New least squares solutions for estimating the average centre of rotation and the axis of rotation

Abstract 

A new method is proposed for estimating the parameters of ball joints, also known as spherical or revolute joints and hinge joints with a fixed axis of rotation. The method does not require manual adjustment of any optimisation parameters and produces closed form solutions. It is a least squares solution using the whole 3D motion data set. We do not assume strict rigidity but only that the markers maintain a constant distance from the centre or axis of rotation. This method is compared with other methods that use similar assumptions in the cases of random measurement errors, systematic skin movements and skin movements with random measurement noise. Simulation results indicate that the new method is superior in terms of the algorithm used, the closure of the solution, consistency and minimal manual parameter adjustment. The method can also be adapted to joints with translational movements.

Keywords:  Joint kinematics, Centre of rotation, Axis of rotation, Geometric algebra