Robotic Arms vs. Lifts

What is an Arm?

A device for grabbing & moving objects using members that rotate

about their ends

What is a Lift?

A device for grabbing and moving objects in a predominately vertical

direction

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

Articulating Arm

• Shoulder• Elbow• Wrist

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.

Types of Lifts

• Elevator

• Forklift

• Four Bar (can also be considered an Arm)

• Scissors

Elevator

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

Forklift: Examples

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 Cascade

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

Four Bar: Examples

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

Scissors: Example

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?

Scissors: Calculations

• I don’t want to go there

THIS IS NOT RECOMMENDED

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

WARNING

Engineering informationbeyond this point

Proceed with cautionif afraid of math

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