RETRACTED: Analysis of governing equations of multibody dynamic systems through kinematic properties of joints and effects of kinematic chains on closed-form mechanism

Abstract

In this investigation, the fundamental equations dictating the behavior of dynamic systems were ascertained by means of an innovative approach that amalgamated the kinematic properties of joints and the intricate kinematic chains of multibody systems into a series of governing equations. Subsequently, the equations that govern the behavior of multibody systems were converted into ordinary differential equations (ODEs) utilizing the calculus of matrix-valued functions. This computational technique is adept at swiftly acquiring recursive differential equations of motion for multibody systems. Thus, the expenditure of computational costs associated with the simulation was efficaciously minimized. The mechanisms of Andrew's squeezing and carpet scrapping were employed in conjunction with kinematic constraints to authenticate the validity of the proposed methodology. The findings suggest that, notwithstanding the fact that the root mean square error (RMSE) in the generalized coordinates between the two ODE and differential algebraic equation (DAE) techniques is small in the Andrew's squeezing mechanism (at approximately 0.02) and in the carpet scraping mechanism (at approximately 0.7), there are still discrepancies between the two methods. The degree of convergence in the aforementioned methodologies, despite the slight RMSE difference between them, shows a clear disparity. By way of illustration, when employing the conventional DAE technique, the duration required to resolve the Andrew's squeezing and carpet scraping mechanisms is 5 and 11.34 s, respectively. However, by utilizing the ODE methodology in the aforementioned mechanisms, the time required to determine a solution is truncated to 1.19 and 2.1 s, sequentially.