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Relative Advantages ofArms Over Lifts
• Very flexible• Can right a flipped robot• Can place object in an infinite number of
positions within reach• Minimal height - Great for going under things
Relative Advantages ofLifts Over Arms
• Typically simple to construct• Easy to control (don’t even need limit switches)• Maintain CG in a fixed XY location• Don’t require complex gear trains
10 lbs
10 lbs
< DD
Example: Lifting at different angles
• Torque = Force x Distance
• Same force, different angle, less torque
Arm: Forces, Angles, & Torque
Arm: Power
• Power = Torque / Time– OR –
• Power = Torque x Rotational Velocity• Power (FIRST definition): How fast you can
move something
Arm: PowerExample: Lifting with different power output
• Same torque with twice the power results in twice the speed
• Power = Torque / Time
125 Watts, 100 RPM
250 Watts, 200 RPM
10 lbs10 lbs
Arm: Design Considerations• Lightweight Materials: tubes, thin wall sheet• Design-in sensors for feedback & control
– limit switches and potentiometers• Linkages help control long arms• KISS
– Less parts… to build or break– Easier to operate– More robust
• Use off-the-shelf items• Counterbalance
– Spring, weight, pneumatic, etc.
Elevator: Advantages & Disadvantages• Advantages
– Simplest structure
– On/Off control
– VERY rigid
– Can be actuated via screw, cable, or pneumatics
• Disadvantages
– Single-stage lift
– Lift distance limited to maximum robot height
– Cannot go under obstacles lower than max lift
Elevator: Design Considerations
• Should be powered down as well as up
• Slider needs to move freely
• Need to be able to adjust cable length--a turnbuckle works great
• Cable can be a loop
• Drum needs 3-5 turns of excess cable
• Keep cables or other actuators well protected
Elevator: Calculations
• Fobject = Weight of Object + Weight of Slider
• Dobject = Distance of Object CG• Tcable = Fobject
• Mslider = Fobject• Dobject
• Fslider1 = - Fslider2 = Mslider / 2Dslider
• Fpulley = 2 Tcable
• Fhit = (Weight of Object + Weight of Slider) • G value [I use .5]
• Mhit = Fhit • Hslider
• Mbase = Mslider + Mhit
Fobject Fslider1
Fslider2
Fpulley
Mslider
Mbase
Dobject Dslider
Tcable
Fhit
Hslider
Forklift: Advantages & Disadvantages• Advantages
– Can reach higher than you want to go
– On/Off control
– Can be rigid if designed correctly
– Can be actuated via screw, cable, or pneumatics, though all involve some cabling
• Disadvantages
– Stability issues at extreme heights
– Cannot go under obstacles lower than retracted lift
Forklift: Design Considerations
• Should be powered down as well as up
• Segments need to move freely
• Need to be able to adjust cable length(s).
• Two different ways to rig (see later slide)
• MINIMIZE SLOP
• Maximize segment overlap
• Stiffness is as important as strength
• Minimize weight, especially at the top
Dupper/2
Hupper
Forklift: Calculations
• Fobject = Weight of Object + Weight of Slider
• Dobject = Distance of Object CG• Mslider = Fobject• Dobject
• Fslider1 = - Fslider2 = Mslider / 2Dslider
• Fhit = G value [I use .5] • (Weight of Object + Weight of Slider)
• Mhitlower = Fhit•Hlower + [(Weight of Upper + Weight of Lower) • (Hlower / 2)]
• Flower1 = - Flower2 = [Mslider + Mhitlower] / 2Dslider
• Mhit = Fhit • Hslider + [(Weight of Lift • G value • Hslider ) / 2]
• Mbase = Mslider + Mhit
Mbase
Fobject Fslider1
Fslider2
Mslider
Dobject DsliderFhit
Hslider
Fupper2
Dupper
Fupper1
Flower2
Dlower
Flower1
Hlower
Dlower/2Mlower
Mupper
Forklift: Rigging (Continuous)
• Cable goes same speed for up and down
• Intermediate sections often jam
• Low cable tension
• More complex cable routing
• Final stage moves up first and down last
• Tcable = Weight of Object + Weight of Lift Components Supported by Cable
Forklift: Rigging (Cascade)
• Up-going and down-going cables have different speeds
