Kinematic and dynamic analysis of an anatomically based knee joint

This paper presents a knee-joint model to provide a better understanding on the interaction between natural joints and artificial mechanisms for design and control of rehabilitation exoskeletons. The anatomically based knee model relaxes several commonly made assumptions that approximate a human knee as engineering pin-joint in exoskeleton design. Based on published MRI data, we formulate the kinematics of a knee-joint and compare three mathematical approximations; one model bases on two sequential circles rolling a flat plane; and the other two are mathematically differentiable ellipses-based models with and without sliding at the contact. The ellipses-based model taking sliding contact into accounts shows that the rolling-sliding ratio of a knee-joint is not a constant but has an average value consistent with published measurements. This knee-joint kinematics leads to a physically more accurate contact-point trajectory than methods based on multiple circles or lines, and provides a basis to derive a knee-joint kinetic model upon which the effects of a planar exoskeleton mechanism on the internal joint forces and torque during flexion can be numerically investigated. Two different knee-joint kinetic models (pin-joint approximation and anatomically based model) are compared against a condition with no exoskeleton. The leg and exoskeleton form a closed kinematic chain that has a significant effect on the joint forces in the knee. Human knee is more tolerant than pin-joint in negotiating around a singularity but its internal forces increase with the exoskeleton mass-to-length ratio. An oversimplifying pin-joint approximation cannot capture the finite change in the knee forces due to the singularity effect.