Instantaneous center/axis of rotation for planar and three-dimensional motion

This article discusses a direct analytical method for calculating the instantaneous center of rotation and the instantaneous axis of rotation for the two-dimensional and three-dimensional motion, respectively, of rigid bodies. In the case of planar motion, this method produces a closed-form expression for the instantaneous center of rotation based on a single point located on the rigid body. It can also be used to derive closed-form expressions for the body and space centrodes. For three-dimensional, rigid body motion, an extension of the technique used for planar motion locates a point on the instantaneous axis of rotation, which is parallel to the body angular velocity vector. In addition, methods are demonstrated that can be used to map the body and space cones for general rigid body motion, and locate the fixed point for the body.

Development of a Robotic Assembly for Analyzing the Instantaneous Axis of Rotation of the Foot Ankle Complex

Ankle instantaneous axis of rotation (IAR) measurements represent a more complete parameter for characterizing joint motion. However, few studies have implemented this measurement to study normal, injured, or pathological foot ankle biomechanics. A novel testing protocol was developed to simulate aspects of in vivo foot ankle mechanics during mid-stance gait in a human cadaveric specimen. A lower leg was mounted in a robotic testing platform with the tibia upright and foot flat on the baseplate. Axial tibia loads (ATLs) were controlled as a function of a vertical ground reaction force (vGRF) set at half body weight (356 N) and a 50% vGRF (178 N) Achilles tendon load. Two specimens were repetitively loaded over 10 degrees of dorsiflexion and 20 degrees of plantar flexion. Platform axes were controlled within 2 microns and 0.008 degrees resulting in ATL measurements within ±2 N of target conditions. Mean ATLs and IAR values were not significantly different between cycles of motion, but IAR values were significantly different between dorsiflexion and plantar flexion. A linear regression analysis showed no significant differences between slopes of plantar flexion paths. The customized robotic platform and advanced testing protocol produced repeatable and accurate measurements of the IAR, useful for assessing foot ankle biomechanics under different loading scenarios and foot conditions.