Study on Transfer Matrix Method for the Planar Multibody System With Closed-Loops

Abstract

The conventional transfer matrix method for multibody systems (MSTMM) with closed-loops (CLs) has superiority of avoiding the global dynamics equations. However, it requires a transfer equation to link multiple-input single-output (MISO) rigid body with multihinge subset and supplement equations caused CLs. In order to simplify the deduction processing and improve the numerical stability, the Riccati transformation is introduced and the Riccati transfer matrix method for multibody systems (RMSTMM) with CLs is proposed. In a system with CLs, each CL is cut off at the connection point, and the new unknowns generated at the cutoff point are introduced into the Riccati recurrence relation. The numerical results of the conventional MSTMM and the RMSTMM are compared, and the reliability of the RMSTMM is verified. Meanwhile, the constrained Jacobian matrix is used to eliminate the constraint violation of the system. The variations of the constraint violation error are compared to validate necessarily of constraints.