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
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
•
•
•
•
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
Fpulley
Fhit
Fobject
Dobject
Mslider
Fslider1
Dslider
Fslider2
Tcable
Hslider
Mbase
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
Fhit
Mslider
Fslider1
Dslider
Fslider2
Fobject
Dobject
Hupper
•
•
•
•
•
•
•
•
•
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
Fupper1
Mupper
Hlower
Dupper
Dupper/2
Fupper2
Flower1
Hslider
Mlower
Dlower/2
Dlower
Flower2
Mbase
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
Tcable3
Slider
(Stage3)
Tcable2
Stage2
Stage1
Tcable1
Base
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
Mgripper
Fhit
Fobject
Dobject
• Under Construction
Check Back Later
Dgripper
Fgripper1
Llink
Fgripper2
Dlink
Flink2
Mlink
Flink1
Hgripper
Dlower/2
Mbase
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
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 lift sections,
more height (difficult) more height (easier)
Complexity
Moderate
High
Powerful lift
Moderate
High
Combination
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 
Ftens
A
Where:
 = Tensile Stress
Ftens = Tensile Force
A = Area of Section
SHEAR
 
Fshear
A
Where:
 = Shear Stress
Fshear = Shear Force
A = Area of Section
Stress Calculations (cont.)
• A, c and I for Rectangular and Circular Sections
bo
do
bi
ho
di
hi
c
A  boho  bihi
c h
2
boh3o bih3i
I

12
12
A

2
d
4 o
 d i2 

d
c o
2
  4 4
I  do  di 

64 
Stress Calculations (cont.)
• A, c and I for T-Sections
A  b1h1  b2h2
Y
cy
h1
b1
cx1
cx1 
X
h2
b2
cx2
b1h1
h1
2

 b2h2  h1 


h 2 
2
cx2  h1  h2  cx1



A
Ix 
b1h13
cy 
b1
12

 b1h1  c x1


2
h1b13 h2b32
Iy 

12
12

h 1 
2



2

b2 h 32
12

 b2 h 2  c x2



h 2 
2



2
Stress Calculations (cont.)
• A, c and I for C-Sections (Assumes Equal Legs)
A  b1h1  2b2 h 2
Y
cy
h1
b1
c x1 
X
h2
b2
b1h1
cx1
cx2
Ix 
2

 2b2 h 2  h 1



h 2 
2
cx2  h1  h2  cx1



A
b1h13
12
cy 
Iy 
h1

 b1h1  c x1


b1
2
h1b13
12
2
h 2 b32
12

h 1 
2



2
2
b2 h 32
12

 2b2 h 2  c x2



h 2 
2



2
Stress Calculations (cont.)
• A, c and I for L-Angles
A  b1h1  b2 h 2
Y
cy2
cy1
h1
b1
cx1
c x1 
X
h2
b2
cx2
Ix 
b1h1
h1
2

 b2 h 2  h 1



h 2 
2
cx2  h1  h2  cx1



A
b1h13
12

 b1h1  c x1


b1

h 1 
2



2

b2 h 32
12

 b2 h 2  c x2



h 2 
2
2



 h 2 b2 b2
c y2  b1  c y1
2
2
c y1 
A
2
2
3
b



b
h1b13
h
b
Iy 
 h1b1  1  c y1   2 2  h 2 b2  c y1  2 
12
12
 2


2 



h1b1
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
(ksi)
O
T6
Alum
Alum
Brass
Copper
Mild Steel
PVC
6061
6061
C36000
C17000
1015-22 HR
Rigid
Yield
Tensile Shear
(ksi)
(ksi)
(msi)
8
18
12
40
45
30
18-45
49-68
30-38
135-165? 165-200?
48
65
6-8
Modulus
10
10
14
19
30
0.3-1