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2. Definition:
Alternate definition:
“A robot is a one-armed, blind idiot with limited memory
and which cannot speak, see, or hear.”
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3. Ideal Tasks
Tasks which are:
Dangerous
Space exploration
chemical spill cleanup
disarming bombs
disaster cleanup
Boring and/or repetitive
Welding car frames
part pick and place
manufacturing parts.
High precision or high speed
Electronics testing
Surgery
precision machining.
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4. Automation vs. robots
Automation –Machinery designed to carry out a specific
task
Bottling machine
Dishwasher
Paint sprayer
Robots – machinery designed
to carry out a variety of tasks
Pick and place arms
Mobile robots
Computer Numerical Control
machines
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5. Types of robots
Pick and place
Moves items between points
Continuous path control
Moves along a programmable path
Sensory
Employs sensors for feedback
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6. Pick and Place
Moves items from one point to
another
Does not need to follow a specific
path between points
Uses include loading and unloading
machines, placing components on
circuit boards, and moving parts off
conveyor belts.
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9540854414
7. Continuous path
control
Moves along a specific path
Uses include welding,
cutting, machining parts.
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9540854414
8. Sensory
Uses sensors for feedback.
Closed-loop robots use sensors
in conjunction with actuators
to gain higher accuracy – servo
motors.
Uses include mobile robotics,
telepresence, search and
rescue, pick and place with
machine vision.
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9540854414
9. Measures of
performance
Working volume
The space within which the robot operates.
Larger volume costs more but can increase the capabilities
of a robot
Speed and acceleration
Faster speed often reduces resolution or increases cost
Varies depending on position, load.
Speed can be limited by the task the robot performs
(welding, cutting)
Resolution
Often a speed tradeoff
The smallest step the robot can take
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10. Performance (cont.)
• Accuracy
–The difference between the
actual position of the robot and
the programmed position
• Repeatability
Will the robot always return to the
same point under the same
control conditions?
Increased cost
Varies depending on position,
load
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11. Control
•Open loop, i.e., no feedback, deterministic
•Closed loop, i.e., feedback, maybe a sense of
touch and/or vision
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12. Kinematics and dynamics
Degrees of freedom—number of independent
motions
Translation--3 independent directions
Rotation-- 3 independent axes
2D motion = 3 degrees of freedom: 2 translation, 1
rotation
3D motion = 6 degrees of freedom: 3 translation, 3
rotation
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13. Kinematics and dynamics (cont.)
Actions
Simple joints
prismatic—sliding joint, e.g., square cylinder in square tube
revolute—hinge joint
Compound joints
ball and socket = 3 revolute joints
round cylinder in tube = 1 prismatic, 1 revolute
Mobility
Wheels
multipedal (multi-legged with a sequence of actions)
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14. Kinematics and dynamics (cont.)
Work areas
rectangular (x,y,z) x'
cylindrical (r,θ,z) x''
x
spherical (r,θ,ϕ)
Coordinates
World coordinate frame
End effector frame
How to get from coordinate system x” to x’ to x
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15. Transformations
General coordinate transformation from x’ to x is x = Bx’
+ p , where B is a rotation matrix and p is a translation
vector
More conveniently, one can create an augmented matrix
which allows the above equation to be expressed as x = A
x’.
Coordinate transformations of multilink systems are
represented as
x0 = A01 A12A23. . .A(n-1)(n)xn
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16. Dynamics
Velocity, acceleration of end actuator
power transmission
actuator
solenoid –two positions , e.g., in, out
motor+gears, belts, screws, levers—continuum of positions
stepper motor—range of positions in discrete increments
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17. A 2-D “binary” robot segment
Example of a 2D robotic link having three
solenoids to determine geometry. All members are
linked by pin joints; members A,B,C have two states—
in, out—controlled by in-line solenoids. Note that
the geometry of such a link can be represented in
terms of three binary digits corresponding to the
states C A,B,C, e.g., 010 represents A,C in, B out.
A B
of A B C A B C A B C
Links can be chained together and controlled by sets
of three bit codes.
A B C A B C A B C A B C
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18. Problems
Joint play, compounded through N joints
Accelerating masses produce vibration, elastic
deformations in links
Torques, stresses transmitted depending on end
actuator loads
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19. Control and programming
Position of end actuator
multiple solutions
Trajectory of end actuator: how to get from point A to B
programming for coordinated motion of each link
problem—sometimes no closed-form solution
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20. Control and programming (cont.)
Example: end actuator (tip) problem with no closed solution.
Two-segment arm with arm lengths L1 = L2, and stepper -motor
control of angles θ1 and θ2. L 2
θ2
y
L1
θ1
Problem: control θ1 and θ2 such that arm tip traverses its range
at constant height y, or with no more variation than δy.
Geometry is easy: position of arm tip
x = L1 (cos θ1 + cos θ2)
y = L1 (sin θ1 + sin θ2)
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21. Control and programming (cont.)
Arm tip moves by changing θ1 and θ2 as a function of time.
x = − L1 (sin θ1 θ1 + sin θ 2 θ 2 )
Therefore
y = L1 (cos θ1 θ1 + cos θ 2 θ 2 ) = 0
So, as θ1 and θ2 are changed, x and yθare −θ cos θ1
= affected.
cos θ 2
2 1
To satisfy y = constant, we must have
. So the rates at which θ1 and θ2 are changed depend on the
values of θ1 and θ2.
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22. Control and programming (cont.)
There is no closed-form solution to this problem. One must use
approximations, and accept some minor variations in y. Moving the
arm tip through its maximum range of x might have to be
accomplished through a sequence of program steps that define
different rates of changing θ1 and θ2.
Possible approaches:
Program the rates of change of θ1 and θ2 for y = const. for initial values
of θ1 and θ2 . When arm tip exceeds δy, reprogram for new values of θ1
and θ2.
Program the rates of change of θ1 and θ2 at the initial point and at
some other point for y = const. Take the average of these two rates,
and hope that δy is not exceeded. If it is exceeded, reprogram for a
shorter distance. Continue program segments until the arm tip has
traversed its range.
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23. Control and programming (cont.)
Program the rates of change of θ1 and θ2 at the initial point
and at some other point for y = const. Take the average of
these two rates, and hope that δy is not exceeded. If it is
exceeded, reprogram for a shorter distance. Continue
program segments until the arm tip has traversed its range.
The rate of change of θ1 and θ2 can be changed in a
programming segment, i.e., the rates of change need not be
uniform over time. This programming strategy incorporates
approaches 1) and 2). Start with rates of change for the
initial values of θ1 and θ2 , then add an acceleration
component so that y = const. will also be satisfied at a
distant position.
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