Modeling a Hand Prosthesis with Word Bond Graph Objects
Anand Vaz Shinichi Hirai
Department of Mechanical Engineering Department of Robotics
SLIET, Longowal, District Sangrur Ritsumeikan University, Noji-higashi 1-1-1
Punjab 148106, India Kusatsu, Shiga 525-8577, Japan
Email: anandvaz@ieee.org Email: hirai@se.ritsumei.ac.jp
Abstract - The bond graph approach is used to model
a hand prosthesis system, which is quite large to
represent conveniently using either single or
multibond graphs. This is usually the case with
modeling biomechanical systems. To facilitate
compact modeling of this system, the concept of Word
Bond Graphs is applied to represent component
subsystems as Objects. Such Word Bond Graph
Objects (WBGO) are compact representations of
subsystems, within the overall system, and have a well
defined structure. They preserve an understanding of
the physical system while facilitating quick and easy
programming for numerical simulations due to their
object oriented structure. WBGO identified and
analyzed here for the hand prosthesis system include
rigid finger link dynamics, translational and
rotational coupling between two consecutive finger
links, and string-tube mechanics for passive prosthetic
joint actuation by natural active joints. The bond
graph details for each WBGO have been presented
together with a derivation of their system equations.
The WBGO are then used to integrate a complete
assembly of the dynamics of the hand prosthesis
system.
I. INTRODUCTION
Biomechanical systems, and especially prosthetic
systems, are usually large with interconnections and are
applications well suited to bond graph modeling. The
method of Bond graphs is an attractive and powerful
technique as it offers a unified framework for modeling
the mechanism, and, the actuation and control systems
due to its capability of handling multi-energy domains
[Karnopp et al., 2000], [Mukherjee and Karmakar, 2000].
In this work the bond graph technique is applied to the
important area of modeling the essential mechanism of a
human hand with a view to the design and development
of hand prosthesis. The prostheses considered in this
work have been proposed earlier by the authors [Vaz and
Hirai, 2003], and are based on actuation of prosthetic
fingers by the remaining natural fingers of a partially
impaired hand.
However, the dynamics for a hand-prosthesis system,
using 1-bonds or scalar bonds, would yield a bond graph
too large to represent and analyze. Vector bond graphs
(VBG) or multibond graphs (MBG) do help to compact
the representation to some extent [Bonderson, 1975],
[Bonderson, 1977], [Breedveld, 1982], [Breedveld 1985].
It would be preferable to have more compact
representation which preserves a clear picture of the
overall system and can be explored analytically.
One way to achieve this is to consider the overall system
model as an integrated assembly of component
subsystems which can interact with each other.
Subsystems whose structure appears more than once in a
system can be identified as a Word Bond Graph Object
(WBGO). Word Bond Graphs (WBG) have been used
extensively in literature to represent models of subsystem
dynamics [Karnopp et al., 2000], [Breedveld 1985],
[Tiernego and Bos, 1985], [Bos and Tiernego, 1985].
WBG have an inherent structure which can be put to
effective use. The detailed structure of a WBG can be
modeled using a combination of MBG and scalar bond
graphs. The structure may or may not be assigned a fixed
causality. The WBG can be treated as an Object with well
defined input and output variables, state variables and
parameters. Inputs and outputs to WBG structure using
conventional bond graph variables of efforts and flows
can be made explicit and used as handles for interfacing
with other Objects or bond graph elements. The resulting
structure of the WBG has properties of Objects as used in
Object oriented programming. Code for simulation based
on WBGO can be developed systematically and rapidly,
or existing bond graph software can be used to exploit
this structure. Hence it will be appropriate to distinguish
them as WBGO. Interaction between these WBGO is
graphically represented using scalar bonds or multibonds
as in usual bond graph methodology. Once a WBGO with
its interface is defined, it can be used as a component in
the assembly of a complete system. Thus WBGO
facilitate modeling of large and complex systems, in a
graphical and intuitive manner.
Applying this concept to the modeling of a hand
prosthesis system requires an identification of the
possible subsystems which can be represented using
WBGO. Modeling of the hand prosthesis can be initiated
from its fingers. These may be considered to be made up
of almost rigid links (bones called phalanges). The joints
between links are generally revolute, though not in a strict
kinematic sense. The joints are roughly spherical in the
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