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IntroductionThe C-Drive Mathematical Model
The C-Drive PrototypeThe PMC Mathematical Model
The PMC PrototypeConclusions
The Development of a Fast Pick-and-Place Robotwith an Innovative Cylindrical Drive
Jorge Angeles
Department of Mechanical Engineering and Centre for Intelligent Machines,McGill University, Montreal, Quebec, Canada
Jorge Angeles The Development of a Fast Pick-and-Place Robot 1
-
IntroductionThe C-Drive Mathematical Model
The C-Drive PrototypeThe PMC Mathematical Model
The PMC PrototypeConclusions
Outline
1 Introduction
2 The C-Drive Mathematical Model
3 The C-Drive Prototype
4 The PMC Mathematical Model
5 The PMC Prototype
6 Conclusions
Jorge Angeles The Development of a Fast Pick-and-Place Robot 2
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IntroductionThe C-Drive Mathematical Model
The C-Drive PrototypeThe PMC Mathematical Model
The PMC PrototypeConclusions
Schonflies Motion GeneratorsConventional Parallel SMGConventional Hybrid Parallel-Serial SMGIsostatic Schonflies Motion GeneratorDesign Principles of the C-drive
Schonflies Motion Generators
Schonflies Motion (SM)
I Three translations and onerotation about one axis of fixeddirection.
I Industrial pick-and-place robotsare capable of SM.
I The speed record is five testcycles per second.
25 mm 300 mm
0 deg 90 deg 180 deg Adept Quattro 650H
Jorge Angeles The Development of a Fast Pick-and-Place Robot 3
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IntroductionThe C-Drive Mathematical Model
The C-Drive PrototypeThe PMC Mathematical Model
The PMC PrototypeConclusions
Schonflies Motion GeneratorsConventional Parallel SMGConventional Hybrid Parallel-Serial SMGIsostatic Schonflies Motion GeneratorDesign Principles of the C-drive
Conventional Parallel SMGAdept Quattro 650H (Delta-Like Robot)
MP
I 4 limbsI rotation amplification required I too many extra joints to accommodate hyperstaticity
Jorge Angeles The Development of a Fast Pick-and-Place Robot 4
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IntroductionThe C-Drive Mathematical Model
The C-Drive PrototypeThe PMC Mathematical Model
The PMC PrototypeConclusions
Schonflies Motion GeneratorsConventional Parallel SMGConventional Hybrid Parallel-Serial SMGIsostatic Schonflies Motion GeneratorDesign Principles of the C-drive
Conventional Hybrid Parallel-Serial SMGABB IRB 360 FlexPicker
I parallel array of 3 limbsI telescopic Cardan shaft in series with end-effector I too many extra joints to accommodate hyperstaticity
Jorge Angeles The Development of a Fast Pick-and-Place Robot 5
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IntroductionThe C-Drive Mathematical Model
The C-Drive PrototypeThe PMC Mathematical Model
The PMC PrototypeConclusions
Schonflies Motion GeneratorsConventional Parallel SMGConventional Hybrid Parallel-Serial SMGIsostatic Schonflies Motion GeneratorDesign Principles of the C-drive
Isostatic Schonflies Motion GeneratorCRRHHRRC Parallel PMC
C
C
R
R
R
R
H
H
I 2 limbsI
::::::isostatic
I::no
::::::rotation
::::::::::amplification
::::::required
I proposed by C.C. Lee and P.C. Lee (2010)
Jorge Angeles The Development of a Fast Pick-and-Place Robot 6
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IntroductionThe C-Drive Mathematical Model
The C-Drive PrototypeThe PMC Mathematical Model
The PMC PrototypeConclusions
Schonflies Motion GeneratorsConventional Parallel SMGConventional Hybrid Parallel-Serial SMGIsostatic Schonflies Motion GeneratorDesign Principles of the C-drive
Design Principles of the C-drivemotor L
Lscrew L
(left-hand)
u
O
collar
nut R
screw R(right-hand)
support unitcoupling
rotor
motor R
R
nut L
