Ranking Static Balancing Methods Based on the Actuating Frictional Effort

Abstract When a linkage is statically balanced, the effort required to actuate it quasi-statically in the absence of friction is zero. This is true irrespective of how the static balancing is accomplished. However, the effort is required to actuate the linkage when the Coulomb friction is present in the joints. This article shows that different static balancing methods lead to different magnitudes of the actuating frictional efforts. We further show that there exists a class of static balancing ways where between any two ways, one of the ways has a distinctively smaller magnitude of the actuating frictional effort for all values of the actuating kinematic variable. Hence, in such a case, the ways of static balancing can be ranked based on the magnitude of the actuating frictional effort. This has practical relevance when a statically balanced linkage has the Coulomb friction in its joints. Furthermore, we demonstrate that a smaller magnitude of the actuating frictional effort can be correlated to a smaller magnitude of the joint reaction forces. Thus, the magnitude of the actuating frictional effort can be used to assess the magnitude of the joint reaction forces irrespective of whether the friction in the joints is real or numerically simulated.