KUKA LWR-IV

!  7R manipulator: spherical shoulder (3R), elbow joint (1R), spherical wrist (3R)

!  the robot is shown in its zero configuration (q=0) !  positive directions of joint rotations are indicated

1

J1

J3

J5

J7

side view (from observer in V)

V

J2

J4

J6

L

M lengths in [mm]

joint ranges in [deg]

frontal view

pW center of wrist

KUKA LWR-IV in motion

videos at DIAG Robotics Lab

VREP video

side view from observer in V

2

KUKA LWR-IV

!  determine !  frames and table of D-H parameters

!  be consistent with positive rotations indicated by KUKA

!  only the two kinematic lengths L and M should be needed

!  homogeneous transformation matrices !  direct kinematics of the center of wrist pW in

symbolic form !  numerically, in the configuration q = (0, !/2, !/2, -!/2, 0, !/2, 0) [rad] the position 0pd in frame 0 of a tool point Pd

whose coordinates in frame 7 are given by 7pd = (0, 0.05, 0.1) [m]

J1

J3

J5

J7

J2

J4

J6

L

M

frontal view

pW center of wrist

3

Assignment of D-H frames

side view (from observer in V) J1

J3

J5

J7

frontal view

y6

V

z1

z2

z4

z6

z7

y7

z3 y4

y5 z5

y3

y1

y0 y2

z0

W=O5=O6=O7 (wrist center)

S=O0=O1=O2 (shoulder center)

O3=O4 (elbow)

x1 x2

x3

x0

x4

x5 x6 x7

zero configuration!

J4

J6

J2

steps!

4

Table of D-H parameters

i "i di ai #i

1 !/2 0 0 q1=0

2 -!/2 0 0 q2=0

3 -!/2 L 0 q3=0

4 !/2 0 0 q4=0

5 !/2 M 0 q5=0

6 -!/2 0 0 q6=0

7 0 0 0 q7=0

with

d3 = L = 0.40, d5 = M = 0.39 [m]

in the shown configuration

5

J1

J3

J5

J7

z0

z3

z5 y6

z6

z1

z2

z4

z7

y7

y4

y5

y3

y1

y0 y2

J4

J6

J2

D-H homogeneous matrices output from Matlab (symbolic) program

6

Direct kinematics of the wrist center

output from Matlab (symbolic) program

pW,hom = A1(q1)A2(q2)A3(q3)A4(q4)A5(q5)A6(q6)A7(q7) [0 0 0 1]T

= A1(q1)A2(q2)A3(q3)A4(q4) [0 0 M 1]T

these can be replaced (by inspection) with [0 0 M 1]T

the last three (spherical) joints do not move W

faster (symbolic) recursive position transformations (matrix ・ vector products, in homogenous coordinates)

7

Tool position evaluation

output from Matlab (numerical) program

0pd,hom = A1(q1)A2(q2)A3(q3)A4(q4)A5(q5)A6(q6)A7(q7) 7pd,hom

!  in the given configuration q = (0, !/2, !/2, -!/2, 0, !/2, 0) [rad] for the tool point Pd of coordinates (in frame 7) 7pd = (0, 0.05, 0.1) [m]

again, (numerical) recursive position transformations (matrix ・ vector products) etc.

numerical evaluation of symbolic quantities

7pd in homogeneous coordinates

y7

z7 7pd

8