1. The number of joints must be as low as possible;I C joint can be synthesized by means of a serial array of two simple LKP
2. A R joint is preferred over a P joint, and a P joint over a H joint;
3. Use as many identical joints as possible, as complexity grows with theirdiversity
Jorge Angeles The Development of a Fast Pick-and-Place Robot 7
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IntroductionThe C-Drive Mathematical Model
The C-Drive PrototypeThe PMC Mathematical Model
The PMC PrototypeConclusions
Schonflies Motion GeneratorsConventional Parallel SMGConventional Hybrid Parallel-Serial SMGIsostatic Schonflies Motion GeneratorDesign Principles of the C-drive
Design Principles of the C-drive (Contd)motor L
Lscrew L
(left-hand)
u
O
collar
nut R
screw R(right-hand)
support unitcoupling
rotor
motor R
R
nut L
4. Reduce the diversity of the actuators; and
5. For purposes of reducing and uniformly distributing the load, fix the motors tothe base
Jorge Angeles The Development of a Fast Pick-and-Place Robot 8
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IntroductionThe C-Drive Mathematical Model
The C-Drive PrototypeThe PMC Mathematical Model
The PMC PrototypeConclusions
KinematicsDynamicsState-Space Representations
Kinematics - Modelmotor L
Lscrew L
(left-hand)
u
O
collar
nut R
screw R(right-hand)
support unitcoupling
rotor
motor R
R
nut L
I u, : the translational and angular displacements of the C-drive collarL, R: the angular displacements of the motorspL, pR : the pitches of the left-hand screw and its right-hand counterpart
pL2
(L) = u,pR2
(R) = u (1)
I pL 6= pR in agreement with the condition from Lie groupsI we introduce symmetry as the sixth design principle
pL = p, pR =p (2)
Jorge Angeles The Development of a Fast Pick-and-Place Robot 9
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IntroductionThe C-Drive Mathematical Model
The C-Drive PrototypeThe PMC Mathematical Model
The PMC PrototypeConclusions
KinematicsDynamicsState-Space Representations
Kinematics Jacobian
I Dimensionally homogeneousChange of variable v (p/2) the actuator Jacobian J is dimensionallyhomogeneous:
w = J (3)
w [
uv
], J p
4
[1 11 1
],
[LR
](4)
I Differential mechanismpure rotation: the actuators turn by the same amount in the same directionpure translation: the actuators turn by the same amount, but in opposite directions
I IsotropicJT J is proportional to the 22 identity matrix 1
JT J =p2
821 (5)
I Kinematic relation between rates
w = J (6)
Jorge Angeles The Development of a Fast Pick-and-Place Robot 10
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IntroductionThe C-Drive Mathematical Model
The C-Drive PrototypeThe PMC Mathematical Model
The PMC PrototypeConclusions
KinematicsDynamicsState-Space Representations
Dynamics
I Mathematical model describing the dynamics of the C-drive
M +D + c = (7)I Generalized inertia matrix M (22):
M Mc +Mh (8)
Mc = JT IdriveJ, Idrive =[
m 00 (2/p)2Ic
], Mh = Ih1 (9)
Mc: generalized inertia matrix of the collarMh: generalized inertia matrix of the screws of the ballscrewsIc, Ih: collar and screws moment of inertia about C-drive axis
Jorge Angeles The Development of a Fast Pick-and-Place Robot 11
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IntroductionThe C-Drive Mathematical Model
The C-Drive PrototypeThe PMC Mathematical Model
The PMC PrototypeConclusions
KinematicsDynamicsState-Space Representations
Dynamics: Friction
I Mathematical model describing the dynamics of the C-drive
M +D + c = (10)I Viscous and Coulomb friction forces:
D
+ 12 12 1
2 +
12
, c = [ sgn(L)+sgn(L R) sgn(R)+sgn(R L)]
(11)
, : viscous friction coefficients , : Coulomb friction coefficients
Jorge Angeles The Development of a Fast Pick-and-Place Robot 12
