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 degree-of-freedom mechanisms with a redundancy. With analytical (geometrical) methods, the solutions of the forward position kinematics problem are significantly found by both solving an 8$^{th}$ -order polynomial equation in one unknown variable and using one over-constraint geometrical equation which can be derived under the condition of a redundancy. The proposed forward kinematics has closed-form solutions and allows Auto-Balancing control of the moving platform in real time. Numerical examples are presented and the results are verified by an inverse kinematics analysis.