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.

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.

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

Knee angles are kinematic quantities that are commonly presented in gait analysis reports. They are typically calculated as the relative angles between the anatomical coordinate systems rigidly attached to the femur and the tibia. To give these angles a biomechanical meaning, the coordinate systems must be defined with respect to some anatomical landmarks. For example, if one axis of the joint coordinate systems is directed along the knee flexion/extension axis, then the relative angle assumes the meaning of flexion/extension angle. Defining accurate anatomical coordinate systems is not an easy task, because it requires skills in marker placement, landmark identification and definition of a biomechanical model. In this paper, we present a novel method to (i) functionally define two coordinate systems attached to femur and tibia and (ii) functionally calculate the knee angle based on the relative differential kinematics between the previously defined coordinate systems. As the main limitation, this method is unable to provide an absolute measurement of the knee flexion/extension angle; however, it is able to accurately capture and display the relative angular motion of the knee. We show that our method produced consistent results even when the measured coordinate systems were randomly modified, removing any anatomical referencing. The proposed method has the advantage of being independent/invariant of the choice of the original coordinate systems of the femur and tibia, removing the need for accurate marker placement. Some major consequences are that (i) the markers may be placed on optimal landmarks, for example, minimizing the soft tissue artifacts or improving the subject's comfort, and (ii) there is no need for anatomical calibration when technical marker clusters/triads are used.

Estimating the Instantaneous Screw Axis and the Screw Axis Invariant Descriptor of Motion by Means of Inertial Sensors: An Experimental Study with a Mechanical Hinge Joint and Comparison to the Optoelectronic System.

The motion of a rigid body can be represented by the instantaneous screw axis (ISA, also known as the helical axis). Recently, an invariant representation of motion based on the ISA, namely, the screw axis invariant descriptor (SAID), was proposed in the literature. The SAID consists of six scalar features that are independent from the coordinate system chosen to represent the motion. This method proved its usefulness in robotics; however, a high sensitivity to noise was observed. This paper aims to explore the performance of inertial sensors for the estimation of the ISA and the SAID for a simple experimental setup based on a hinge joint. The free swing motion of the mechanical hinge was concurrently recorded by a marker-based optoelectronic system (OS) and two magnetic inertial measurement units (MIMUs). The ISA estimated by the MIMU was more precise, while the OS was more accurate. The mean angular error was ≈2.2° for the OS and was ≈4.4° for the MIMU, while the mean standard deviation was ≈2.3° for the OS and was ≈0.2° for the MIMU. The SAID features based on angular velocity were better estimated by the MIMU, while the features based on translational velocity were better estimated by the OS. Therefore, a combination of both measurements systems is recommended to accurately estimate the complete SAID.