinematics & Applications of Robots

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INTRODUCTION ROBOT ARM KINEMATICS

• Prof. Tarun Kanti Naskar,
• Mechanical Engineering Department,
• Jadavpur University, Kolkata, India

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Nomenclature
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6-axis Robotic Arm
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Six-Servo-Robot-Arm-RA-001
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Edge Robotic Arm
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PUMA Robot Programmable Universal Machine for
Assembly
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What is Robot

• Czech word robota meaning slave labour
• Industrial robot, is called a robotic manipulator
  or a robotic arm.
• A robotic arm is similar to a human arm and can
  be modelled as a chain of rigid links
  interconnected by flexible joints.
• The links resemble the human organs like chest,
  upper arm and fore arm, while the joints
  correspond to the shoulder, elbow, and wrist.

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What is Robot

• Webster dictionary an automatic device that
  performs functions normally ascribed to humans or
  a machine in the form of a human.
• Longman dictionary a machine that can move and
  do some work of a human being and is usually
  controlled by computers.
• The Robot Institute of America (1969) a
  re-programmable, multi-functional manipulator
  designed to move materials, parts, tools or
  specialized devices through various programmed
  motions for the performance of a variety of
  tasks.

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What is Robot

• Finally
• A robot is a software-controllable mechanical
  device that uses sensors to guide one or more
  end-effectors through programmed motions in a
  workspace in order to manipulate physical
  objects.
• Modern day industrial robots are not androids to
  impersonate humans.
• Rather
• Anthropomorphic - patterned after human arm
• Called robotic manipulator or a robotic arm.

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Robot Classification

• On the basis of number of degrees of freedom
• (i) 6 DOF, (ii) 5 DOF, (iii) 4 DOF, (iv) 5 or
  6 DOF mounted on 3-axes structure gtgt 8 or 9 DOF
• On the basis drive technologies
• (i) Hydraulic drive, (ii) Electric drive
  (AC/DC servomotors, DC stepper motors), (iii)
  Pneumatic drive
• On the basis of configuration
• (i) Cartesian robot (ii) Cylindrical robot
  (iii) Spherical robot
• (iv) SCARA robot (Selective Compliance
  Adaptive Robot Arm) (v) Articulated robot.
• On the basis of motion control
• (i) Point to point method uses spot
  welding
• (ii) Continuous path motion uses - paint
  spraying, arc welding, or application of glue and
  sealant.

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Cartesian Robot P-P-PCylindrical Robot R-P-P
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Spherical Robot SCARA (Selective Compliance
Assembly Robot Arm )Robot
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Articulated Robot R-R-R
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Technology of Robots

• Mechanical components links, joints
• Actuators drivers like servo or stepper motors,
  hydraulic or pneumatic cylinders
• Power transmission devices spur gears, chains,
  sprockets, belts
• Sensors LVDT (linear variable differential
  transformer), cameras, force-torque transducers
• Electronic controller microprocessors with A/D
  or D/A conversions, memory etc.
• Computers.

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Robot Specifications
(i) Drive technologies, (ii) work-envelope
geometries, and (iii) motion control methods are
broadly the basis of robot specification.
Following are additional characteristics
Characteristics Units
Number of axes -----
Load carrying capacity kg
Maximum speed, cycle time mm/sec
Reach and stroke mm
Tool orientation deg
Repeatability mm
Precision and accuracy mm
Operating environment -----
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Axes of Robotic Manipulator
Axes Type Function
1-3 Major Position the wrist
4-6 Minor Orient the tool
7-n Redundant Avoid obstacles
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3 Minor Axes of the Wrist of a Robot
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Tool OrientationYaw, Pitch Roll
Right-handed coordinate frame
Right-handed coordinate frame is that for which
the direction of rotation from OA to OB propels a
right-handed screw in the direction OC. The
system of OA-OB-OC is an orthogonal triad and
right-handed one is positive.
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Load Carrying Capacity

• Load carrying capacity of a robot depends on
• size,
• configuration,
• construction, and
• drive system.
• Robots arm is the weakest position particularly
  when the arm is at maximum extension, just as in
  the case of a human being.
• Varies greatly between robots from 2.2 to 5000
  kg.
• This weight is the gross weight, i.e., the weight
  of the end effector the load that it caries.

