Computer-Aided Design 39 (2007) 540–547 www.elsevier.com/locate/cad Accurate geometrical constraints for the computer aided modelling of the human upper limb Davide Gattamelata ∗ , Eugenio Pezzuti, Pier Paolo Valentini Department of Mechanical Engineering, University of Rome Tor Vergata, Via del Politecnico 1, 00133 Rome, Italy Received 17 July 2006; accepted 25 January 2007 Abstract For medical and surgical applications, human modelling and simulation have to be very accurate and realistic. This means that both geometries and movements have to be reproduced precisely, investigating both physiological properties and anatomical shapes. This paper deals with the description of geometrical constraints to mimic the movement of the upper limb segments subjected to physical joints. Anatomical studies show that relative motion cannot be approximated with basic constraints such as revolute or spherical joints, but requires the definition of specific geometrical and kinematic pairs. For this purpose, for each joint the authors deduce a set of equations which can be embedded into a virtual environment in order to simulate the relative motion among body segments in a detailed way. c  2007 Elsevier Ltd. All rights reserved. Keywords: Upper limb; Physical joint; Geometrical constraint; Human modelling 1. Introduction In medicine, surgery and biomechanics, there is an increasing demand for computer aided instruments in order to assist doctors, technicians and engineers and to optimize clinical treatments and prosthetic devices. Due to the growing number of surgical operations and the improvement of quality standards, surgeons and prosthesis designers are seeking tools that can support them in optimizing their activities, improving rehabilitative techniques and reducing the risk for patients [1, 2]. For these delicate purposes, computer aided tools have to model and mimic human behaviour, being accurate in terms of both geometries and movements. Improvements in computer graphics and animation tech- niques have surely supported these methodologies, promoting virtual environments and digital mock-ups with an outstanding level of realism and interactivity [3,4]. Many computer aided biomechanical applications that have been developed during last years are based on human models that are static or are able to mimic only gross motions [5,6]. Even accurate three-dimensional models including joints and ∗ Corresponding author. Tel.: +39 0672597134. E-mail addresses: gattamelata@ing.uniroma2.it (D. Gattamelata), valentini@ing.uniroma2.it (P.P. Valentini). Fig. 1. Schematic representation of an upper limb model with ideal (approximated) joints (7 degrees-of-freedom), adapted from [8]. muscles appear to reproduce only the relative motion between body segments, with some approximations. In 2003, da Silva in his doctoral dissertation proposed a biomechanical model suitable for the accurate computer sim- ulation of human motion, with emphasis on the musculoskele- tal apparatus of the lower limbs [7]. In his proposed model, all the physical joints have been approximated using standard kine- matic pairs. In 2005 Valentini et al. presented a paper concerning the modelling of the human upper limb with 7 d.o.f. and 24 muscles [8] (see Fig. 1). A revised model with experimental validation is about to be published [9]. Although both these models were very accurate, the physiological joints between body segments have been simulated with approximated ideal constraints. This means that 0010-4485/$ - see front matter c  2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.cad.2007.01.009