Optimal average path of the instantaneous helical axis in planar motions with one functional degree of freedom

This paper presents a model for determining the path of the instantaneous helical axis (IHA) that optimally represents human planar motions with one functional degree of freedom (fDOF). A human movement is said to have one fDOF when all degrees of freedom (DOFs) are coordinated such that all the kinematic variables can be expressed, across movement repetitions, as functions of only one independent DOF, except for a small natural intercycle variability quantified as lower than a prespecified value. The concept of fDOF allows taking into account that, due to motor coordination, human movements are executed in a repeatable manner. Our method uses the measurement of several repetitions of a given movement to obtain the optimal average IHA path. The starting point is a change of variables, from time to a joint position magnitude (generally an angle). In this way, instead of operating with the time-dependent single-valued trajectory of the successive cycles, our model permits the representation of any motion variable (e.g. positions and their time derivatives) as a cloud of points dependent on the joint angle. This allows the averaging to be performed over the displacements and their derivatives before determining the mean IHA path. We thus avoid the nonlinear magnification of errors and variability inherent in the IHA computation. Moreover, the IHA path can be considered as a geometric attribute of the joint and the type of motion, rather than of each single movement execution. An experiment was performed that show the accuracy and usefulness of the method.