Graphics Reference
In-Depth Information
LB
C
C
C
A
A
LC
B
LA
B
FIGURE B.29
Simple manipulator using three revolute joints.
Table B.3
Parameters for Three-revolute Joint Armature
Joint/Parameter
Link Displacement
Joint Angle
Link Length
Link Twist
A
0
y
A
0
0
B
0
y
B
LA
0
C
0
y
C
LB
0
B.4.3
Including a ball-and-socket joint
Some human joints are conveniently modeled using a ball-and-socket joint. Consider an armature with
a hinge joint, followed by a ball-and-socket joint followed by another hinge joint, as shown in
The DH notation can represent the ball-and-socket joint by three single degree of freedom (DOF)
joints with zero-length links between them (see
Figure B.31
).
Notice that in a default configuration with joint angles set to zero, the DH model of the ball-and-
socket joint is in a gimbal lock position (incrementally changing two of the parameters results in rota-
tion about the same axis). The first and third DOFs of that joint are aligned. The
z
-axes of these joints
are colinear because the links between them are zero length and the two link twist parameters relating
them are 90 degrees. This results in a total of 180 degrees and thus aligns the axes. As a consequence,
the representation of the ball-and-socket joint is usually initialized with the middle of the three joint
B.4.4
Constructing the frame description
Because each frame's displacement and joint angle are defined relative to the previous frame, a Frame
0
is defined so that the Frame
1
displacement and angle can be defined relative to it. Frame
0
is typically
defined so that it coincides with Frame
1
with zero displacement and zero joint angle. Similarly, because
the link of the last frame does not connect to anything, the
x
-axis of the last frame is chosen so that it
coincides with the
x
-axis of the previous frame when the joint angle is zero; the origin of the
n
th frame is
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