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IntroductionThe C-Drive Mathematical Model
The C-Drive PrototypeThe PMC Mathematical Model
The PMC PrototypeConclusions
KinematicsDynamicsState-Space Representations
State-Space Representations
Standard Linear State-Space Form
x = Ax+Bu (12)
y = Cx (13)
with the output vector y defined as
y (14)
: vector of joint (motor) displacementsx: state vectoru: input vector, i.e., applied motor torques
In the following models, the state vectors are dimensionally homogeneous
Jorge Angeles The Development of a Fast Pick-and-Place Robot 13
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IntroductionThe C-Drive Mathematical Model
The C-Drive PrototypeThe PMC Mathematical Model
The PMC PrototypeConclusions
KinematicsDynamicsState-Space Representations
State-Space Representations: Collar Coordinates as StatesI Second-order generalized-coordinate model:
M +D + c = (15)
I Substituting with its expression in terms of collar coordinates w:
MJ1w+DJ1w = (16)
I Upon premultiplication by Jacobian matrix J:
JMJ1 E
w+JDJ1 G
w = J (17a)
E
[22 0
0 21
], G
[2 0
0 1
], i = 1, 2 (17b)
I 2i and i are the eigenvalues of M and D, respectively
Jorge Angeles The Development of a Fast Pick-and-Place Robot 14
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IntroductionThe C-Drive Mathematical Model
The C-Drive PrototypeThe PMC Mathematical Model
The PMC PrototypeConclusions
KinematicsDynamicsState-Space Representations
Dynamics in Monic FormI The dynamics is obtained in monic form, with Coulomb friction forces
neglected + = u (18)
via the substitutions
E1
G
E1,
Ew, u
E1
J (19)
where
[2 0
0 1
],
E1
J p4
[1/2 1/21/1 1/1
](20)
withi i/2i , i = 1, 2 (21)
Jorge Angeles The Development of a Fast Pick-and-Place Robot 15
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IntroductionThe C-Drive Mathematical Model
The C-Drive PrototypeThe PMC Mathematical Model
The PMC PrototypeConclusions
KinematicsDynamicsState-Space Representations
State-Space Representations: 2D and 4Dx = Ax+Bu, y = Cx (22)
2D Representation
x (23a)
y (23b)
A, B 1 (23c)
C J1
E1
(23d)
4D Representation
x[T TT
]T(24a)
y (24b)
A
[O
O
], B
[O
1
](24c)
C[J1
E1
O]
(24d)
I 1 and O are the 22 identity and zero matrices, respectivelyI The 2D system is simpler; the response of the system is readily derivedI The 4D system has an observable state vector, as is measured
Jorge Angeles The Development of a Fast Pick-and-Place Robot 16
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IntroductionThe C-Drive Mathematical Model
The C-Drive PrototypeThe PMC Mathematical Model
The PMC PrototypeConclusions
MechanismControl SystemControl ArchitecturePure TranslationPure RotationHelical Motion
Mechanismmotor L
motor R
screw Lcollar (left-hand)
screw R
support unit
(right-hand)
Jorge Angeles The Development of a Fast Pick-and-Place Robot 17
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IntroductionThe C-Drive Mathematical Model
The C-Drive PrototypeThe PMC Mathematical Model
The PMC PrototypeConclusions
MechanismControl SystemControl ArchitecturePure TranslationPure RotationHelical Motion
Control System
Jorge Angeles The Development of a Fast Pick-and-Place Robot 18
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IntroductionThe C-Drive Mathematical Model
The C-Drive PrototypeThe PMC Mathematical Model
The PMC PrototypeConclusions
MechanismControl SystemControl ArchitecturePure TranslationPure RotationHelical Motion
Control Architecture
Jorge Angeles The Development of a Fast Pick-and-Place Robot 19
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IntroductionThe C-Drive Mathematical Model
The C-Drive PrototypeThe PMC Mathematical Model
The PMC PrototypeConclusions
MechanismControl SystemControl ArchitecturePure TranslationPure RotationHelical Motion
