Journal of Biomechanics 34 (2001) 177}185 Assessment of the accuracy of a human arm model with seven degrees of freedom R.A. Prokopenko*, A.A. Frolov, E.V. Biryukova, A. Roby-Brami  Institute of Higher Nervous Activity and Neurophysiology of Russian Academy of Sciences, Butlerov str., 5A, 117865 Moscow, Russia INSERM U 483, Universite & Pierre & Marie Curie, 9 Quai Saint Bernard, 75005 Paris, France Accepted 20 August 2000 Abstract We are proposing a human arm model that consists of three rigid segments with seven degrees of freedom. The shoulder joint was modeled as a ball-and-socket joint and the elbow and wrist joints were modelled as skew-oblique joints. Optimal parameters for this model were calculated on the base of in vivo recordings with a spatial tracking system. The criterion of optimality was de"ned as the minimum of the mean-square deviation between the experimentally obtained sensor positions and orientations and their positions and orientations calculated by solving the direct kinematics problem. The minimal value of the direct kinematics error was found to be 0.5}0.6 cm for sensor positions and 5}73 for sensor orientations. We are proposing that these values serve as the assessment for the accuracy of the arm model.  2001 Elsevier Science Ltd. All rights reserved. Keywords: Arm model; Parameters of the joints; Joint angles; Direct kinematics error 1. Introduction In biomechanical literature, the representation of the human arm as three rigid segments, connected by fric- tionless joints with a total of seven degrees of freedom (DoF), is a generally accepted model (Desmurget and Prablanc, 1997; Lemay and Crago, 1996; Raikova, 1992; Seireg and Arvikar, 1989). The three rigid segments are the upper arm, the forearm and the hand. The three DoFs in the shoulder joint can be attributed to abduc- tion}adduction, #exion}extension and external}internal rotation of the humerus relative to the scapula. The two DoFs in the elbow joint correspond to pronation} supination (P}Se) and #exion}extension (F}Ee), while the two DoFs in the wrist joint correspond to #exion} extension (F}Ew) and abduction}adduction (Ab}Adw). In the seven DoF arm models the shoulder (glenohumeral) joint is usually considered as a ball-and- socket joint and the axes in elbow and wrist joints are assumed to be orthogonal and intersecting. However, studies specially aimed to reveal the geometry of the * Corresponding author. Tel.: #7-095-338-85-00; fax: #7-095-334- 42-31. E-mail address: roman@enz.siobc.ras.ru (R.A. Prokopenko). joints, have shown that for di!erent subjects the angle between F}Ee and P}Se axes is in the range 84}943 and the distances between them is in the range 0.25}0.41 cm (Veeger et al., 1997a, b). The range for the angle between F}Ew and Ab}Adw has shown to be even larger: from 603 to 1333, the distance between them being in the range 0.03}0.96 cm (Andrews and Youm, 1979; Sommer III and Miller, 1980). As for the shoulder, its center of rotation moves by about 1 cm relative to the adjacent segments (Harryman et al., 1990, 1992; Poppen and Walker, 1976; Veeger et al., 1997a, b; Wang, 1996). We have recently proposed a human arm model that corresponds better with the experimental data and main- tains the model of rigid bodies connected by the joints of invariant geometry (Biryukova et al., 2000). A two-de- grees-of-freedom skew-oblique joint with the axes "xed in relation to the adjacent segments modeled the elbow and wrist joints. Distance and angle between the axes were assumed to be constant. The shoulder joint was still modeled by a joint with the center of rotation "xed in relation both to the scapula and the upper arm. The proposed model allowed a description of the human arm kinematics in terms of rotations about natural anatom- ical axes. However, there are much evidence showing that this model is not exact either. First, the forearm segment is not rigid because of the rotations of the radius relative 0021-9290/01/$ - see front matter  2001 Elsevier Science Ltd. All rights reserved. PII: S 0 0 2 1 - 9 2 9 0 ( 0 0 ) 0 0 1 7 9 - 2