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Transcript
Manipulators and Mechanisms
June 8, 2008
Meredith Evans
Andrew Aguinaldo
Gabby Salo
Agenda
• Physics Concepts
• Arms and Lifts
• Handling Objects
• Mechanisms
• Gear Ratio
Physics Concepts
Forces, Vectors, Angles, and
Torque
Force and Vectors
• In mechanics, forces are seen as the
causes of linear motion
– Forces are vector quantities
• A vector is a geometric object with magnitude and a
direction
• Magnitude and a direction must be specified
– The SI unit for force is the Newton
• Newton = kg m/s2
Torque
• A torque is an influence which tends to change the
rotational motion of an object.
– Torque = Force applied x lever arm
– The direction of the torque is given be the right hand rule
– Note that the torque is maximum when the angle is 90 degrees.
Point of
application
of the force
Applied force
r
Lever arm is
measured from
the axis of
rotation.
θ
Axis of
rotation
F
Radius from axis
of rotation to point
of application of the
force.
 
torque  r  F  rF sin 
Torque
• Example #1 - Lifting
Θ=90°
5 kg
10 m
torque  rF sin 
torque  (10m)[(5kg)(9.8m / s 2 )] sin( 90)
torque  490 N  m
Torque
• Example #2 – Lifting
5 kg
– Same force, different angle,
less torque
Θ=50°
Θ=90°
torque  rF sin 
torque  (10m)[(5kg)(9.8m / s 2 )] sin( 90  50)
torque  314.9 N  m
Power
• Power is all about how fast you can move
something
 distance 
power  ( force)(velocity)  force