Pure Translation
0 500 1000 1500 200050
0
50
100
150
200
Time (ms)
Pos
ition
(m
m)
Achieved uAchieved vDesired uDesired v
0 500 1000 1500 20000.1
0.08
0.06
0.04
0.02
0
0.02
0.04
0.06
0.08
0.1
Time (ms)
Err
or (
mm
)
Error in uError in v
Jorge Angeles The Development of a Fast Pick-and-Place Robot 20
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IntroductionThe C-Drive Mathematical Model
The C-Drive PrototypeThe PMC Mathematical Model
The PMC PrototypeConclusions
MechanismControl SystemControl ArchitecturePure TranslationPure RotationHelical Motion
Pure Rotation
0 500 1000 1500 200050
0
50
100
150
200
Time (ms)
Pos
ition
(m
m)
Achieved uAchieved vDesired uDesired v
0 500 1000 1500 20000.2
0.15
0.1
0.05
0
0.05
0.1
0.15
0.2
Time (ms)
Err
or (
mm
)
Error in uError in v
Jorge Angeles The Development of a Fast Pick-and-Place Robot 21
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IntroductionThe C-Drive Mathematical Model
The C-Drive PrototypeThe PMC Mathematical Model
The PMC PrototypeConclusions
MechanismControl SystemControl ArchitecturePure TranslationPure RotationHelical Motion
Helical Motion
0 500 1000 1500 2000100
50
0
50
100
150
200
250
Time (ms)
Pos
ition
(m
m)
Achieved uAchieved vDesired uDesired v
0 500 1000 1500 20000.5
0.4
0.3
0.2
0.1
0
0.1
0.2
0.3
0.4
0.5
Time (ms)
Err
or (
mm
)
Error in uError in v
Jorge Angeles The Development of a Fast Pick-and-Place Robot 22
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IntroductionThe C-Drive Mathematical Model
The C-Drive PrototypeThe PMC Mathematical Model
The PMC PrototypeConclusions
PMC Kinematic ModelPMC Inverse Displacement AnalysisPMC Forward Displacement AnalysisPMC KinematicsSingularity Analysis
Kinematic Model of the PMC
O xy
z
CO1
1
2
1
2
O2
A1r1
d2
b0
b0
d1
r2l2
l1u1
u2
a1
a
i
jk
2
v1
v2A2
B1
B2
P2
P1C
R
RH
HR
R
C
I The PepperMill-Carrier (PMC):CRRHHRRC parallel mechanism
I di and i (for i = 1, 2): the translational androtational displacement variables of the ithC joint
I The pose x of the PepperMill is given byc = [x, y, z]T , the position vector of point C,and angle :
x[
c
](25)
Jorge Angeles The Development of a Fast Pick-and-Place Robot 23
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IntroductionThe C-Drive Mathematical Model
The C-Drive PrototypeThe PMC Mathematical Model
The PMC PrototypeConclusions
PMC Kinematic ModelPMC Inverse Displacement AnalysisPMC Forward Displacement AnalysisPMC KinematicsSingularity Analysis
Kinematic Model of the PMC
O xy
z
CO1
1
2
1
2
O2
A1r1
d2
b0
b0
d1
r2l2
l1u1
u2
a1
a
i
jk
2
v1
v2A2
B1
B2
P2
P1C
R
RH
HR
R
C
I Points Oi: the intersection of the ith-driveaxis with the common normal to the two,for i = 1, 2
I The fixed origin O of the base frame is set atthe midpoint of segment O1O2
I i, j and k: unit vectors parallel to the x, yand z axes
Jorge Angeles The Development of a Fast Pick-and-Place Robot 24
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IntroductionThe C-Drive Mathematical Model
The C-Drive PrototypeThe PMC Mathematical Model
The PMC PrototypeConclusions
PMC Kinematic ModelPMC Inverse Displacement AnalysisPMC Forward Displacement AnalysisPMC KinematicsSingularity Analysis
Kinematic Model of the PMC
O xy
z
CO1
1
2
1
2
O2
A1r1
d2
b0
b0
d1
r2l2
l1u1
u2
a1
a
i
jk
2
v1
v2A2
B1
B2
P2
P1C
R
RH
HR
R
C
For i = 1, 2,
I i: the angle of rotation of the proximalpassive R joint
I ui and vi: unit vectors parallel to the axes ofthe proximal and the distal links
I ri and li: the lengths of the proximal and thedistal links
I The end of the distal link of the ith limb iscoupled with the passive R pair of thePepperMill at point Pi
Jorge Angeles The Development of a Fast Pick-and-Place Robot 25
