Degeneracy of velocity constraints in rigid body systems

The equations governing the dynamics of rigid body systems with velocity constraints are singular at degenerate configurations in the constraint distribution. In this report, we describe the causes of singularities in the constraint distribution of interconnected rigid body systems with smooth configuration manifolds. A convention of defining primary velocity constraints in terms of orthogonal complements of one-dimensional subspaces is introduced. Using this convention, linear maps are defined and used to describe the space of allowable velocities of a rigid body. Through the definition of these maps, we present a condition for non-degeneracy of velocity constraints in terms of the one dimensional subspaces defining the primary velocity constraints. A method for defining the constraint subspace and distribution in terms of linear maps is presented. Using these maps, the constraint distribution is shown to be singular at configuration where there is an increase in its dimension.

MIMU sensors for joint kinematic estimation: anatomical landmarking and frame correction

The ability to capture human motion allows researchers to evaluate an individual’s gait. Gait can be measured in different ways, from camera-based systems to Magnetic and Inertial Measurement Units (MIMU). The former uses cameras to track positional information of photo-reflective markers, while the latter uses accelerometers, gyroscopes, and magnetometers to measure segment orientation. Both systems can be used to measure joint kinematics, but the results vary because of their differences in anatomical calibrations. The objective of this thesis was to study potential solutions for reducing joint angle discrepancies between MIMU and camera-based systems. The first study worked to correct the anatomical frame differences between MIMU and camera-based systems via the joint angles of both systems. This study looked at full lower body correction versus correcting a single joint. Single joint correction showed slightly better alignment of both systems, but does not take into account that body segments are generally affected by more than one joint. The second study explores the possibility of anatomical landmarking using a single camera and a pointer apparatus. Results showed anatomical landmark position could be determined using a single camera, as the anatomical landmarks found from this study and a camera-based system showed similar results. This thesis worked on providing a novel way for obtaining anatomical landmarks with a single point-and-shoot camera, as well aligning anatomical frames between MIMUs and camera-based systems using joint angles.