Title: Introduction to Robot Arm Kinematics & Applications of Robots
1INTRODUCTION ROBOT ARM KINEMATICS
 Prof. Tarun Kanti Naskar,
 Mechanical Engineering Department,
 Jadavpur University, Kolkata, India
2Nomenclature
36axis Robotic Arm
4SixServoRobotArmRA001
5Edge Robotic Arm
6PUMA Robot Programmable Universal Machine for
Assembly
7What 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.
8What 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
reprogrammable, multifunctional manipulator
designed to move materials, parts, tools or
specialized devices through various programmed
motions for the performance of a variety of
tasks.
9What is Robot
 Finally
 A robot is a softwarecontrollable mechanical
device that uses sensors to guide one or more
endeffectors 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.
10Robot 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 3axes 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.
11Cartesian Robot PPPCylindrical Robot RPP
12Spherical Robot SCARA (Selective Compliance
Assembly Robot Arm )Robot
13Articulated Robot RRR
14Technology 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, forcetorque transducers  Electronic controller microprocessors with A/D
or D/A conversions, memory etc.  Computers.
15Robot Specifications
(i) Drive technologies, (ii) workenvelope
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 
16Axes of Robotic Manipulator
Axes Type Function
13 Major Position the wrist
46 Minor Orient the tool
7n Redundant Avoid obstacles
173 Minor Axes of the Wrist of a Robot
18Tool OrientationYaw, Pitch Roll
Righthanded coordinate frame
Righthanded coordinate frame is that for which
the direction of rotation from OA to OB propels a
righthanded screw in the direction OC. The
system of OAOBOC is an orthogonal triad and
righthanded one is positive.
19Load 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.
20Speed of Motion
 Defined by the cycle time  the time required to
perform a periodic motion. It is more meaningful
than the maximum tooltip 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.
21Influence of distance versus speed
22Reach and Stroke of a Cylindrical Robot
23Repeatability
 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.
24Precision
 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.
25Forward Kinematics
26Robotic manipulator as chain
27Direct Inverse Kinematics
28Reference 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
29Development of Transformation Matrices
30Composite 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
OXYZsystem premultiplication by the previous
rotation matrix
 3. Rotation about one of its own axes
postmultiplication by the previous rotation
matrix
 4. If there are more fundamental rotations to be
performed, go to step 2 else stop.
31Composite 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
32Rotation Matrix about an Arbitrary Axis
33Rotation Matrix About An Arbitrary Axis
 Following rotations should be done consecutively
to get the required rotation  Rx,? (Makes r to align with XZplane)
 Ry,? (Makes r to align with Zaxis)
 Rz,? (Makes the rotation about Z or raxis)
 Ry,? (Restores r to position stated in 2)
 Rx,? (Restores r back to original position)
 The resultant matrix
 Rr,? Rx,? Ry,? Rz,? Ry,? Rx,?
34Perspective 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.
35Perspective 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.
36Perspective 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.
37Perspective Transformation
38Euler Angle Representations
Euler Angles (system I) Euler Angles (system II) Euler Angles (system III)
Sequence Of Rotations ? about Zaxis ? about Zaxis ? about Xaxis
Sequence Of Rotations ? about Uaxis ? about Vaxis ? about Yaxis
Sequence Of Rotations ? about Waxis ? about Waxis ? about Zaxis
III XYZ here YawPitchRoll
39Yaw, Pitch, and Roll of tool
40Homogeneous 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.
41Homogeneous 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.
42Homogeneous Coordinates Transformation Matrix
,
 A homogeneous transformation matrix has the
following submatrices
,
Rotation only, no translation
43Homogeneous Coordinates Transformation Matrix
44Scale
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.
45Scale


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.
46 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
47 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
48Normal, Sliding Approach Vectors of Tool
49Link Coordinate System Its Parameters
Link parameters ?i, di Joint parametersai, ai
50Parameters
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.
51DenavitHartenberg 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.