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IntroductionThe C-Drive Mathematical Model
The C-Drive PrototypeThe PMC Mathematical Model
The PMC PrototypeConclusions
PMC Kinematic ModelPMC Inverse Displacement AnalysisPMC Forward Displacement AnalysisPMC KinematicsSingularity Analysis
PMC Inverse Displacement Analysis
O xy
z
CO1
1
2
1
2
O2
A1r1
d2
b0
b0
d1
r2l2
l1u1
u2
a1
iu
iu ixcos= +
i
i
i iysini
x
iy
a
i
jk
2
v1
v2A2
B1
B2
P2
P1
I Displacement analysis performed vialoop-closure equations
I The translational displacements of eachC-drive are obtained directly from thehorizontal displacements of thePepperMill:
d1 = x, d2 = y (26)
Jorge Angeles The Development of a Fast Pick-and-Place Robot 26
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IntroductionThe C-Drive Mathematical Model
The C-Drive PrototypeThe PMC Mathematical Model
The PMC PrototypeConclusions
PMC Kinematic ModelPMC Inverse Displacement AnalysisPMC Forward Displacement AnalysisPMC KinematicsSingularity Analysis
PMC Inverse Displacement Analysis
O xy
z
CO1
1
2
1
2
O2
A1r1
d2
b0
b0
d1
r2l2
l1u1
u2
a1
iu
iu ixcos= +
i
i
i iysini
x
iy
a
i
jk
2
v1
v2A2
B1
B2
P2
P1p1
p2
I The angular displacements i,i = 1, 2, of each C-drive arecomputed from
(qTi xi) cos i +(qTi yi)sini (27)
=qTi qi + r2i l2i
2ri
where
qi pidiai (28)
Jorge Angeles The Development of a Fast Pick-and-Place Robot 27
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IntroductionThe C-Drive Mathematical Model
The C-Drive PrototypeThe PMC Mathematical Model
The PMC PrototypeConclusions
PMC Kinematic ModelPMC Inverse Displacement AnalysisPMC Forward Displacement AnalysisPMC KinematicsSingularity Analysis
Forward Displacement AnalysisCRRHHRRC Parallel PMC
O xy
z
CO1
1
2
1
2
O2
A1r1
d2
b0
b0
d1
r2l2
l1u1
u2
a1
iu
iu ixcos= +
i
i
i iysini
x
iy
a
i
jk
2
v1
v2A2
B1
B2
P2
P1
I The horizontal displacements of thePepperMill are simply
x = d1, y = d2 (29)
I The vertical and angular displacementsof the PepperMill are computed from[
1 p11 p2
] [z
]= (30)[
r1 sin1 + l1 sin(1 +1)b0r2 cos2 + l2 cos(2 +2)+b0
]
I The leftmost matrix is invertible whenp1 6= p2
Jorge Angeles The Development of a Fast Pick-and-Place Robot 28
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IntroductionThe C-Drive Mathematical Model
The C-Drive PrototypeThe PMC Mathematical Model
The PMC PrototypeConclusions
PMC Kinematic ModelPMC Inverse Displacement AnalysisPMC Forward Displacement AnalysisPMC KinematicsSingularity Analysis
PMC Kinematics: Jacobian Analysis
I The PepperMill pose x and proximallink displacements are
x [x y z ]T (31)
[d1 d2 1 2]T (32)
I Vectors li are defined as shown in thefigure, for i = 1, 2
Jorge Angeles The Development of a Fast Pick-and-Place Robot 29
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IntroductionThe C-Drive Mathematical Model
The C-Drive PrototypeThe PMC Mathematical Model
The PMC PrototypeConclusions
PMC Kinematic ModelPMC Inverse Displacement AnalysisPMC Forward Displacement AnalysisPMC KinematicsSingularity Analysis
PMC Kinematics: Jacobian AnalysisI Kinematics relation
Ax = B (33)where Jacobian matrices A and B are
A =
1 0 0 00 1 0 00 vy1 v
z1 p1v
z1
vx2 0 vz2 p2v
z2
(34)
B =
1 0 0 00 1 0 00 0 vT1 l1 00 0 0 vT2 l2
(35)For i = 1, 2 and j = x, y, z, vji is thejth component of vi
Jorge Angeles The Development of a Fast Pick-and-Place Robot 30
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IntroductionThe C-Drive Mathematical Model
The C-Drive PrototypeThe PMC Mathematical Model
The PMC PrototypeConclusions
PMC Kinematic ModelPMC Inverse Displacement AnalysisPMC Forward Displacement AnalysisPMC KinematicsSingularity Analysis
The Singularity of the First Kind (inverse-kinematics singularity)
B =
1 0 0 00 1 0 00 0 vT1 l1 00 0 0 vT2 l2
