A survey of formal methods for determining the centre of rotation of ball joints.
The interpretation of joint kinematics data in terms of displacements is a product of the type of movement, the measurement technique and the underlying model of the joint implemented in optimization procedures. Kinematic constraints reducing the number of degrees of freedom (DOFs) are expected to compensate for measurement errors and noise, thus, increasing the reproducibility of joint angles. One approach already successfully applied by several groups approximates the healthy human knee joint as a compound hinge joint with minimal varus/valgus rotation. Most of these optimizations involve an orthogonality constraint. This contribution compares the effect of a model with and without orthogonality constraint on the obtained joint rotation angles. For this purpose, knee joint motion is simulated to generate kinematic data without noise and with normally distributed noise of varying size. For small noise the unconstrained model provides more accurate results, whereas for larger noise this is the case for the constrained model. This can be attributed to the shape of the objective function of the unconstrained model near its minimum.