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Speed of Motion

• Defined by the cycle time - the time required to
  perform a periodic motion. It is more meaningful
  than the maximum tool-tip speed.
• Cycle Time depends on
• The accuracy with which the end effector must be
  positioned
• The weight of the payload
• The distances to be moved.

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Influence of distance versus speed
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Reach and Stroke of a Cylindrical Robot
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Repeatability

• Its a design characteristic.
• Its defined by the measure of the ability of the
  robot to position the tool tip in the same place
  repeatedly.
• On account of backlash in gears and flexibility
  in the links, there occurs some repeatability
  error on the order of a small fraction of mm.

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Precision

• It is the distance in the spatial workspace
  between one position of a tool tip and the next
  closest position to which the tool tip can be
  positioned.

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Forward Kinematics
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Robotic manipulator as chain
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Direct Inverse Kinematics
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Reference Body Attached Coordinate System OUVW
Body attached coordinate frame OXYZ Reference
coordinate frame. P a point in space and
fixed w r t OUVW frame. Vectors ix, jy, kz
iu, jv, kw are unit vectors
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Development of Transformation Matrices

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Composite Rotation Matrices
Algorithm

• Initialize the rotation matrix to R I3, which
  corresponds to the two coordinate frames being
  coincident
• Rotation about one of the principal axes of the
  OXYZ-system pre-multiplication by the previous
  rotation matrix

• 3. Rotation about one of its own axes
  post-multiplication by the previous rotation
  matrix

• 4. If there are more fundamental rotations to be
  performed, go to step 2 else stop.

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Composite Rotation Matrices

• 1. (I) ? about OX then (II) ? about OY and
  finally (III) ? about OZ R R z,? R y,? Rx,?I3

I3
2. (I) ? about OY then (II) ? about OX and
finally (III) ? about OW R Rx,? Ry,?I3 Rz,?

I3
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Rotation Matrix about an Arbitrary Axis
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Rotation Matrix About An Arbitrary Axis

• Following rotations should be done consecutively
  to get the required rotation
• Rx,? (Makes r to align with XZ-plane)
• Ry,-? (Makes r to align with Z-axis)
• Rz,? (Makes the rotation about Z or r-axis)
• Ry,? (Restores r to position stated in 2)
• Rx,-? (Restores r back to original position)
• The resultant matrix
• Rr,? Rx,-? Ry,? Rz,? Ry,-? Rx,?

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Perspective Transformation

• When the human eye looks at a scene, objects in
  the distance appear smaller than objects close by
  - this is known as perspective. While
  orthographic projection ignores this effect to
  allow accurate measurements, perspective
  definition shows distant objects as smaller to
  provide additional realism.

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Perspective Transformation

• Parallel projections are used to project points
  onto the image plane along parallel line.
• Perspective projection projects points onto the
  image plane along lines that emanate from a
  single point, called the center of projection.
• So an object has a smaller projection when it is
  far away from the center of projection and a
  larger projection when it is closer.

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Perspective Transformation

• It is like treating the 2D projection as being
  viewed through a camera viewfinder. The camera's
  position, orientation, and field of view (extent
  of the observable world that is seen at any given
  moment) control the behavior of the projection
  transformation.

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Perspective Transformation
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Euler Angle Representations
Euler Angles (system I) Euler Angles (system II) Euler Angles (system III)
Sequence Of Rotations ? about Z-axis ? about Z-axis ? about X-axis
Sequence Of Rotations ? about U-axis ? about V-axis ? about Y-axis
Sequence Of Rotations ? about W-axis ? about W-axis ? about Z-axis
III X-Y-Z here Yaw-Pitch-Roll
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Yaw, Pitch, and Roll of tool
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Homogeneous Coordinates Transformation Matrix

• Transformation matrices so far discussed have
  rotation only
• There is need for translation, scaling,
  perspective transformation. For this, homogeneous
  coordinates are used.

