An improved Kane's method for multibody dynamics

This paper presents an improved Kane's method for automatically generating the equations of motion of arbitrary multibody systems. The notions of partial velocity matrix and partial angular velocity matrix are introduced. Each body's contribution to the system's generalized inertial force is expressed in a similar manner, which makes it amenable to computer solutions. All the kinematic quantities' recursive relations are developed to improve the modeling efficiency. The motion constraints are handled by the new form of Kane's equation. The final mathematical model is of the same dimensions with the generalized speeds and involves no Lagrange multipliers; therefore, it's useful for control system design. The simulation of a space platform with two manipulators is compared between the proposed method and recursive algorithm. The results validate the algorithm's accuracy.