Biomedical Engineering Reference
In-Depth Information
CHAPTER
8
Predictive Dynamics: Lifting
With contributions by Dr. Yujiang Xiang
First they ignore you, then they laugh at you, then they fight you,
then you win.
Mahatma Gandhi (18691948)
8.1
Human skeletal model
Lifting is a common task that is performed by humans every day. It is described
as holding an object with two hands and moving the object from a lower position
to a higher position. There have been several studies involving lifting, as it is a
common task that often leads to injury (
Arisumi et al., 2007; Dysart and
Woldstad, 1996; Huang et al., 2005; Xiang et al., 2009b; Zhang et al., 2000
).
For this predictive dynamics task, we shall use the same kinematic skeleton and
corresponding DH representation as that shown in Section 7.4.1, Figure 7.2 (shown
again in
Figure 8.1
), with 55 DOFs, and the link lengths and mass properties shown
in Table 7.1. The majority of the chapter is adapted from
Xiang et al. (2009b, 2012)
.
8.2
Equations of motion and sensitivities
We shall use the recursive formulation introduced in Chapter 4 to formulate the
predictive dynamics task of lifting. Forward kinematics propagates the motion
from the base point to the end-effectors. In contrast, the backward dynamics
transfer the forces from the end-effectors to the base point.
8.2.1
Forward recursive kinematics
Position, velocity, and acceleration characterized by the 4
4 matrices A
j
, B
j
, and
C
j
, respectively, are recursively defined for the
j
th joint. Given the link transforma-
tion matrix, T
j
, and the kinematics state variables for each joint, angular displace-
ment, velocity, and acceleration,
q
j
,
3
q
j
, and
_
q
j
, we define for
j
€
1to
n
as follows:
5
A
j
5
T
1
T
2
T
3
?
T
j
5
A
j
2
1
T
j
(8.1)
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