 time 
OR
 velocity 
power  (torque)
  (torque)angular ve locity 
 distance 
Power
• Example – Lifting
– Same torque, different speed
5 kg
0.1 HP, 100 RPM
Motor w/ 1” sprocket
5 kg
0.2 HP, 200 RPM
Motor w/ 1” sprocket
OR
100 RPM w/ 2”
sprocket
Power
• In Summary:
– Given the proper gear ratio and assuming 100%
efficiency, any motor can lift any object. It’s the rate
of lift that varies from motor to motor.
• But no power transfer mechanisms are 100%
efficient
– If you do not account for these inefficiencies, your
performance will not be what you expected
Arms and Lifts
Vertical Lifts - Scissors
• Overview
– The scissor lift is unique in that it
doesn't use a straight support to raise
workers or objects into the air.
– Rather, the scissor lift platform raises
when the linked, folding supports
underneath it draw together, stretching
it upward.
– It can be powered by hydraulics or an
electric motor,
but it's a bumpy ride to the top.
– The scissor lift's design keeps it from
traveling with a
constant velocity,
instead traveling
faster in the middle
of its journey and
slower with more
extension.
Vertical Lifts - Scissors
• Pros
– The max height of the platform is flexible
– The height is determined by the number and length
of the linkages
– Great for straight lifts
– Can be used in a robotic arm to reach out
straight
• Cons
–
–
–
–
–
–
–
–
13
Requires great force to get the lift started
Synchronizing two scissors is difficult
Complex design
Needs to be heavy to be stable enough
Doesn’t deal well with side loads
Must be built very precisely
Stability decreases as height increases
Loads very high to raise at beginning
of travel
Vertical Lifts - Extension
•
Overview
– Two types
• Continuous rigging
• Cascade rigging
•
Pros
– The max height of the platform is flexible
– The height is determined by the number and
length
of the linkages
– Great for straight lifts
•
Cons
– Needs to be heavy to be stable enough
– Doesn’t deal well with side loads
– Must be built very
precisely
– Stability decreases as
height increases
– Loads very high to
raise at beginning
of travel
Vertical Lifts - Extension
• Tips
– Power down and up
• If not, make sure to add a device to take
up the slack if it jams
–
–
–
–
Segments need to move freely
Need to be able to adjust cable length(s).
Minimize slop / freeplay
Maximize segment overlap
• 20% minimum
• more for bottom, less for top
– Stiffness is as important as
strength
– Minimize weight,
especially at the top
– Keep the CG aft
Extension - Rigging
Continuous
Cascade
Extension - Rigging - Continuous
• Speed of cable same
for up and down
• Intermediate sections
may jam
• Cable tension is low
• Cable routing is more
complex
• The final stage moves
up first and down last
Slider
(Stage3)
Stage2
Stage1
Base
Extension - Rigging - Continuous
• All internal cabling
• Cable routing more
complex
Slider
(Stage3)
Stage2
Stage1
Base
Extension - Rigging - Cascade
• Cables going up and cables
going down have different
speeds
– Different cable speeds can be
handled with different drum
diameters or multiple pulleys
• Intermediate sections do not
jam
• Lower stage cables have
more tension
– Needs lower gearing to deal
with higher forces
Slider
(Stage3)
Stage2
Stage1
Base
Extension - Rigging (i.e. Telescope)
• Overview
– Telescoping lifts are most commonly used within forklifts and
cranes.
– They extend in one direction and are usually
powered by a chain or piston.
• Pros
– Extends “within the box”
– Mechanism protected by the base
– Generally operates on a fairly
uncomplicated electrical system
– Only requires one power source
• Cons
– Multiple segments translate up,
resulting in a higher center of gravity
– Can become complex
20
Rotary Jointed Arms
•
Overview
– Rotary Jointed Arms work on the basic principle of the human arm.
– They have a wrist, a shoulder, and an elbow.
– Depending on what the robotic arm is used for,
a gripper, like that of a hand can be added to
the end of the arm, and ultimately give the
user 3 axes of motion, generally referred
to as pitch, yaw, and roll.
•
Pros
– Allows for 3 axes of motion
– Can emulate the human arm
– Great idea when gripping objects is required
•
Cons
– Large moments can develop at the shoulder
and base plate, which can ultimately lead to
failure of the joint.
– A motor is required at each joint, and each
has to be operated independently
– Programming a system to work on several
independent motors can be quite tricky
21
Combined Mechanisms
•
Overview
– When one system doesn’t cut it, combining
the mechanisms might help.
– You may need reach, but the 4 bar doesn’t
reach that high.
– Attaching a 4 bar to a telescoping lift might
be your answer.
•
Pros
– Combines the pros of the various mechanisms
•
Cons
– Complex
22
Four Bar Lifting Mechanism
• Overview
– The 4 bar mechanism is
simple and effective.
– The opposite bars always
remain parallel
retaining the orientation of the
object.
– Many industrial robots use this
mechanism.
4 Bar Lifting Mechanism
•
Pros
–
–
–
–
–
•
Simple
Object retains orientation
1 joint to power
Easily programmed
Provides reach
Cons
– Large moments can develop
at the joint location
– Pin Loadings can be high
– Required to lift “outside of the box”
– Can be vulnerable to side hits
•
Tips
– Watch for buckling in lower member
– If possible, counterbalance
– Keep the center of gravity (CG) aft
24
Multi-Bar
Mechanisms
Crossed 8 bar
Multi-Bar Mechanisms
Parallel 8 bar
Arms vs. Extension Lifts
• Arms
– Can reach over objects
– Can help right a flipped
robot
– Can fold down to allow
moving through barriers
– Require complex controls
and counter-balances
– Harder to maintain CG over
base
– Need space to swing up
