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In contact with human body

Specific

safeties Specific functionalities

Easily movable

Optimal size

Manually controllable

Specific

kinematics

Unstructured environment, No repetitive tasks,

Sterilization of the components

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f KHz

fKHz

Actuated Joints

Passive Joints

Links

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1900 200065 86

Machine-tool

Pioneers

(Gough, Stewart)

Delta(Clavel, EPFL) Variax

(Gidding & Lewis)

N.C.

55

Robots

PKM

ROBODOC CASPAR

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NeuromateACROBOT

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)cos()sin()det( 5343 DDJ

22

5 ,2atan zzz sna

55

6 ,2atanC

s

C

n zz

5641 CDRpr z

1000

0

zzzz

yyyy

xxxx

pans

pans

pans

U

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Tool MotorsV VJ

Motors Tool V VJ

ToolP MotorsP

J

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Zeus

Da Vinci

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ROBODOCCASPAR

Zeus

Da Vinci

Actuated Joints

Passive Joints

Links

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Revolute Prismatic Universal Spherical

Passive R P U S

Passive + measurement R P U S

Actuated R P U S

Actuated + measurement R P U S

table 1. Symbols for Joint-and-Loop graphs.

(not easy to implement)

R RP

R RP

R RP

P RR

P RR

P RR

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R RR

R RR

R RR

P RR

P RR

P RR

Surgiscope

R RP

R RP

R RP

U SP

U SP

U SP

R RR

R RP

R RP

R RP

R RP

R RP

R RP

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Flexion

Traction / Compression

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Delta

Tricept

S S

S S

R

S S

S SR

S S

S S

R

C R

Surgiscope

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22,, ibibi qCA

A

Cq

A

B

C

d

q

A

BC

d

q

nOv

22,, ibibi dCB

ir

vri niiiniiiiiii OCCBOCBCBABq

il

vli niiiniiiiiii OCCBOCBCBABq

is

svs ii nini OCOq

nO

xJqJ xq

kq

q

q

2

1

q

vx

nO

t

nkk

t

k

t

n

t

t

n

t

x

OC

OC

OC

J

bb

bb

bb 11

222

1

A

C

q

A

B

C

d

q

A

BC

d

q

kq IdentJ

kk.bl

.bl

.bl

J

11

q

000

000

000

000

22

kk

22

11

br

br

br

kk

q

AB

AB

AB

J

000

000

000

000

22

11

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(x,y,z,a,b,c)IKM: closed form

FKM :

Few nice cases with closed form

Often: numerical resolution (polynomial of 4th, 8th , 16th , ... order)

(Drive #1,

Drive #2,Drive #n)

Two options for numerical solving:

Solving the polynomial ( all solutions, computation cost)

Looking for ONE solution ( fast, instability risk)

thresholdaccuracyeifstop

eJxxqqe

JJJJJx

xmgiqx

k

mesur

qxqx

...

.

),(

)(

000100

1000

000

PID MachineIKM

PID Machine

FKM

1J

q

estimatedx

x

x

measuredq

measuredq

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ROBODOCCASPAR

Zeus

Da Vinci

Neuromate

ACROBOT

Surgisc

ope

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-20

0

20

40

60

80

100

0 0,4 0,8 1,2 1,6 2

Temps en s

Efforts

en

N

20 000 tr/mn

40 000 tr/mn

60 000 tr/mn

0

5

10

15

20

25

30

35

40

45

0 2 4 6

Temps en S

Eff

orts

en

N

40 000 Tours/min

60 000 Tours/min

75 000 Tours/min

0

1

2

3

4

5

6

7

8

9

5 10 15 20 25 30

Force (N)

Displacement(mm)

+ x

+y

- z

-20

-15

-10

-5

0

5

10

15

20

0,01 0,11 0,21 0,31 0,41 0,51 0,61 0,71 0,81 0,91

time (s)

acceleration(m/s2)

x

y

z

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