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 of Arms 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 of Lifts 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

• Shoulder • Elbow • Wrist

Articulating Arm

Arm: Forces, Angles, & Torque

Example: Lifting at different angles • Torque = Force x Distance • Same force, different angle, less torque 10 lbs 10 lbs < D D

Arm: Power

• Power = Torque / Time –

OR

– • Power = Torque x Rotational Velocity • Power (

FIRST

definition): How fast you can move something

Arm: Power

Example: Lifting with different power output • Same torque with twice the power results in twice the speed • Power = Torque / Time 10 lbs

125 Watts, 100 RPM

10 lbs

250 Watts, 200 RPM

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

• • • • • F object = Weight of Object + Weight of Slider • • • D object = Distance of Object CG T cable = F object M slider = F object • D object • F slider1 = - F slider2 = M slider / 2D slider F pulley = 2 T cable F hit = (Weight of Object + Weight of Slider) • G value [I use .5] M hit = F hit • H slider M base = M slider + M hit F hit F object D object F pulley M slider F slider1 D slider F slider2 T cable H slider M base

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

Forklift: Calculations

• • • • • • • • • F object = Weight of Object + Weight of Slider D object = Distance of Object CG M slider = F object • D object F slider1 = - F slider2 = M slider / 2D slider F hit = G value [I use .5] • (Weight of Object + Weight of Slider) M hitlower = F hit •H lower + [(Weight of Upper + Weight of Lower) • (H lower / 2)] F lower1 = - F lower2 = [M slider + M hitlower ] / 2D slider M hit = F hit • H slider value • H slider + [(Weight of Lift • G ) / 2] M base = M slider + M hit F hit F object D object H upper M upper H lower D upper /2 M slider F slider1 D slider F slider2 F D upper1 upper H slider M D lower /2 lower F upper2 F lower1 D lower F lower2 M base

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 T cable = 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 T cable3 = Weight of Object + Weight of Slider T cable2 = 2T cable3 + Weight of Stage2 T cable1 = 2T cable2 + Weight of Stage1 Much more tension on the lower stage cables – Needs lower gearing to deal with higher forces Stage2 Stage1 Base T cable3 Slider (Stage3) T cable2 T cable1

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 • Under Construction Check Back Later F hit M gripper F object D object D gripper F gripper1 L link F gripper2 D link F link2 M link F link1 H gripper D lower /2 M base

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: Summary Feature Reach over object Fall over, get up Go under barriers Arm Lift Yes No Yes, if strong enough No Yes, fold down Not centralized Maybe, lift height may be limited Centralized mass Center of gravity (CG) Small space operation How high?

Complexity Powerful lift Combination No, needs room to swing More articulations, more height (difficult) Yes More lift sections, more height (easier) Moderate Moderate High High Insert 1-stage lift at bottom of arm

WARNING

Engineering information beyond this point Proceed with caution if afraid of math

Stress Calculations

• It all boils down to 3 equations:

BENDING

  Mc I Where:  = Bending Stress M = Moment (calculated earlier) I = Moment of Inertia of Section c = distance from Central Axis

TENSILE

 tens  F tens A Where:  = Tensile Stress F tens = Tensile Force A = Area of Section

SHEAR

  F shear A Where:  = Shear Stress F shear = Shear Force A = Area of Section

Stress Calculations (cont.)

• A, c and I for Rectangular and Circular Sections b o d o b i h o d i h i c A  b o h o  b i h i c  h 2 I  b o h 3 o 12  b i h i 3 12 A   4   d 2 o  d i 2   I   c  64   d d 2 4 o o  d i 4  

Stress Calculations (cont.)

• A, c and I for T-Sections h 1 h 2 b 2 c y Y b 1 c x1 c x2 A  b 1 h 1  b 2 h 2 c x1  b 1 h 1 h 1 2  b 2 h 2    h 1 A  h 2 2    c x2  h 1  h 2  c x1 X I x  b 1 h 1 3 12  b 1 h 1    c x1  h 1 2   2   b 2 h 3 2 12  b 2 h 2    c x2  h 2 2   2  c y  b 1 2 I y  h 1 b 3 1 12  h 2 b 3 2 12

Stress Calculations (cont.)

b 2 • A, c and I for C-Sections (Assumes Equal Legs) h 1 h 2 c y Y b 1 c x1 c x2 A  b 1 h 1  2 b 2 h 2 c x1  b 1 h 1 h 1 2  2 b 2 h 2    A h 1  h 2 2    c x2  h 1  h 2  c x1 X I x  b 1 h 1 3 12  b 1 h 1    c x1  h 1 2   2   2 b 2 h 3 2 12  2 b 2 h 2    c x2  h 2 2   2  c y  b 1 2 I y  h 1 b 1 3 12  2 h 2 b 3 2 12

Stress Calculations (cont.)

c y1 h 1 b 2 • A, c and I for L-Angles h 2 Y b 1 c y2 c x1 c x2 X A  b 1 h 1  b 2 h 2 c x1  b 1 h 1 h 1 2  b 2 h 2    h 1 A  h 2 2    c x2  h 1  h 2  c x1 I x  b 1 h 1 3 12  b 1 h 1    c x1  h 1 2   2   b 2 h 3 2 12  b 2 h 2    c x2  h 2 2   2  I y c y1  h 1 b 1 b 1 2  h 2 b 2 b 2 2 A  h 1 b 3 1 12  h 1 b 1    b 1 2 c y2  b 1  c y1  c   2 y1   h 2 b 3 2 12  h 2 b 2    c y1  b 2 2   2 

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 Alum Alum Brass Copper Mild Steel PVC Desig 6061 6061 C36000 Temper (ksi) O T6 C17000 1015-22 HR Rigid Yield (ksi) 8 Tensile (ksi) 18 Shear (msi) 12 40 18-45 45 49-68 135-165? 165-200?

48 65 6-8 30 30-38 Modulus 10 10 14 19 30 0.3-1