– Need extra joints to reach
higher which adds more
complexity
• Lifts
– Limited reach
– Can't not help right a
flipped robot
– Stay tall limiting movement
through barriers
– Simple controls
– Maintain a better CG over
the base
– Can operaet in confined
spaces
– Lifts can reach higher with
minimal added complexity
Handling Objects
Manipulation
Storage
Acquisition Size
Placement and Alignment
Accumulators
Conveyers
Ball Manipulation
• Both Continuous intakes and single object
grabbers are useful when manipulating small
or medium sized balls.
• Types of Manipulators for Balls
–
–
–
–
–
Two tank treads horizontally or vertically aligned.
Three and Four Pronged Grabber
Two Point Grabber/ Fork
Bucket Intake
Roller
• Should be soft grip to be able to effectively
control and contain the ball.
29
Ring Manipulation
• Both Continuous intakes and single object
grabbers are useful when manipulating small
or medium sized rings.
• Types of Manipulators for Rings
–
–
–
–
–
Two tank treads horizontally or vertically aligned.
Three and Four Point Grabber
Two Point Grabber/ Fork
Bucket Intake
Roller
• Should be soft grip to be able to effectively
control and contain the Ring.
30
Square Manipulation
• Both Continuous and single object
grabbers are useful when manipulating
small or medium sized squares.
• Types of Manipulators for Squares:
– Three and Four Pronged Grabber with Grip
– Two Point Grabber
• Should be a strong grip to be able to
effectively control and contain the
square.
31
Triangle Manipulation
• Single object grabbers are useful when
manipulating triangles.
• Types of Manipulators for Triangles:
– Three and Four Point Grabber
– Flat Bottom and X Shaped Intake Roller
• Should be strong grip to be able to
effectively control and contain the
Triangle.
32
Storing Objects
• All items of the same size can be
similar
• Storage Method
– Stack
– Tank Tread
– Divide
– Dump Tank
– Or Simple Grab and Drop to Goal
33
Storing Manipulator Arm
• This must be decided with the base so
the arm and manipulator have a place
to go when a) trying to fit the size and
b) to effectively pick up the objects
• Storage Method
– U Shaped Base
– 360` Pivot Joint (and Arm Extender)
– Manipulator Attached to Base
34
Acquisition Size
• Acquisition is the intake area of the object.
• Large acquisition area is optimal when
picking up
• During match, need easiest and quickest
pick up for driver
• Able to get the most amount of objects at
once
• When deciding acquisition intake, keep in
mind what object you’re manipulating.
35
Placement and Alignment
• Along with the acquisition zone, the placement of the object
on/into the goal must be able to have accuracy with ease.
• Along with the storage of the arm, you must work with the drive
train to be able to fit the robot against the goal for optimal
stability (Unable to be pushed away from the goal when
attempting to score) and accuracy.
• Alignment is the drive train’s responsibility. Make sure they
know exactly how your mechanism works and where it needs
to be positioned to make a goal.
• Placement must be easy to work from a drivers standpoint. In
contrast to the large acquisition zone, the manipulator should
be small enough to accurately place the object on or in.
36
Gripping Objects
• Why is the grip important?
– The manipulator cannot effectively hold on to the
object if both the object and the manipulator have
no grip.
• You need friction.
– Friction is the force that opposes the relative
motion or tendency toward such motion of two
surfaces in contact
– In this case, the force that opposes is gravity and
the two surfaces are the manipulator and the
object.
37
Mechanisms
Motors and Servos
Limits
Motors and Servos
• The Motors and Servos make the arm and manipulator move.
• Motors can turn a shaft* clockwise and counterclockwise as
many degrees as desired.
• Motors are generally used for continuous intake.
• Servos can only turn a shaft* 180 degrees in either direction
(360 degrees in total)
• Servos should be used on < 360 degree pivot joints for both the
arm and the manipulator.
• *The shaft allows the motor to connect to the arm for a powered
pivot point.
39
Limits
• There are two types of stops:
– Hard stop
• The hard stop is a sturdy metal part of the robot’s structure.
• This does not allow the manipulator / arm to go any farther.
• However, the hard stop does not tell the motors to stop
working, thus, the motors will break.
• This is why we have soft stops.
– Soft stop
• Soft stops are limit switches.
• When programmed correctly, the limit switch tells the motor or
servo to stop.
• Limits should be placed anywhere that contains a
hard stop.
– i.e. Arm pivot joints, two+ prong gabber, fork lifts, etc.
40
Gear Ratio
Gear Ratio
• “There is no way that this motor can pull the arm and
manipulator up against gravity. It’s just too heavy.”
• If the motor is expected to work against a lot of weight, gear the
ratio down.
– i.e. 1:2 meaning for every one shaft revolution (360 degrees), the
motor does two.
• If the motor is not expected to work against a lot of weight and
work quickly, gear the ratio up.
– i.e. 2:1 meaning for every two shaft revolutions (two * 360
degrees), the motor does one.
• However, you must have enough torque to pull the arm and
manipulator up and down.
• You must also have enough torque to keep hold on the object
the robot is manipulating. It is not just friction holding it there.
42
Gear Ratio Calculations
•
The gear ratio is the relationship
between the number of teeth on
two gears that are meshed or two
sprockets connected with a
common roller chain, or the
circumferences of two pulleys
connected with a drive belt.
d
D
d 2r r
Gear Ratio  

