A study of the effects of the lower index methods on ADAMS sparse tableau formulation for the computational dynamics of multi-body mechanical systems

Abstract

This paper studies the effects of reducing the index of the original ADAMS (automatic dynamic analysis of mechanical systems) formulation. For this, a pilot computer program MECH-SIM (MECHanical SIMulations) was developed on the basis of the original ADAMS attributes such as sparse tableau formulation (STF) and backward difference formula (BDF) [1].

The STF implemented in the original ADAMS computer program uses differential and algebraic equations (DAE). In the new formulation it eliminates the three relations connecting the body angular velocities and the angular momentum. It also reformulates the implicit force equations by substituting their functions directly into the corresponding differential equations of motion. The above reduction maintains a reasonable number of equations when the geometric constraints stabilize the velocity and/or the acceleration constraints. A method is found to measure ‘the drift’ allowed by the velocity or acceleration constraints. This permits the use of constraints stabilization only ‘when needed’. Consequently, the BDF error control improves maintenance of the efficiency of the method.

The pilot computer program MECH-SIM incorporates these improvements. The program was used to test the numerical accuracy and efficiency on mechanical systems used in agricultural mechanization, industrial equipment and auto suspensions. Hence, such results can be extended to the modern ADAMS computer program.