I The singularity of the first kind occurs when the Jacobianmatrix B is singular, i.e., when
det(B) (vT1 l1)(vT2 l2) = 0 (36)
I Geometrically, this singularity occurs when v1 l1 or v2 l2,i.e., when the unit vector ui of the proximal link and the unitvector vi of the distal link are parallel in at least one limb
Jorge Angeles The Development of a Fast Pick-and-Place Robot 31
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IntroductionThe C-Drive Mathematical Model
The C-Drive PrototypeThe PMC Mathematical Model
The PMC PrototypeConclusions
PMC Kinematic ModelPMC Inverse Displacement AnalysisPMC Forward Displacement AnalysisPMC KinematicsSingularity Analysis
The Singularity of the Second Kind (direct-kinematics singularity)
ui
vk
i
vi =
vxivyivzi
I The singularity of the second kind occurs when the Jacobianmatrix A is singular:
det(A) = det
1 0 0 00 1 0 00 vy1 v
z1 p1v
z1
vx2 0 vz2 p2v
z2
= det([
1 00 1
])det([
vz1 p1vz1
vz2 p2vz2
])= vz1v
z2(p2p1) = 0 (37)
I The pitches of the two H joints of the PepperMill are distinct:
p1 6= p2 (38)
I Geometrically, these conditions occur when the unit vector ofthe distal link of at least one limb is normal to the z-axis
Jorge Angeles The Development of a Fast Pick-and-Place Robot 32
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IntroductionThe C-Drive Mathematical Model
The C-Drive PrototypeThe PMC Mathematical Model
The PMC PrototypeConclusions
PMC Kinematic ModelPMC Inverse Displacement AnalysisPMC Forward Displacement AnalysisPMC KinematicsSingularity Analysis
The Singularity of the Third Kind (complex-kinematics singularity)
I The singularity of the third kind occurs when the the twoJacobian matrices A and B become singular
det(A) = vz1vz2(p2p1) = 0
det(B) = (vT1 l1)(vT2 l2) = 0
I This singularity depends on the robot architecture. Given thesymmetries with which the PepperMill was designed, this robotadmits the singularity of the third kind, as illustrated in thefigure
Jorge Angeles The Development of a Fast Pick-and-Place Robot 33
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IntroductionThe C-Drive Mathematical Model
The C-Drive PrototypeThe PMC Mathematical Model
The PMC PrototypeConclusions
Prototype: PepperMill MechanismPrototype (Contd)Magnetic GripperMechanical Interference Detection
PepperMill Motion
Jorge Angeles The Development of a Fast Pick-and-Place Robot 34
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IntroductionThe C-Drive Mathematical Model
The C-Drive PrototypeThe PMC Mathematical Model
The PMC PrototypeConclusions
Prototype: PepperMill MechanismPrototype (Contd)Magnetic GripperMechanical Interference Detection
PMC Prototype
Jorge Angeles The Development of a Fast Pick-and-Place Robot 35
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IntroductionThe C-Drive Mathematical Model
The C-Drive PrototypeThe PMC Mathematical Model
The PMC PrototypeConclusions
Prototype: PepperMill MechanismPrototype (Contd)Magnetic GripperMechanical Interference Detection
Magnetic Gripper Functionality
Wireless Magnetic Gripper Assembly
I 10W 24VDC electromagnet actuatedwirelessly
I Lithium-Ion battery recharged incircuit
I 1 mW Xbee radio communicates via2.4 GHz 802.15.4 protocol
I Digital I/O line passing betweencontrol module and embeddedmodule
Jorge Angeles The Development of a Fast Pick-and-Place Robot 36
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IntroductionThe C-Drive Mathematical Model
The C-Drive PrototypeThe PMC Mathematical Model
The PMC PrototypeConclusions
Prototype: PepperMill MechanismPrototype (Contd)Magnetic GripperMechanical Interference Detection
Magnetic Gripper Features
Wireless Magnetic Gripper AssemblyI External 1/4 wave monopole antenna
I Uses gripper enclosure asground plane