D 2R R
For the angular speed
(r )(r )  ( R)(R )
Which implies :
r R

R r
Appendix
Force
• In mechanics, forces are seen as the
causes of linear motion
• Forces are vector quantities,
– They require vector math
– Magnitude and a direction must be specified for
a vector quantity
• The SI unit for force is the Newton
– Newton = kg m/s2
Vectors
• Geometric object with magnitude
and a direction
• Represented by a line segment
connecting the initial point A with
the terminal point B
• Vector Math
D
C+D
– Addition
• Tip to toe method
C
– C+D
– Subtraction
E
• Flip the direction of vector
-E
A
AB
B
Angles
• Measuring angles
• Trigonometry
sin  
Opposite
Hypotenuse
Opposite
cos  
tan  
Adjacent
Hypotenuse
Opposite
Adjacent
θ
Adjacent
• Note: Units in Radians.
• Radians to Degrees  180° = π rad
Introduction – Center of Mass
• Unique point in an object or system which can be used to
describe the system's response to external forces and
torques.
• The concept of the center of mass is that of an average of
the masses factored by their distances from a reference
point.
x2
xcm
x1
Center of
mass
xcm
m1 x1  m2 x2

m1  m2
Friction
•
Friction is the force resisting the
relative motion of two surfaces in
contact
– The heavier an object is the
larger the frictional force
– The material on which the
object is sliding also affects
the frictional force.

v

N  mg


fk  ( k )( N )

F

Fg

N  Normal Force

Fg  Force Gravity

F  Force of Motion

v  Velocity (constant)

fk  Force of Kinetic Friction
k  coeficient of Kinetic Friction
Power
• Example #1 - Lifting
angular ve locity 
rev  1 min  rad 
rad

100

 
  5.2
min  60 sec  rev 
sec

10 lbs
power 
Power = 100W
Motor w/ 1” sprocket
(torque)(angular ve locity ) 
rad
(490 N  m)(5.2
)  2565.6W
sec
Accumulators
• Accumulator = rotational device that pulls objects in
• Types:
– Horizontal tubes - best for gathering balls from floor or
platforms
– Vertical tubes - best for sucking or pushing balls between
vertical goal pipes
– Wheels - best for big objects where alignment is predetermined
• Most efficient in gathering balls
– If set up in the proper orientation, will not knock the ball away,
just suck it in
Conveyors
• Conveyor - device for moving multiple objects,
typically within your robot
• Types:
– Continuous Belts
• Best to use 2 running at same speed to avoid jamming
– Individual Rollers
• best for sticky balls that will usually jam on belts and each other
Conveyors
Why do balls jam on belts?
- Sticky and rub against each
other as they try to rotate along
the conveyor
Solution #1
- Use individual rollers
- Adds weight and complexity
Solution #2
- Use pairs of belts
- Increases size and complexity
Solution #3
- Use a slippery material for the nonmoving surface (Teflon sheet works
great)
Passive Assistance
• What is passive assistance?
–
–
–
–
–
–
SPRINGS or BRAKES!
Use Elastic Energy to your advantage.
Surgical Tubing
Constant Force Springs
Gas Springs
Torsion Springs
Braking - to Prevent Back-driving
• Ratchet Device - completely lock in one direction in
discrete increments – ie. winches
• Clutch Bearing - completely lock in one direction
• Brake pads - simple device that squeezes on a
rotating device to stop motion - can lock in both
directions
– Disc brakes - like those on your car
– Gear brakes - applied to lowest torque gear in gearbox
• High ratio worm gear (window, van-door motors)
– Note : any gearbox that cannot be back-driven is probably
very inefficient
Torque
• Example #3 - Pulling on object
– One angle helps secure object
– The other does not
This one wants to
rotate clockwise and
let go
This one wants to rotate
counter- clockwise and
grab even harder