## Materials and Methods  
### The Enhanced Chaffin's LSM  
The angle of the thorax relative to the pelvis (TP) used by [PERSON] and [PERSON] to predict the SEM moment arm and line of action is defined as the sagittal plane component of the Euler rotation of a 3D thorax-embedded anatomical frame with respect to a 3D pelvis-embedded anatomical frame [16]. Thorax and pelvis anatomical reference systems were defined according to [PERSON] [16,17]. Figure 2 depicts an angle functionally related to TP that is supposed to be linearly related to it. This angle (\(\varphi\)) is formed in the sagittal plane by the segment joining the L5/S1 joint to the shoulder joint center S and the longitudinal axis of a pelvis-embedded frame (\(y_{\mathrm{PV}}\)). \(y_{\mathrm{PV}}\) is perpendicular to the axis joining the posterior superior iliac spine (PSIS) anterior with the anterior superior iliac spine (ASIS). The planar Chaffin's LSM depicted in Figure 3 and used to predict \(\varphi\) consists of some selected points on the subject's body, whose position can be measured from an image through photogrammetry, and other points whose positions can be estimated by anatomical assumptions:  
* The position of S can be estimated as a function of the inter-acromial distance from the position of the acrom (AC) (note that in the Chaffin's LSM, the position of S is usually made to coincide  
Figure 2: The angle \(\varphi\) is supposed to be linearly related to the thorax-to-pelvis angle used by [PERSON] to predict the back extensor muscle moment arm and line of action. The position of the origin of the pelvis-embedded anatomical reference frame, whose axes are depicted as dotted lines, is placed for graphical convenience to highlight the angle that the segment joining L5/S1 to S forms with the longitudinal axis of the pelvis-embedded anatomical reference frame. K = knee joint center; H = hip joint center; L5/S1 = intervertebral disc joint center; S = shoulder joint center; ASIS: anterior superior iliac spine  
with the position of the acromion instead) [18]. This requires the user to measure the inter-ASIS distance beforehand to analyze the task. * The position of the hip joint center (H) can be estimated as a function of the inter-ASIS distance and pelvic width with respect to a pelvis-embedded frame [19]. This requires the user to measure the inter-ASIS distance beforehand to analyze the task, while the pelvic width can be measured by photogrammetry as the ASIS-to-PSIS distance. Note that, among all the anthropometry-based equations for predicting the hip joint center position, the equation proposed by [PERSON] has been proved as the most accurate [20]. However, pelvic width is originally defined as the line joining the midpoint between the right and the left ASIS and the midpoint between the right and left PSIS. Since such measures are not available in two dimensions (we can only consider either the right- or the left-sided ASIS-PSIS distance), the user may decide to use the Bell and Brand approach, which relies on the sole inter-ASIS distance [21]. H can be then expressed with respect to the global reference frame XY through a rigid transformation by using the position and orientation of the pelvis-embedded reference frame defined above. * The planar positions of the knee (K) and ankle (A) joint centers can be assumed to correspond to the positions of the lateral femur epicondyle and of the peroneal malleolus, respectively. Note that AC, ASIS, PSIS, K and A are all superficial and, hence, palpable anatomical landmarks, and their planar positions can be easily measured through photogrammetry (with the help of well-visible markers, for instance). * Finally, the position of L5/S1 (labeled as O in Figure 3 for space convenience) in the absolute reference frame XY can be estimated as follows:  
Figure 3: [PERSON]’s linked segment model (LSM) (upper arm and forearm are excluded) used to estimate the position of the L5/S1 (O) joint center.