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

Articulating Arm Shoulder Elbow Wrist

10 lbs < D D 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: Power Example: 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 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 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 object F slider1 F slider2 F pulley M slider M base D object D slider T cable F hit H slider

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

D upper /2 H upper 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 + [(Weight of Lift G value H slider ) / 2] M base = M slider + M hit M base F object F slider1 F slider2 M slider D object D slider F hit H slider F upper2 D upper F upper1 F lower2 D lower F lower1 H lower D lower /2 M lower M upper

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 T cable1 T cable2 T cable3 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 L link M base F object F gripper1 F gripper2 M gripper D object D gripper F hit H gripper F link2 D link F link1 D lower /2 M link 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: Summary FeatureArmLift Reach over objectYesNo Fall over, get upYes, if strong enoughNo Go under barriersYes, fold downMaybe, lift height may be limited Center of gravity (CG) Not centralizedCentralized mass Small space operation No, needs room to swing Yes How high?More articulations, more height (difficult) More lift sections, more height (easier) ComplexityModerateHigh Powerful liftModerateHigh CombinationInsert 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: Where:  = Bending Stress M = Moment (calculated earlier) I = Moment of Inertia of Section c = distance from Central Axis Where:  = Tensile Stress F tens = Tensile Force A = Area of Section Where: = Shear Stress F shear = Shear Force A = Area of Section BENDINGTENSILESHEAR

Stress Calculations (cont.) A, c and I for Rectangular and Circular Sections bobo c hoho bibi hihi dodo didi

Stress Calculations (cont.) A, c and I for T-Sections X Y b1b1 h2h2 b2b2 cycy h1h1 c x1 c x2

Stress Calculations (cont.) A, c and I for C-Sections (Assumes Equal Legs) X Y b1b1 h2h2 b2b2 cycy h1h1 c x1 c x2

Stress Calculations (cont.) A, c and I for L-Angles X Y b1b1 h2h2 b2b2 c y1 h1h1 c x1 c x2 c y2

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: MaterialDesigTemperYieldTensileShearModulus (ksi)(ksi)(ksi)(msi) Alum6061O Alum6061T BrassC CopperC ? ?19 Mild Steel HR PVCRigid