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Homogeneous Coordinates Transformation Matrix

• p (px, py, pz)T a position vector in 3D
  space.
• p (wpx, wpy, wpz,, w)T represents
  homogeneous coordinates, w is the scale factor.
• px wpx/w, py wpy/w and pz wpz/w.

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Homogeneous Coordinates Transformation Matrix
,

• A homogeneous transformation matrix has the
  following sub-matrices

,
Rotation only, no translation
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Homogeneous Coordinates Transformation Matrix

• Translation only

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Scale

• For

First three diagonal elements produce local
scaling. The coordinate values are stretched by
the scalars a, b and c
Basic rotation matrices like produce no scaling.
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Scale

• 
  Where s gt 0. It produces global scaling.
• The physical coordinates of the vector are
• For 1 gt s gt 0, the homogeneous transformation
  matrix globally enlarges the coordinates
• For s gt 1, it globally reduces the coordinates.

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Inverse Composite Homogeneous Rotation Matrices

• T is a homogeneous transformation matrix with
  rotation R, translation p, f 0 and s 1. Then
  the inverse of T
• Proof Since R is a pure rotation between
  orthonormal coordinate frames, .
  Therefore, . It can also be proved
  that

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PUMA
Links and joints are numbered outwardly from base
with joint 1 connecting link 0 and link 1, and so
on
Joint i connects two links (i - 1) i, when i
1, , 6
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Normal, Sliding Approach Vectors of Tool
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Link Coordinate System Its Parameters
Link parameters ?i, di Joint parametersai, ai
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Parameters

• Kinematic Parameters

Arm Parameters Symbol Revolute Joint (R) Prismatic Joint (P)
Joint angle ? Variable Fixed
Joint distance d Fixed Variable
Link length a Fixed Fixed
Link twist angle a Fixed Fixed
Joint parameters and link parameters come in
pairs. Link parameters are always constant while
either of two joint parameters varies.
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Denavit-Hartenberg Algorithm
A systematic and generalized approach of
utilizing matrix algebra to describe and
represent the spatial geometry of the links of a
robot arm with respect to a fixed reference plane.
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Transformation from (i-1)-th coordinate frame to
i-th frame
Screw Transformations
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Inverse of this transformation matrix is

transformation matrices are expressed in the
forms
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Joint-Type Parameter
The i-th joint variable
is expressed as
selects
either
or
in the following way
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Partitioning at Wrist

• Base to wrist
• Wrist to tool

Maps shoulder into base
Maps elbow into shoulder
Maps wrist into elbow
Maps pitch into yaw
Maps roll into pitch
Maps tool-tip into roll
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Determining Robot Arm Kinematics
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Link coordinate parameters 3R Planar Manipulator
Axis ?i di ai ?i
1 ?1 0 l1 0
2 ?2 0 l2 0
3 ?3 0 l3 0
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Cylindrical Robot
Axis ai ai di ?i qi C?i S?i Cai Sai
1 0 0 0 ?1 ?1 C?1 S?1 1 0
2 0 -p/2 d2 0 d2 1 0 0 -1
3 0 0 d3 0 d3 1 0 1 0
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3-DOF Articulated Arm
Axis ai ai di ?i qi Cai Sai
1 0 p/2 0 ?1 ?1 0 1
2 a2 0 0 ?2 ?2 1 0
3 a3 0 0 ?3 ?3 1 0
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4-Axis SCARA Robot
Axis ?i di ai ?i
1 ?1 d1 a1 p
2 ?2 0 a2 0
3 0 d3 0 0
4 ?4 d4 0 0
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5-DOF industrial robot
Axis ai ai di ?i qi C?i S?i Cai Sai
1 0 -p/2 L1 ?1 ?1 C1 S1 0 -1
2 L2 0 0 ?2 ?2 C2 S2 1 0
3 L3 0 0 ?3 ?3 C3 S3 1 0
4 0 -p/2 0 ?4-p/2 ?4 S4 -C4 0 -1
5 0 0 L5 ?5 ?5 C5 S5 1 0
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Alpha II Robotic Arm
Axis ? d a ? Soft Home ?
1 ?1 d1 0 - p/2 0
2 ?2 0 a2 0 0
3 ?3 0 a3 0 0
4 ?4 0 0 - p/2 - p/2
5 ?5 d5 0 0 0
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Link coordinate parameters of PUMA
Axis ? d a ?
1 p/2 0 0 - p/2
2 0 d2 a2 0
3 p/2 0 - a3 p/2
4 0 d4 0 - p/2
5 0 0 0 p/2
6 0 d6 0 0
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A problem to solve
Draw the link coordinate diagram, construct the
parameter table and find the arm matrix by
forward kinematics.
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Inverse Kinematics
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Human Skeleton as a Robotic Chain
A model of the human skeleton as a kinematic
chain allows positioning using inverse kinematics
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OBJECTIVE

