**1. Introduction**

The sit to stand (STS) analysis and particularly the 5-repetition sit-to-stand test (FRSTST) introduced by Bohannon [1] are widely used measurements of functional strength and disability level of young and elderly subjects. For example in rehabilitation and orthopedics, these tests are mainly used for the functional evaluation of :


The STS analysis also currently helps to develop :


Usually, the functional strength and the disability level during STS are evaluated by calculating the total forces of hip and knee extensors [1] and the center of mass (COM) accelerations [19]. Nevertheless, it is known that determining with accuracy the kinematics (including the COM) and dynamics (including the joint forces and torques) in the human body is still a great challenge in biomechanical modeling [20]. Consequently, the aim of the present study consists in presenting a rigorous methodology for the non-invasive assessment of joint efforts and the associated kinematic variables during STS movement. This method is based on a three-dimensional dynamical inverse model of the human body. Like other classical *dynamical inverse* analyzes [21–25] in biomechanics of motion, the model proposed here [18] uses measurements of external interactions (forces **F***ext* and torques **M***ext*) between the body and its environment, and also measurements of the system configuration *xexp*. The corresponding joint coordinates *q* are numerically determined by a kinematic identification process, and the corresponding velocities *q*˙ and accelerations *q*¨ are presently estimated from the *q*, using a numerical derivative. Finally, the model provides the joint interactions with the use of a symbolically generated recursive Newton-Euler formalism [26, 27].

know the three-dimensional configuration of each body. Further, these bodies are linked by spherical joints corresponding to 12 anatomical landmarks (referring to [31]): the C7 vertebra, both shoulders (acromioclavicular joints), both elbow joint centers, the sacrum, both greater trochanters, both knee joint centers, both lateral heads of the malleolus. Consequently, the system is fully described by a total of *13 (bodies)* × *6 variables - 12* × *3 spherical joint constraints = 42 generalized coordinates*, representing the 42 degrees of freedom of the model. As shown in Fig. 1, the inverse dynamical model provides the column vector *Q* of joint forces and torques,

Methodology for the Assessment of Joint Eff orts During Sit to Stand Movement 137

**Figure 2.** Human body model, featuring the 28 optokinetic sensors that define the 13 articulated rigid

A few characteristics and assumptions must be formulated about these three sets of inputs:

• The external forces **F***ext* and torques **M***ext* between the body and its environment are measured by a dynamometric device. The external pure torques are not considered. • The body inertia parameters, i.e. the masses *mi*, moments of inertia *Ii* and center of

tables of de Leva [31] (1996) readjusted from the Zatsiorsky-Seluyanov's mass inertia parameters [32] (1990). The inertia parameter identification is not part of this research: indeed, previous investigations [33] showed that non-invasive in-vivo identifications of the body parameters are presently inappropriate to the human body dynamics, because the resulting body parameters have significant errors due to experimental errors in the input data, such as the body configuration, or the external force and torque measurements. • The system configuration, i.e. the experimental absolute coordinates *xexp* of the reference points, are measured by the 28 optokinetic sensors. The corresponding joint coordinates *q* are numerically determined by a kinematic identification process and the corresponding velocities *q*˙ and accelerations *q*¨ are presently estimated from the *q* by a numerical derivative

*th* body member (i = 1,. . . ,13) are taken from the inertia

bodies, each defined by three points, articulated via 12 spherical joints.

using three sets of inputs:

2. The inertia parameters.

1. The external forces and torques.

mass positions −−→*OMi* of the *<sup>i</sup>*

3. The joint coordinates, velocities and accelerations.

**Figure 1.** Principle of the inverse dynamical model: from the experiment to the vector *Q* of the joint efforts.

This model is applied to experiments of STS : the subject, initially seated, is asked to get up without moving the feet, and without arm or hand contact with the environment or with any part of the body. In this paper, both postural behaviors of slow and fast STS are analyzed and compared.
