Abstract
The Grood and Suntay coordinate system is a well-known framework for defining relative joint motions referenced to clinically meaningful anatomical directions. However, in general the Grood and Suntay unit vectors do not intersect at a point, and the “floating” (second) unit vector does not have a fixed location relative to the joint. These characteristics can introduce complications when analyzing joint forces such as the forces resulting from contact or from soft tissue structures. We have developed a methodology to address these issues by resolving forces along directions that intersect at a point fixed to one of the joint bodies. The work is demonstrated using Vivo Sim Control and Vivo Sim Visualization software.
The Vivo joint motion simulator, Figure 1, and Vivo Sim Visualization software were developed to investigate joint dynamics. They use the Grood and Suntay coordinate system. Figure 2, produced using Vivo Sim Visualization, shows a solid-body model of a knee, with Grood and Suntay frames in red and green. The light blue lines are a partial soft tissue model. Figure 3 is a representation of the Grood and Suntay coordinate system for a joint set in an arbitrary pose. Figure 3 shows the primary and secondary Grood and Suntay coordinate frames, labeled “F” and “T” (light arrows), the unit vectors e1, e2 and e3 (short dark arrows), and the displacement coordinates q1, q2, q3, α, β and γ. In general, there is no point in space about which there is zero net moment resulting from forces acting collinearly with the unit vectors. In order to obtain a zero-moment reaction condition, compensating moments must be computed and applied. In addition, because e2 floats, force collinear with that vector has a line of action that translates relative to the joint. These issues are inconvenient from an analytical standpoint and could be confusing for practitioners.
In Vivo's control system and in the Vivo Sim Visualization software, commanded joint forces and moments are resolved to axes parallel to the e1, e2 and e3 unit vectors but passing through the T origin. The origin of T is chosen to lie approximately collinear with the resultant of contact forces. A multi-fiber ligament model calculates forces collinear with the ligament fibers, which are resolved to equivalent forces and moments acting through the origin of T.
With this methodology, forces along anatomically-meaningful directions can be applied to or reported from the joint without the need to compute compensating moments. The lines of action of these forces can change orientation according to joint movements, but they always pass through a point fixed to the second body. We have implemented this methodology in the Vivo Joint Simulator and the Vivo Sim Visualization software.
