Post on 07-May-2018
rotation αααα
αααα motor 1
Epycloidal gear
-0.2 -0.1 0 0.1 0.2 0.3-0.1
0
0.1
0.2
0.3
0.4
0.5
X [m]
Y
[m]
+0.5e0
+0.6e0
+0.7e0
+0.8e0
-0.2 -0.1 0 0.1 0.2 0.3-0.1
0
0.1
0.2
0.3
0.4
0.5
X [m]
Y
[m]
+0.8e0
+1.0e0
+1.2e0
+1.4e0
λ
Drill tip movement λλλλ
Linear track
slideBall skrew
motor 3
Kinematics, dynamics and control of a hybrid
parallel-serial redundant manipulator
Diego Tosi, Giovanni Legnani, Pier Luigi Magnani
Dip. Ing. Meccanica, Università di Brescia
Via Baranze 38, 25123 Brescia, Italy
diego.tosi@ing.unibs.it giovanni.legnani@ing.unibs.it
Applications
SURGICAL ROBOT
• high precision and dexterity
• mini-invasive surgery
• easier surgical procedure planning
• intra-surgical co-ordination with other
medical equipment
Pedicle screws
Metal plate
=
gz
gy
gx
zzx
zyx
zyx
V
V
V
aaa
aaa
aaa
q
q
q
323
222
111
3
2
1
&
&
&
iii
iu
a λλ ⋅
=1
gJVQ =&
Slide:
Pi position
ui unit vector
linear velocity
Vi vector velocity
linear acceleration
Ai vector acceleration
platform:
Vgi vector velocity
Agi vector accelerationiq&&
iq&
leg:
Li leg vector
li length
λλλλi unit vector
wi unit vector of velocity
angular velocity (module)
angular velocity (vector)
angular acceleration (module)
angular acceleration (vector)
iΩiω
iΩ&iω&
=
z
y
xT
f
f
f
J
f
f
f
3
2
1
gripper forcesactuator forcesgripper velocityactuator velocity
iiii quPP += *
lL ii λ=
iii quV &=
iii quA &&=
gigigi AVP ,,
iii wω=Ω iiii
igi
quPP
lPP
+=
=−*
( ) lwquLquV iiiiiiiiigi ωλ×+=×Ω+= &&
0=⋅ iiw λii
giii
u
Vq
⋅
⋅=λ
λ&
( ) iiiiiiiiiiiiiiigi llwquLLquA λωλω 2−×+=×Ω×Ω+×Ω+= &&&&&&
( )ii
iigiii
u
lAq
⋅
+⋅=
λ
λωλ 2
&&
l
VV igii
−=ω
slide
leg
moving platformposition analysis
velocity analysis
acceleration analysis
• 3 d.o.f.
• 3 motors
• isostatics
• pure translation
• 3 d.o.f.
• 4 motors• over-constrained
• structure preloaded toreduce backlash andsingularity
• improved workspace
• 4 d.o.f.
• 4 motors• isostatics
• 4 dof “complex”rototranslation
• improve rotation ofserial wrist
• 4 d.o.f. (type B)
• 4 motors
• isostatics
•translation plusrotation aroundaxis u
u
(in cooperation with Politecnico di Milano)
36 parameters
24 significant combinations
of parameters
13° 25°
ideal geometry
with errors
13°
25°
σσσσi
104
102
100
10-2
10-4calibration simulations predict the following accuracy
5mm / 50 mrad before calibration
0.5 mm / 3 mrad after calibration
effect of significant structural errors (left) and non-significant errors (right)
Parallel structure
3 pairs of parallel rods
• spherical joints at the ends
• slides on guides inclined of 30°
• 3+1 axes
The platform
translates
Serial wrist
• α rotation
• β lifting
• λ drill tip movement
(redundant)
roof
Mobile
platform
slides
Spherical
joints
α
β
λ
INTERVERTEBRAL PEDICLE
SCREW INSERTION
working space: 400x400x300 mm
rotations: +\- 40°
velocity: 1.5 m/s
acceleration: 20 m/s2
Kinetostatic analysis
Hybrid kinematic structure
rods
Parallel part re-configurability
Geometry optimisation
Parallel structure
supporting frame
high mobility
spherical joints
support for the
serial wrist
precision plate for
the laser calibration
of the slides
Brushless
linear motor
Serial wrist
flexible cable support
linear tracks
permanentmagnets
optical encoder
support for
spherical joints
Calibration is performed moving the
axis and measuring the x-y position of
the incoming beam
precision laser support (8 positions)
encoder
lift ββββ
ββββ
motor 2
Calibration
-0.2 -0.1 0 0.1 0.2 0.3-0.1
0
0.1
0.2
0.3
0.4
0.5
X [m]
Y
[m]
+1.6e0
+1.7e0
+1.8e0+1.9e0
-0.2 -0.1 0 0.1 0.2 0.3-0.1
0
0.1
0.2
0.3
0.4
0.5
X [m]
Y
[m]
+3.0e0
+2.5e0
+2.0e0
Det(J) σmin(J) σmax(J) cond(J)
laser source
laser beam
x-y sensor
D. Tosi, G. Legnani, Calibration of a Parallel-Serial Hybrid Redundant Manipulator, Proc.
of ISR 2003, Chicago, 2-5 June 2003
-H. Giberti, P. Righettini, D. Tosi, G. Legnani, R. Adamini, Progetto di “CHEOPE”: un
manipolatore ridondante ibrido palallelo-seriale, Proc. of AIMETA 2003, Ferrara 9-12 Sept.
2003
-D.Tosi, G. Legnani, P. L. Magnani, Calibration of “CHEOPE” a parallel-serial redundant
manipulator, Proc. of AIMETA 2003, Ferrara 9-12 Sept. 2003
References