An optimal method for calculating an average screw axis for a joint, with improved sensitivity to noise and providing an analysis of the dispersion of the instantaneous axes

Abstract

The instantaneous (ISA) and average (ASA) screw axes are techniques commonly adopted in motion analysis to functionally locate the rotation axis and center of rotation of a joint. Several approaches for calculating such axes were proposed in literature and the main limitations were identified as the need for using a threshold on angular displacements or velocities for handling the cases where the ISA is ill-defined and the need for a method for reliably estimating the center or rotation in limit cases, such as a purely rotational motion in the three-dimensional space. Furthermore, in many applications, such as in biomechanics, it is useful to statistically estimate the dispersion or variation of the ISA with respect to the ASA. In this paper we propose a novel method for estimating an ASA. Our method represents an improvement over previous methods as it: (i) exploits an optimization procedure based on the instantaneous differential kinematics (screw twist); (ii) removes the need for a threshold by introducing a weighting based on the norm of angular velocity; (iii) handles the singular cases where the position of the ASA is ill-defined by proposing a regularization term in the optimization. In addition, we proposed a method for estimating the uncertainty in the ASA calculation. The same quantities serve as a measure of the dispersion of the ISAs with respect to the ASA. The method was tested on real data and surrogate data: (i) a human gait analysis trial representing the motion of a knee, (ii) the experimental recording of the free swing motion of a mechanical hinge and (iii) synthetically generated motion data of a purely rotational (cylindrical) motion. The results showed that the new method had a lower sensitivity to noise, was able to reasonably handle the singular cases and provide a detailed analysis of ISA dispersion.

Three-dimensional kinematics of leaf-cutter ant mandibles: not all dicondylic joints are simple hinges

“…These methods may be broadly split into one of two categories: the orientation of the IHA is still obtained through determination of the angular velocity vector, but filtering or other optimization routines are deployed to reduce noise (e.g. [69,75,80]); or finite difference approximations are avoided altogether, and a representative axis is estimated through minimization of cost functions that allow absorption of experimental uncertainty into an error term (e.g. [71,77,[81][82][83]).…”

3D kinematics of leaf-cutter ant mandibles: not all dicondylic joints are simple hinges

“…its orientation and location can be prohibitively inaccurate, even for the much simpler case of planar motion, where it reduces to an instantaneous axis of rotation [e. g. 69,75,80]. Indeed, even relatively small noise can reduce the estimate obtained through eq.…”

“…To overcome this difficulty, numerous alternative methods have been proposed. These methods may be broadly split into one of two categories: the orientation of the IHA is still obtained through determination of the angular velocity vector, but filtering or other optimisation routines are deployed to reduce noise [e. g. 69,75,80]; or finite difference approximations are avoided altogether, and a representative axis is estimated through minimisation of cost functions which allow absorption of experimental uncertainty into an error term [e. g. 71,77,[81][82][83].…”

A Novel Procedure for Knee Flexion Angle Estimation Based on Functionally Defined Coordinate Systems and Independent of the Marker Landmarks

“…The proposed method is based on representing the knee motion around an average screw (helical) axis (ASA), which is functionally determined across a gait cycle [35]. In more detail, the proposed method aims to exploit the knee ASA to define a local coordinate system (CS) relative to a body segment [34,35].…”

“…The only requirement are the measured coordinates of at least three non-collinear markers attached to each segment composing the knee joint. This method is based on the exploitation of differential kinematics in screw theory and an invariant representation of motion as defined in previous studies [24,34,35].…”