actuators - laboratory for perceptual roboticsgrupen/603/slides/actuators.pdf · artiﬁcial...

Actuators

...physical devices that transform electrical, chemical, or thermalenergy into mechanical energy...

• muscle

• electric

– stepper motors

– permanent magnet DCmotors

• hydraulic

• pneumatic

• artificial muscles

– shape memory alloys

– polymers

– protein-based actuators

– bucky tubes

1 Copyright c©2015 Roderic Grupen

Muscle: Contractile Proteins

LMM

HMM

DTNB A−1, A−2segments

HMM S−1

HMM S−2

A1500

[adapted from Wilkie 1974, McMahon 1984]

Myosin molecules consist of multiple molecular subchains that par-ticipate in specialized roles.


Muscle: Sliding Filament Model

a bundle ofmuscle fibers quadriceps

myofibril

Z Z

sarcomere

Myosinthick filament

a singlemuscle fiber

M

F−actinthin filament

tropomyosin

actin

troponin

[adapted from McMahon 1984]

• Neural stimuli causes actin to bind free Ca++ ions and thus prepare attachment sitesfor the S-1 subchain of myosin

• because of attachment, the head of the myosin changes shape and angle of attach-ment, producing a shear force between filaments

• the thin filament slides 50-100 angstroms relative to the thick filament causing theactin and myosin proteins to detach.


The Huxley Model (1957)

myosin (thick) filamenth

actin (thin) filament

x

x=0M(a) (b)

f(x)g(x)

x x=h


let 0 ≤ n(x) ≤ 1 be the probability that a crossbridge exists at displacement x, then

dn(x)

dt= [1− n(x)] f(x)− n(x)g(x),

where f(x) is the probability of a new attachment and g(x) describes the probabilitythat an existing crossbridge will detach.

The shape of functions f(x) and g(x) is chosen so that musclestend to shorten in response to neural excitation.


Twitch and Tetanic Responses

time (msec)100 200 300

40 Hz

60 Hz

20 Hz

5 Hz

force

fusedtetanus

unfusedtetanus

muscle twitch


large mammalian muscles subject to periodic activation at 5, 20,40, and 60 Hz.


Muscle Force Generation

0.5 1.0 1.5

0l / l

1.0

0.0

passive

developed

total

maxv / v

1.0

0.2 0.4 0.6 0.8 1.0

2.0

(a) (b)

maxT / TmaxT / T

contractextend

00

1.0

maxP / P

The force capacity of muscle as a function of length and velocity.Tension is normalized by the maximum developed tension, lengthby muscle free length (l0), and velocity by the maximum unloadedcontractile velocity (vmax).


Muscle: Linear Model

B

F(x,t)

K muscle

K tendon

active and passive muscle dynamics


Actuators: Stepper Motors

• precise (low torque), open-loop position control

• resonance - typically between 50 and 150 steps/sec

• cogging

N

SN

S

NS

(A)

N

S

off off N S

off

off(B)

S

N

N

N

S

S

SN

S

NS

(C)

S

N

off offN

NS

off

off

S

N

N

N

S

S

(D)


Permanent Magnet DC Motors

• run continuously in both directions

• closed-loop servo control w/position feedback

• reliable, good power/weight, high torques possible

Lorentz Force

N

S

Bqv+ _

F = qv ×B


Permanent Magnet DC Motor

Iron Core:

• high inertia, cogging

• very reliable

• cheap

B

N

S

Moving Coil:

• rare earth magnets - coil is rotor

• low rotor inertia - minimal cogging

• large torque

• can be thin (0.02′′), large diameter(12′′)

• printed-circuit motors

• very expensive


DC Motors - Electrodynamics

force: Newton N = kg ·m/sec2

torque: the product of a force and a moment arm

N ·m =kg ·m2

sec2

power: energy per unit time (Watts)

P = V I(electrical)

= τω(mechanical)

Watt =volt · coulomb

sec=

Nm

sec


DC Motors - Electrodynamics

B

SN

F

Fqv

qv

_++Vs

I

The Lorentz Force

B

F F

qv

qv

+Vgen

mechanical input

SN

_+

Iload

Backward ElectromotiveForce (Back EMF)

• commutation - the rotor runs out of torque when the currentloop is perpendicular to B, reversing the current can continueto provide torque in the same direction.

• Km: overall motor torque constant - total number of currentloops, magnetic field strength, supply voltage, rotor resistance

– torque production: τ = KmI

– back emf: Vb = Kmω


DC Motors - Electrodynamics (cont.)

