An improved kane's method for multibody dynamics

This paper presents an improved Kane's method forautomatically generating the equations of motion of arbitrary multibodysystems. The notions of partial velocity matrix and partial angular velocitymatrix are introduced. Each body's contribution to the system's generalizedinertial force is expressed in a similar manner, which makes it amenable tocomputer solutions. All the kinematic quantities' recursive relations aredeveloped to improve the modeling efficiency. The motion constraints arehandled by the new form of Kane's equation. The final mathematical model isof the same dimensions with the generalized speeds and involves no Lagrangemultipliers; therefore, it's useful for control system design. Thesimulation of a space platform with two manipulators is compared between theproposed method and recursive algorithm. The results validate thealgorithm's accuracy.