Mathematical Modeling and Measurement of the 6-DOF Force and Momont at the Human Knee Joint

在这项研究中，最初由Grood和Suntay开发的六自由度(DOF)运动学模型的力和力矩的数学描述使用6×6雅可比矩阵。值得注意的是，雅可比是4自由度膝关节位移(内翻外翻、前后平移、内旋外旋和近端远端平移)的函数，因此必须测量膝关节的运动以确定膝盖力和力矩。在不允许关节自然运动的情况下，使用机器的十字头将前抽屉移位应用于膝关节。利用万能力-力矩传感器(UFS)测量施加在胫骨上的力和力矩，并将其代入数学计算，以计算人体膝关节的力和力矩。结果发现，在100N的前力作用下，关节的所有其他自由度都产生了显著的力和力矩，在100N的后力作用下也出现了显著的力和力矩。这一结果与胫骨内旋转和前力等临床观察结果相一致。

A mathematical description of forces and moments with respect to a six degree-of-freedom (DOF) kinematic model, originally developed by Grood and Suntay, was performed using a 6*6 Jacobian matrix in this study. Note that the Jacobian is a function of 4-DOF knee displacements (Varus-valgus rotation, Anterior-posterior translation, Internal-external rotation, and Proximal-distal translation), therefore the knee motion has to be measured to determine knee force and moment.A human knee cadaveric specimen was dissected down to joint capsule and mounted in an Instron material testing machine. Anterior drawer displacement was applied to the knee using the cross-head of the machine without allowing the natural motion of the joint. Forces and moments applied to the tibia were measured with a universal force-moment sensor (UFS), and were substituted to the mathematics to calculate the forces and moments at the human knee joint. It was found that, under anterior force up to 100 N,significant forces and moments develop in all other DOF of the joint, that was also found under posterior force up to 100 N.These results corresponded well with clinical observations such as internal tibial rotation with anterior force.