Geometric approach to forward kinematics of casing oscillator

This paper presents the forward kinematics of the casing oscillator that is a construction machine. The structure of the casing oscillator is similar to those of 4 degrees of freedom parallel mechanisms with a redundancy. With geometric methods, an 8^th-order polynomial in an unknown variable is derived for the forward kinematics using an over-constraint condition which is obtainable from the redundant operation. The proposed forward kinematics has a closed-form solution and enables the auto-balancing control to be achieved in real time. Also, numerical example is presented, and the result is verified by an inverse kinematics analysis.