• The direct kinematics finds the origin of the
  tool for known values of joint and link
  parameters. That is, it answers the question
  Where lies the origin of the tool? The direct
  kinematics, thus, specifies the frame-n w r to
  the base frame-0 for an n-DOF robotic
  manipulator.

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OBJECTIVE

• In order to control the position and orientation
  of the end-effector of a robot to reach its
  object, the inverse kinematics solution is more
  important. That is, given the position and
  orientation of the end-effector of a robot arm
  and its joint and link parameters, we like to
  find the corresponding joint angles of the robot
  so that the end-effector can be positioned as
  required.

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OBJECTIVE

• Manipulation tasks of a robot are formulated in
  terms of the desired tool position and
  orientation. This is the case, for example, when
  external sensors such as overhead cameras are
  used to plan robot motion. The information
  provided by the camera is not in terms of joint
  variables it specifies the positions and
  orientations of the objects that are manipulated.

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Reachable workspace dexterous workspace
Reachable workspace The region that can be
reached by the origin of the tool frame with at
least one orientation is called the reachable
workspace. Dexterous workspace The space where
the end-effector can reach every point from all
orientations is called dexterous workspace.
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Existence of Solutions

• Twelve equations, out of which only six are
  independent, obtained by equating the elements of
  the transformation matrix. They are nonlinear
  algebraic equations in n unknowns (the joint
  variables). Out of these, 9 equations arise from
  the 3X3 rotation matrix and the rest 3 from the
  3X1 displacement vector.

The 9 equations of the rotation matrix involve
only 3 unknowns corresponding to the
roll-pitch-yaw angles of the end-effector. So 3
from orientation and 3 from displacement.
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Existence of Solutions

• This leads to the very important conclusion for
  a manipulator to have all position and
  orientation solutions, the number of DOF n (equal
  to the number of unknowns) must at least match
  the number of independent constraints. That is,
  for a general dexterous manipulation is

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Existence of Solutions

• With , the manipulator cannot attain the
  general position and orientation in a 3-D space
  mathematically it is an over-determined case,
  with six independent equations in less than 6
  unknowns. With , it is a case of six
  independent equations in more than 6 unknowns
  an under-determined case.

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Multiple Solutions
Fig shows a 2-DOF planar manipulator in two
positions. Two sets of values of joint
displacements and . Two
solutions are identical as they produce the same
configuration (position orientation).
The elbow up position is preferred
while the elbow down position may
not be preferred as the latter may collide with
the object or work-floor.
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Solution Techniques
Closed form solution technique would be pursued
here.
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Closed Form Solution

• Several approaches Inverse transform, algebra,
  kinematic approach etc.
• None of them is alone able to solve all problems.
• A combined approach of direct inspection, algebra
  and inverse transform is presented here.

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Guideline to Closed Form Solution
The LHS of the above Eq. has n joint displacement
variables, while the elements of the RHS matrix
are desired position and orientation of the
manipulator and are constant. As the matrix
equality implies element-by-element equality, 12
equations are obtained.
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Steps to solve n-number of joint variables

• Look for equations with only one joint variable
  and find it out
• Look for pairs of set of equations, which could
  be reduced to one equation in one joint variable
  and solve it.
• Use 2 -argument atan2 (y, x) function to get a
  pair of values of angles in the range of
  by examining the sign of both y and x
  and detecting whether either x or y is zero.
• Solutions in terms of the elements of the
  position vector components of are more
  efficient than those in terms of elements of the
  rotation matrix, as latter may involve solving
  more complex equations.