τ

R

L

Vm

lignoring rotor

inductance L

forwardcurrent

∑

τ = Jθ̈ = KmI = Km

[

V

R−

Kmθ̇

R

]

backcurrent

θ̈ +K2

JRθ̇ +

KV

JR= 0


DC Motor Performance

manufacturers publish physical parameters:rotor inertia J , resistance R, inductance L, as well as overall massand geometry of the motor package

and integrated motor performance data:

ω0: no-load velocityI0: no-load current

τs: stall torqueIs: stall current

%no−load speed

20 40 60 80 100

% stall torque

0

10

20

30

40

50

60

70

80

90

100

% stallcurrent

%maximum power

0

10

20

30

40

50

60

70

80

90

100

0

10

20

30

40

50

60

70

80

90

100

0

10

20

30

40

50

60

70

80

90

100

%efficiency

1

mK

no−load current: I

no−load speed: ω0

0

stall current: I s

stall torque: τs


DC Motor Performance

%no−load speed

20 40 60 80 100

% stall torque

0

10

20

30

40

50

60

70

80

90

100

% stallcurrent

%maximum power

0

10

20

30

40

50

60

70

80

90

100

0

10

20

30

40

50

60

70

80

90

100

0

10

20

30

40

50

60

70

80

90

100

%efficiency

1

mK

no−load current: I

no−load speed: ω0

0

stall current: I s

stall torque: τs

Power: the product of torque and speed (τω) for loads [0, τs]

Pout = τload ωτ = τload

[

ω0 −∆ω

∆ττload

]

= −

(

∆ω

∆τ

)

τ 2load+(ω0)τload

Efficiency: ητ =mechanical power outelectrical power in

= PoutVsI

ητ =−(

∆ω∆τ

)

τ 2load + (ω0)τloadV (I0 + τload/Km)


Roger’s Motor Parameters

PARAMETER wheel shoulder elbow eye

ω0 [rad/sec]no-load speed 175.0 30.1 50.3 122.2

I0 [A]no-load current 0.38 0.26 0.17 0.12

τs [N ·m]stall torque 475.0 205.3 120.7 2.7

Km

[

N ·mA

] [

V ·secrad

]

torque constant 0.105 0.623 0.364 0.163


DC Motors/Gearhead Combinations

J

τ

J

τM

M

L

L

+Vin

η =0.01

if the transmission is perfectly efficient:

τoutωout = τinωin

τout(ηωin) = τinωin

τout = (1/η)τin

if η = 0.01, the output shaft carries one hundred times the torqueat one hundredth the velocity of the input shaft


DC Motors/GearheadCombinations — Compound Loads

dynamic equation of motion - equate the torque derivedfrom Lorentz forces with the torques required to accelerate theload and to overcome viscous friction.

τM =[

JM θ̈M

]

+ η[

JLθ̈L

]

but:

θL = ηθM ,

θ̇L = ηθ̇M , and

θ̈L = ηθ̈M

so:τM =

[

JM + η2JL]

θ̈M

and:

Jeff = JM + η2JL

if η = 0.01, this means the relative influence of themotor dynamics is amplified 10,000 fold


Driving DC Motors

H-Bridge

V

s2

s3

s4

s1

V

s2

s3

s4

s1

• continuous forward/backward speedcontrol

• (s1, s2, s3, s4) open - freewheel

• (s1, s2, s3, s4) closed - (regenerative)braking

• RMS voltages - pulse width modu-lation (PWM)


Pulse Width Modulation

−V

+V

RMS V

ton

toff

t

+100

−100

−V

+V

ton

toff

+100

−100

−V

+VRMS V

ton

toff

t

+100

−100

RMS V


Actuators: Hydraulic

servo servo

• energy in the high pressure fluid reservoir (1000-3000 psi)

• open-loop control - fork lifts, back hoes

• good bandwidth (5 KHz - fluid reverses direction 5 msec)

PROS

1. good power/weight

2. safe in explosive environments

CONS

1. expensive servos

2. messy

3. high maintenance


Actuators: Pneumatic

• compressible fluid (air)

• jet-pipe servo control

NcontrolV

glasscylinder

graphite pistonS

reservoir 80 psi

PROS

1. light and cheap

2. passively backdrivable

CONS

1. stiction

2. delicate


Artificial Muscles

McKibben Air Muscles - non-linear pneumatic actuators, at-tract interest because they are among the strongest and fastestof the “artificial” muscles.

Shape Memory Alloys - Nitinol “muscle wire” (nickel-titaniumalloy) relatively slow, commercially available, a few grams force(similar to all options below this on in the list), low bandwidth( 1Hz)

Polymers - electrostatic, chemical, and thermal, polymer gelscan exhibit abrupt, reversible 1000 fold volume changes, forcesup to 100 N/cm2, contraction rates on the order of a second.

Synthetic Muscle - extracted actin and myosin protein, possi-bly avoiding tissue rejection

Bucky Tubes - Fullerenes (“Bucky Balls”) and nanotubes (“BuckyTubes”), crystalline configurations of graphitic carbon.


actuators - laboratory for perceptual roboticsgrupen/603/slides/actuators.pdf · artiﬁcial...

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