Approximate determination of the joint reaction forces in the drive system with double universal joints

In this study, a drive system connected by rolling bearings and double universal joints is modeled as a closed-loop multibody system. Because of the existence of redundant constraints, the joint reaction forces cannot be determined uniquely through dynamic analysis. Based on the physical mechanism where the joint reaction forces are the resultants of contact forces at the joint definition point, a methodology of frictionless contact analysis is presented to identify joint reaction forces. In terms of D'Alembert's principle, the dynamic equations of constrained multibody systems are equivalent to the equilibrium equations of all bodies composed of joint contact forces, externally applied forces, and inertial forces. The equivalent equilibrium equations provide a set of complementary equations to identify the contact positions and contact forces in the rolling bearings and double universal joints. The drive system is also simulated using ADAMS software, where all the joints are released and the corresponding constraint functions are replaced by the impact forces between the joint components. Some conclusions are obtained through the comparison of numerical examples between the proposed method and the ADAMS model. In the double universal joints, the equations are adequate and independent, which results in that the corresponding contact positions and contact forces can be solved uniquely. Then, the correlation between the data produced by these two models is acceptable in the engineering practices. Furthermore, contact details in the double universal joints can be obtained without the calculation of the relative motion between the cross-pin and yokes. However, the reaction forces in the rolling bearings are indeterminate due to that their complementary equations are not independent. The proposed method has high efficiency and acceptable precision.