Page 307 - Handbook of Biomechatronics

Upper and Lower Extremity Exoskeletons 299

description of mechanics in vector functions, while the Lagrange-Euler for-
mulation is based on scalar functions, as shown in Eqs. (2), (3), respectively
(Barrientos et al., 1997).

:
X X
F ¼ mv T ¼ I w + w I wÞ (2)
ð
where F is the force, m is the mass, and _v the linear acceleration of the link. In
the other equation, T is the torque, I is the inertial matrix, and w the angular
velocities of the link.

d ∂ζ ∂ζ
¼ τζ ¼ k u (3)
dt∂q_ ∂q i
i
where:
q i , generalized coordinates (in this case articulates)
τ, vector of forces and applied pairs in the
ζ, Lagrangian function
k, kinetic energy
u, potential energy
In addition, equations of motion are equations that describe the behavior of a
system as a function of time (Barrientos et al., 1997). Robot dynamics can be
represented by linear state-space variable equations. On the other hand, the
interaction between different links is described by nonlinear differential
equations. It is possible to use the state-space formulation for control design,
in either the nonlinear or the linear forms (Barrientos et al., 1997).

3.2 Human Factors and Biomechanics

The exoskeleton should be anthropomorphic and ergonomic, not only in
shape but also in function. The exoskeleton should be analogous to the
human limbs in the case of joint positions and distribution of DOF. In most
of cases, designing the kinematics of an exoskeleton generally consists on try-
ing to replicate human limb kinematics. This approximation has a major dis-
advantage due to the fact that it is impossible to replicate human kinematics
with a mechanic structure and conventional robotic joints (Scott and
Winter, 1993). Also, morphology varies among people and several models
of human kinematics in the biomechanics literature differ in some aspects,
due to the complex geometry, redundancy, and DOF of the human limbs.
Furthermore, unpredictability of joint axes locations and body segment
sizes, for instance, can disturb interaction between an exoskeleton and
the human operator, depending on the exoskeleton’s kinematic design.