I Robust 802.15.4 protocol supportspoint-to-point, point-to-multipointand peer-to-peer network topologies
I Scalable: multiple modulesmay be used in close proximity
I Can be configured to actuatedifferent types of gripper (e.g.clamp)
Jorge Angeles The Development of a Fast Pick-and-Place Robot 37
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IntroductionThe C-Drive Mathematical Model
The C-Drive PrototypeThe PMC Mathematical Model
The PMC PrototypeConclusions
Prototype: PepperMill MechanismPrototype (Contd)Magnetic GripperMechanical Interference Detection
Mechanical Interference Detection
Figure: Single C-drive
I Robot dimensions chosen such that moving links cannot collideI Proximal linksthe C-drivescan collide with the base in four waysI C-drives present unusual challenges in detecting extreme positions
Jorge Angeles The Development of a Fast Pick-and-Place Robot 38
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IntroductionThe C-Drive Mathematical Model
The C-Drive PrototypeThe PMC Mathematical Model
The PMC PrototypeConclusions
Prototype: PepperMill MechanismPrototype (Contd)Magnetic GripperMechanical Interference Detection
Mechanical Interference Detection Switches: Contactless
Translation Limit Switch
I Magnetic proximity switch detectsedge of C-drive cap
I Cap edge angled 30 to increasesensor sensitivity
Rotation Limit Switch
I Laser photo-electric switchI Laser beam interrupted by proximal
link when close to extreme position
Jorge Angeles The Development of a Fast Pick-and-Place Robot 39
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IntroductionThe C-Drive Mathematical Model
The C-Drive PrototypeThe PMC Mathematical Model
The PMC PrototypeConclusions
ConclusionsAcknowledgements
Conclusions
I The development of an innovative two-DOF cylindrical drive wasdescribed
I The kinematics and dynamics of the C-drive were derived, as well asconvenient state-space representations thereof
I The C-drive mechanism and control system were described; test resultsyielded low error
I PMC prototype assembly shown, including safety featuresI The singularity analysis of the PMC was reportedI The embedded electromagnetic gripper was described
Jorge Angeles The Development of a Fast Pick-and-Place Robot 40
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IntroductionThe C-Drive Mathematical Model
The C-Drive PrototypeThe PMC Mathematical Model
The PMC PrototypeConclusions
ConclusionsAcknowledgements
Ackowledgements
The work described here is the result of team work. Team members: DamienTrezieres, Masters Visitor from Lyon, France; Takashi Harada, Kinki U.,Japan; Thomas Friedlaender, M.Eng. student at McGill U.
The support from various sources is to be acknowledged: NSERC (CanadasNatural Sciences and Engineering Research Council), James McGillProfessorship to J. Angeles; Japans MEXT-supported Program for theStrategic Research Foundation to Private Universities; and THK Co., Ltd fortheir support.
Jorge Angeles The Development of a Fast Pick-and-Place Robot 41
IntroductionSchnflies Motion GeneratorsConventional Parallel SMGConventional Hybrid Parallel-Serial SMGIsostatic Schnflies Motion GeneratorDesign Principles of the C-drive
The C-Drive Mathematical ModelKinematicsDynamicsState-Space Representations
The C-Drive PrototypeMechanismControl SystemControl ArchitecturePure TranslationPure RotationHelical Motion
The PMC Mathematical ModelPMC Kinematic ModelPMC Inverse Displacement AnalysisPMC Forward Displacement AnalysisPMC KinematicsSingularity Analysis
The PMC PrototypePrototype: PepperMill MechanismPrototype (Cont'd)Magnetic GripperMechanical Interference Detection
ConclusionsConclusionsAcknowledgements
fd@Trans: mbtn@0: fd@Rot: mbtn@1: fd@Helix: mbtn@2: fd@pepper: mbtn@3: