Short communication The error of L5/S1 joint moment calculation in a body-centered non-inertial reference frame when the fictitious force is ignored Xu Xu a,n , Gert S. Faber b , Idsart Kingma b , Chien-Chi Chang a , Simon M. Hsiang c a Liberty Mutual Research Institute for Safety, 71 Frankland Road, Hopkinton, MA 01748, USA b Institute for Fundamental and Clinical Human Movement Sciences, Faculty of Human Movement Sciences, VU University, Van der Boechorststraat 9, 1081 BT Amsterdam, The Netherlands c Department of Industrial Engineering, Texas Tech University, Box 43061, Lubbock, TX 79409, USA article info Article history: Accepted 20 May 2013 Keywords: Lifting Linked segment model Centrifugal force Coriolis force abstract In ergonomics studies, linked segment models are commonly used for estimating dynamic L5/S1 joint moments during lifting tasks. The kinematics data input to these models are with respect to an arbitrary stationary reference frame. However, a body-centered reference frame, which is defined using the position and the orientation of human body segments, is sometimes used to conveniently identify the location of the load relative to the body. When a body-centered reference frame is moving with the body, it is a non-inertial reference frame and fictitious force exists. Directly applying a linked segment model to the kinematics data with respect to a body-centered non-inertial reference frame will ignore the effect of this fictitious force and introduce errors during L5/S1 moment estimation. In the current study, various lifting tasks were performed in the laboratory environment. The L5/S1 joint moments during the lifting tasks were calculated by a linked segment model with respect to a stationary reference frame and to a body-centered non-inertial reference frame. The results indicate that applying a linked segment model with respect to a body-centered non-inertial reference frame will result in overestimating the peak L5/S1 joint moments of the coronal plane, sagittal plane, and transverse plane during lifting tasks by 78%, 2%, and 59% on average, respectively. The instant when the peak moment occurred was delayed by 0.13, 0.03, and 0.09 s on average, correspondingly for the three planes. The root-mean-square errors of the L5/S1 joint moment for the three planes are 21 Nm, 19 Nm, and 9 Nm, correspondingly. & 2013 Elsevier Ltd. All rights reserved. 1. Introduction Linked segment models have been used for estimating dynamic L5/S1 joint moments of various occupations (Chaffin, 1999; Kingma et al., 1996; Larivière and Gagnon, 1998; Shin and Mirka, 2004; Skotte, 2001; Skotte et al., 2002). The net moment at L5/S1 is expressed as (Hof, 1992; Plamondon et al., 1996): M L5=S1 ¼ -∑ p a ¼ 1 ½ðr a -r L5=S1 Þ F a -∑ q b ¼ 1 M b -∑ k i ¼ 1 ½ðr i -r L5=S1 Þ m i g þ ∑ k i ¼ 1 ½ðr i -r L5=S1 Þ m i a i þ ∑ k i ¼ 1 dðI i ω i Þ=dt ð1Þ It should be noted that as Hof (1992) mentioned, the kine- matics data used in Eq. (1) need to be defined with respect to a stationary reference frame. When a motion tracking system is used for kinematics data collection, the stationary reference frame can be arbitrarily defined on the ground. A ground-fixed stationary reference frame, however, may not always be determined and sometimes a human body-centered reference frame is more convenient to use. For example, when a biomechanical model is reconstructed based on segment angles abstracted from the video frames, it could be hard to determine the positions, based on the video, of body segments relative to a ground-fixed stationary reference frame. Instead, one can conve- niently define the origin of a body-centered reference frame at the mid-point between the ankles, one axis pointing upward, and one axis being perpendicular to the sagittal plane of neutral posture. Such a reference frame will be a stationary reference frame if foot positions are fixed and Eq. (1) still holds. The L5/S1 moment can then be estimated by the kinematics of each body segment based on the identified joint angular trajectories and anthropometry data (Chang et al., 2003; Hsiang et al., 1998). However, when foot movement or the rotation of the sagittal plane exists, such a body- centered reference frame will be a non-inertial reference frame and the effect of fictitious force needs to be considered when calculating L5/S1 moments (Jha, 2005). Contents lists available at SciVerse ScienceDirect journal homepage: www.elsevier.com/locate/jbiomech www.JBiomech.com Journal of Biomechanics 0021-9290/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jbiomech.2013.05.012 n Corresponding author. Tel.: +1 508 497 0218. E-mail address: Xu.Xu@libertymutual.com (X. Xu). Journal of Biomechanics 46 (2013) 1943–1947