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Steps to solve n-number of joint variables
Contd...
5.
Since has one unknown pre-multiplying
both sides by we get, The LHS of it has
(n-1) unknowns and the RHS
has only one unknown that can be solved.
This way we can solve all
This is known as inverse transform approach.
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APPLICATIONS in INDUSTRIES

• Robots can do better in the following fields
• Handling dangerous materials
• Assembling products
• Spray finishing
• Polishing and cutting
• Inspection
• Repetitive, backbreaking and unrewarding tasks
• Tasks involving danger to humans or dangerous
  tasks

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APPLICATIONS in INDUSTRIES
An industrial robot performing arc
welding. Inverse kinematics computes the joint
trajectories needed for the robot to guide the
welding tip along the part.
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Process Applications
End-effectors are sometimes tools themselves,
Sometimes they are used as grippers for
different manufacturing jobs. The later
provides greater flexibility.
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Process Applications

• Processes where robots used
• Welding
• Spot-welding
• Spray-painting
• Drilling
• Other machining operations.

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Arc welding
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Requirements from a Robot for Arc Welding
Application
Manipulator should be capable of moving its tool
point along a trajectory in 3D space. Continuous
path movement point-to-point movement is not
sufficient for continuous arc welding. Feeding
arrangement for consumable electrode or filler
metal. Controller should coordinate the motions
electrode/wire feed, spark gap, welding current
and other activities in the work cell.
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Requirements from a Robot for Arc Welding
Application
Two robots may be used one for material
handling, loading/unloading, and the other for
welding. Workspace should be large enough to
accommodate all the accessories. A 5 DOF
manipulator is used for welding parts in a plane
while a 6 DOF manipulator can negotiate complex
contours.
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Requirements from a Robot for Arc Welding
Application
Necessary robot programming, for continuous arc
welding, with algorithms for interpolating
straight curved path. Proper sensors for
tracking weld path and weld produced.
These can help in overcoming most of the
difficulties.
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Sensors in Robotic Welding
These are used for tracking the weld seam and
providing information to the controller to help
guiding the weld path.
Contact sensors
Non Contact sensors
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Contact Sensors
They make use of a mechanical tactile probe to
touch the sides of the groove ahead of the
welding torch and to feed back position data so
that corrections can be made by the controller.
Different control units are sometimes used for
interpreting the probe data. The probe may be
required to oscillate from one side of the groove
to another for acquiring data.
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Non-contact Sensors
No tactile measurement is done. Sensing is done
by through-the-arc systems in the form of
either electric current (in constant-voltage
welding) or voltage (in constant-current
welding). This is done by causing the arc to
weave back and forth across the joint. Weave
pattern is achieved by robot programming or by a
servo system. The weaving motion permits the
electrical signal to be interpreted in terms of
vertical and cross seam position of the torch.
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Applications
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APPLICATIONS in INDUSTRIES

• Robot makes manufacturing operations more
  profitable and competitive and gives improved
  productivity and quality.
• Robot applications in todays industries
• Material handling,
• Operations,
• Assembly, and
• Inspection.

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APPLICATIONS in INDUSTRIES
Common material handling applications are

• In hazardous environment of foundry
• Die casting
• Plastic moulding
• Forging operations

This requires suitable gripper to hold
radioactive or red-hot material.
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MATERIAL HANDLING
For this a robot requires a basic pick-and-place
operation. Examples