52Transformation from (i1)th coordinate frame to
ith frame
Screw Transformations
53Inverse of this transformation matrix is
transformation matrices are expressed in the
forms
54JointType Parameter
The ith joint variable
is expressed as
selects
either
or
in the following way
55Partitioning 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 tooltip into roll
56Determining Robot Arm Kinematics
57Link 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
58Cylindrical 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
593DOF 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
604Axis 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
615DOF 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 ?4p/2 ?4 S4 C4 0 1
5 0 0 L5 ?5 ?5 C5 S5 1 0
62Alpha 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
63Link 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
64A problem to solve
Draw the link coordinate diagram, construct the
parameter table and find the arm matrix by
forward kinematics.
65Inverse Kinematics
66Human Skeleton as a Robotic Chain
A model of the human skeleton as a kinematic
chain allows positioning using inverse kinematics
67OBJECTIVE
 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 framen w r to
the base frame0 for an nDOF robotic
manipulator.
68OBJECTIVE
 In order to control the position and orientation
of the endeffector of a robot to reach its
object, the inverse kinematics solution is more
important. That is, given the position and
orientation of the endeffector of a robot arm
and its joint and link parameters, we like to
find the corresponding joint angles of the robot
so that the endeffector can be positioned as
required.
69OBJECTIVE
 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.
70Reachable 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 endeffector can reach every point from all
orientations is called dexterous workspace.
71Existence 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
rollpitchyaw angles of the endeffector. So 3
from orientation and 3 from displacement.
72Existence 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
73Existence of Solutions
 With , the manipulator cannot attain the
general position and orientation in a 3D space
mathematically it is an overdetermined 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 underdetermined case.
74Multiple Solutions
Fig shows a 2DOF 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 workfloor.
75Solution Techniques
Closed form solution technique would be pursued
here.
76Closed 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.
77Guideline 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 elementbyelement equality, 12
equations are obtained.
78Steps to solve nnumber 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.
79Steps to solve nnumber of joint variables
Contd...
5.
Since has one unknown premultiplying
both sides by we get, The LHS of it has
(n1) 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.
80APPLICATIONS 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
81APPLICATIONS 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.
82Process Applications
Endeffectors are sometimes tools themselves,
Sometimes they are used as grippers for
different manufacturing jobs. The later
provides greater flexibility.
83Process Applications
 Processes where robots used
 Welding
 Spotwelding
 Spraypainting
 Drilling
 Other machining operations.
84Arc welding
85Requirements 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 pointtopoint 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.
86Requirements 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.
87Requirements 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.
88Sensors 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
89Contact 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.
90Noncontact Sensors
No tactile measurement is done. Sensing is done
by throughthearc systems in the form of
either electric current (in constantvoltage
welding) or voltage (in constantcurrent
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.
91Applications
92APPLICATIONS 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.
93APPLICATIONS 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 redhot material.
94MATERIAL HANDLING
For this a robot requires a basic pickandplace
operation. Examples
 Material transfer applications
 Machine loading/unloading operations
Basic Material Handling Operations
Movements in addition to material handling
 4. Inspection
 5. Process application like spot welding
95Material Handling
96Work 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)
ABCD.
The object may be dropped, at point C, if not
fragile. Work cycles may be more complex like
instead of being a just twopoint delivery, need
may be of changing delivery points from cycle to
cycle, avoiding obstacles, etc.
97MACHINE 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.
98MACHINE 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.
99MACHINE 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.
100A Robot Centered Work Cell
101Robot Programming
102ROBOT 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.
103Features 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.
104Robot 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.
105Robot 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.
106Applications in Surgery
107Applications 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.
108Applications 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.
109Surgical 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.  .
110Surgical Robots
 Robotic surgery either of the two following
methods to control the instruments  Telemanipulator
 Computer controlled
 A Telemanipulator 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
endeffectors and manipulators to perform the
actual surgery on the patient.
111Surgical Robots
 In computercontrolled systems the surgeon uses
a computer to control the robotic arms and its
endeffectors. 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.
112Surgical Robots da Vinci
Manipulators
Surgeon
Surgeon Console
Patient cart
113Surgical 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.
114THANKS