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 .....