• Material transfer applications
• Machine loading/unloading operations

Basic Material Handling Operations

Movements in addition to material handling

• 3. Assembly operations

• 4. Inspection
• 5. Process application like spot welding

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Material Handling
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Work Cycle
Material Transfer Work Cycle
Feeder mechanism (conveyor belt)
Pickup point (A) Moving away to a
safe distance (B) ---------- Moving close to
delivery point (C) ----------- Delivery point (D)
A-B-C-D.
The object may be dropped, at point C, if not
fragile. Work cycles may be more complex like
instead of being a just two-point delivery, need
may be of changing delivery points from cycle to
cycle, avoiding obstacles, etc.
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MACHINE LOADING UNLOADING OPERATION
Robots are employed for loading of material and
unloading it from a machine. Robot picks a part
from a specific location, places it in a desired
position of a machine holding device (chuck or
vice). After the specific machining operation is
done, the job may again be picked up and placed
in the holding device of another machine and so
on till the desired operations are completed.
The job may then be picked up from the last
machine and carried to and unloaded at the output
position.
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MACHINE LOADING UNLOADING OPERATION
It needs coordination between timing of robot and
machine. For this coordination, the robot
controller must establish communication with the
machine or monitor the machining operation with
the help of suitable sensors and controllers.
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MACHINE LOADING UNLOADING OPERATION
A robot centered work cell is best suited for the
purpose with more than one production machine to
perform different machining jobs, pickup and
delivery points. Robot can be used for complex
work cells with multipoint material handling and
multiple machining and manufacturing processes.
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A Robot Centered Work Cell
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Robot Programming
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ROBOT PROGRAMMING

• These are more or less similar to higher level
  computer programming languages.
• Programming languages make robots more
  intelligent, capable of complex tasks.
• Commercially available languages are AML, RAIL,
  MCL, and VAL II.

103
Features of Robot Programming languages

• Motion control
• Advanced sensor capabilities.
• Intelligence ability to utilize information
  received about the work environment to modify
  system behavior in a programmed manner.
• Communications and data processing provisions
  for interacting with computers for keeping
  records, generating reports and controlling
  activities in the work cell.

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Robot Language Structure
Operating system is a mechanism that permits the
user to determine whether to write a new program,
edit an existing program, execute or run a
program etc.
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Robot Language Elements and Functions

• Basic elements and functions are
• Constants, variables, and other data objects
• Motion commands
• End effector sensor commands
• Computations operations
• Program control subroutines
• Communications data processing
• Monitor mode commands.

106
Applications in Surgery
107
Applications in Surgery

• Laparoscopic surgery has advantages over
  conventional open procedure
• Pain hemorrhaging reduced due to small
  incisions
• Comparison
• 4 incisions of 0.5 to 1 cm for laparoscopic
  removal of gallbladder against 20 cm incision for
  open surgery.

108
Applications in Surgery

• Laparoscope is a long fibre optic cable system
  that allows viewing the affected area by snaking
  the cable from a more distant, but easily
  accessible location
• A telescopic rod lens system usually connected to
  a video camera
• A monitor used for viewing the affected abdominal
  or pelvic region.

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Surgical Robots

• Major advances by surgical robots
• Improved laparoscopic surgery
• Remote surgery and unmanned surgery
• More precision, smaller incisions
• Decreased blood loss, less pain, and quicker
  healing time
• 3D magnification and high definition (3D HD) by
  surgeon console helps resulting in improved
  ergonomics
• Reduced duration of hospital stays, blood loss,
  transfusions, and use of pain medication. 
• .

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Surgical Robots

• Robotic surgery either of the two following
  methods to control the instruments
• Tele-manipulator
• Computer controlled
• A Tele-manipulator is a remote manipulator that
  allows the surgeon to perform the normal
  movements associated with the surgery whilst the
  robot arms carry out those movements using
  end-effectors and manipulators to perform the
  actual surgery on the patient.

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Surgical Robots

•  In computer-controlled systems the surgeon uses
  a computer to control the robotic arms and its
  end-effectors. One advantage of using the
  computerised method is that the surgeon does not
  have to be present in the OT, but can be anywhere
  in the world, leading to the possibility
  for remote surgery.

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Surgical Robots da Vinci
Manipulators
Surgeon
Surgeon Console
Patient cart
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Surgical Robots Warning

• The process is VERY Expensive
• Time lapse between the moments when the surgeon
  moves the controls and when the robots respond
• The computer program cannot be changed during
  surgery in case the doctor incorrectly programs
  the robot prior to surgery
• A human surgeon can make needed adjustments.

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THANKS