• Different cable speeds can be handled with different drum diameters or multiple pulleys
• Intermediate sections don’t jam
• Very fast
• Tcable3 = Weight of Object + Weight of Slider
• Tcable2 = 2Tcable3 + Weight of Stage2
• Tcable1 = 2Tcable2 + Weight of Stage1• Much more tension on the lower stage cables
– Needs lower gearing to deal with higher forces
Tcable1
Tcable2
Tcable3
Base
Stage1
Stage2
Slider(Stage3)
Four Bar: Advantages & Disadvantages• Advantages
– Great for fixed heights
– On/off control
– Lift can be counter-balanced or spring-loaded to reduce the load on actuator
– Good candidate for pneumatic or screw actuation
• Disadvantages
– Need clearance in front during lift
– Can’t go under obstacles lower than retracted lift
– Have to watch CG
– If pneumatic, only two positions (up & down)
Four Bar: Design Considerations
• Pin Loadings can be very high• Watch for buckling in lower member• Counterbalance if you can• Keep CG back• Limit rotation• Keep gripper on known location
Four Bar: Calculations
Llink
Mbase
Fobject
Fgripper1
Fgripper2
Mgripper
Dobject DgripperFhit
Hgripper
Flink2DlinkFlink1
Dlower/2
Mlink
• Under Construction Check Back Later
Scissors: Advantages & Disadvantages
• Advantages
– Minimum retracted height
• Disadvantages
– Tends to be heavy
– High CG
– Doesn’t deal well with side loads
– Must be built precisely
– Loads very high on pins at beginning of travel
Scissors: Design Considerations
• Members must be good in both bending and torsion
• Joints must move in only one direction
• The greater the separation between pivot and actuator line of action, the lower the initial load on actuator
• Best if it is directly under load
• Do you really want to do this?
Arm vs. Lift: SummaryFeature Arm Lift
Reach over object Yes No
Fall over, get up Yes, if strong enough No
Go under barriers Yes, fold down Maybe, lift height may be limited
Center of gravity (CG)
Not centralized Centralized mass
Small space operation
No, needs room to swing
Yes
How high? More articulations, more height (difficult)
More lift sections, more height (easier)
Complexity Moderate High
Powerful lift Moderate High
Combination Insert 1-stage lift at bottom of arm
Stress Calculations
• It all boils down to 3 equations:
IMc
A
Ftens
tens
A
Fshear
Where: = Bending StressM = Moment (calculated earlier)I = Moment of Inertia of Sectionc = distance from Central Axis
Where: = Tensile StressFtens = Tensile ForceA = Area of Section
Where: = Shear StressFshear = Shear ForceA = Area of Section
BENDING TENSILE SHEAR
Stress Calculations (cont.)
• A, c and I for Rectangular and Circular Sections
1212
3ii
3oo
hbhbI
bo
c
2
hc
iioohbhbA
ho
bi
hi
2
i
2
odd
4A
do
di
2o
dc
4
i
4
odd
64I
Stress Calculations (cont.)
• A, c and I for T-Sections
X 2
2
x222
322
2
1
x111
311
x 2
hchb
hb
2
hchb
hbI
1212
A2
hhhb
2
hhb
c
2
1221
11
x1
2211hbhbA Y
b1
h2
b2
cy
h1 cx1
cx2
x121x2chhc
2
bc 1
y
1212
322
311
y
bhbhI
Stress Calculations (cont.)
• A, c and I for C-Sections (Assumes Equal Legs)
X 2
2
x222
322
2
1
x111
311
x 2
hchb2
hb2
2
hchb
hbI
1212
A2
hhhb2
2
hhb
c
2
1221
11
x1
2211hb2hbA Y
b1
h2
b2
cy
h1 cx1
cx2
x121x2chhc
2
bc 1
y
1212
322
311
y
bh2
bhI
Stress Calculations (cont.)
• A, c and I for L-Angles
X 2
2
x222
322
2
1
x111
311
x 2
hchb
hb
2
hchb
hbI
1212
A2
hhhb
2
hhb
c
2
1221
11
x1
2211hbhbA Y
b1
h2
b2
cy1
h1 cx1
cx2
x121x2chhc
cy2
A2bbh
2
bbh
c2
221
11
y1
y11y2
cbc
2
2
y122
322
2
y1
111
311
y 2
bcbh
bhc
2
bbh
bhI
1212
Allowable Stresses
allowable = yeild / Safety Factor• For the FIRST competition, try to use a Static
Safety Factor of 4. • While on the high side it allows for
unknowns and dynamic loads• Haven’t had anything break yet!
Allowable Stresses
Here are some properties for typical robot materials:
Material Desig Temper Yield Tensile Shear Modulus(ksi) (ksi) (ksi) (msi)
Alum 6061 O 8 18 12 10Alum 6061 T6 40 45 30 10Brass C36000 18-45 49-68 30-38 14Copper C17000 135-165? 165-200? 19Mild Steel 1015-22 HR 48 65 30PVC Rigid 6-8 0.3-1