Forces and moments in six-DOF at the human knee joint: mathematical description for control

A mathematical description of six-degree of freedom (6-DOF) forces and moments with respect to a commonly utilized knee joint coordinate system was performed using a [6 x 6] Jacobian matrix developed in this study. The presented Jacobian allows the proper transformation of the forces and moments measured at a sensor coordinate system (attached to the tibia in this case) into the joint coordinate system and is dependent on the kinematics of the joint itself. Experimental application of the developed mathematics to A-P drawer tests of the intact knee confirmed that it is possible to determine the forces and moments applied to a human knee within the joint coordinate system during joint loading. More importantly, the inverse Jacobian was also determined for implementation in the force-moment control of the joint during testing using a robotic testing system. This approach is demonstrated for the joint coordinate system for the human knee in the current study, although it may be more generally applied to allow determination and control of forces and moments within any description of motions, and for any additional joints in the human body.