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					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                      F
                                                                             
  Lever arm is       θ           Radius from axis                  torque  r  F  rF sin 
                                 of rotation to point
  measured from
                                 of application of the
  the axis of
                                 force.
  rotation.
                  Axis of
                  rotation
                         Torque
• Example #1 - Lifting



                           Θ=90°           5 kg


                                 10 m




             torque  rF sin 
             torque  (10m)[(5kg)(9.8m / s 2 )]sin(90)
             torque  490N  m
                          Torque
• Example #2 – Lifting
   – Same force, different angle,                    5 kg
     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 velocity 
                 distance 
                                Power
• Example – Lifting
   – Same torque, different speed




                            5 kg                           5 kg



         0.1 HP, 100 RPM                0.2 HP, 200 RPM
         Motor w/ 1” sprocket           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
        –   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

13
             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
                                      Slider
• Intermediate sections
                                     (Stage3)
  may jam
• Cable tension is low
                           Stage2
• Cable routing is more
  complex
• The final stage moves     Stage1
  up first and down last
                            Base
Extension - Rigging - Continuous
• All internal cabling
• Cable routing more                Slider
  complex                          (Stage3)


                         Stage2

                          Stage1


                          Base
 Extension - Rigging - Cascade
• Cables going up and cables
  going down have different
  speeds                                        Slider
   – Different cable speeds can be             (Stage3)
     handled with different drum
     diameters or multiple pulleys
                                     Stage2
• Intermediate sections do not
  jam
                                      Stage1
• Lower stage cables have
  more tension
   – Needs lower gearing to deal      Base
     with higher forces
     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                           • Lifts
  – Can reach over objects          – Limited reach
  – Can help right a flipped        – Can't not help right a
    robot                             flipped robot
  – Can fold down to allow          – Stay tall limiting movement
    moving through barriers           through barriers
  – Require complex controls        – Simple controls
    and counter-balances            – Maintain a better CG over
  – Harder to maintain CG over        the base
    base                            – Can operaet in confined
  – Need space to swing up            spaces
  – Need extra joints to reach      – Lifts can reach higher with
    higher which adds more            minimal added complexity
    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
•                                                    d 2r r
    The gear ratio is the relationship
    between the number of teeth on
                                         Gear Ratio    
                                                     D 2R R
    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.          For theangular speed
                                         (r )(r )  ( R )(R )



     d                       D           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                               A
                                                    AB
                                                         B
• Represented by a line segment
  connecting the initial point A with
  the terminal point B

                                       D
• Vector Math                 C+D
   – Addition
      • Tip to toe method              C
          – C+D
   – Subtraction                           E
      • Flip the direction of vector
                                           -E
                        Angles
• Measuring angles



• Trigonometry
            Opposite
 sin  
           Hypotenuse
                        Opposite
            Adjacent                             θ
 cos 
           Hypotenuse
                                          Adjacent
           Opposite
 tan  
           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                           m1 x1  m2 x2
            xcm                           xcm 
     x1
                           Center of
                            mass                 m1  m2
                                 Friction
•   Friction is the force resisting the                
    relative motion of two surfaces in
                                                       N  Normal Force
                                                       
    contact                                            Fg  ForceGravity
     – The heavier an object is the                    
                                                       F  Forceof Motion
        larger the frictional force                    
     – The material on which the                       v  Velocity (constant)
                                                       
        object is sliding also affects                 fk  Forceof Kinetic Friction
        the frictional force.
                                                       k  coeficient of Kinetic Friction
                           
                          N  mg
                v
                                                
                                    fk  ( k )( N )
                 
                 F
                            
                            Fg
                                    Power
• Example #1 - Lifting
                                    angular velocity 
                                        rev  1 min  rad         rad
                                    100                   5.2
                                        min  60 sec  rev        sec
                           10 lbs

                                    power 
                                    (torque)(angular velocity) 
    Power = 100W
    Motor w/ 1” sprocket                            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 pre-
     determined
• 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 non-
   moving 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                 This one wants to rotate
   rotate clockwise and              counter- clockwise and
   let go                            grab even harder

				
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