Determining Equations Governing Multibody Dynamic Systems Through Joint Kinematics and Kinematic Chain Effects in Closed-Form Mechanisms

In this study, the governing equations of dynamic systems were derived using a novel method that integrated the kinematic properties of joints and the complex kinematic chains of multibody systems into a set of governing equations. The governing equations of multibody systems were then transformed into an ordinary differential equation (ODE) using the calculus of matrix-valued functions. This algorithm can efficiently obtain recursive differential equations of motion for multibody systems. Consequently, the computational cost of the simulation was reduced successfully. Andrew's squeezing and carpet scrapping mechanisms were utilized with kinematic constraints to validate the proposed method. Results indicated that the proposed method was 4.2 and 5.4 times faster than the other methods based on differential algebraic equations in Andrew's squeezing and carpet scrapping mechanism, respectively.