A comparative study on some different methods for complete balancing of shaking force and moment of linkages using force counterweights and inertia counterweights

摘要

A systematical comparative study of some methods for complete force and moment balance is presented in this paper, such as, the linearly independent vectors method, the mass-moment substitution method, the complex mass substitution method and a numerical method by a few kinematic positions for force balance; the quasi-linearly independent vectors method and the momentum-moment substitution method for complete moment balance. Their fundamental principles and characteristics are described and their relative merits and some limitations are discussed. This comparative study shows. (1) for complete force balance, the linearly independent vectors method and the mass-moment substitution method are two systematical methods. Relatively, the latter has two merits: i) according to the derived formula, the force balance conditions can be written down directly instead of extracting them from kinematic equations of a linkage, and derivation of the formula is rather simple; ii)there need not to introduce the complex masses and to determine their loci. (2) for complete moment balance, the momentum-moment substitution method is a systematical theory and there are two merits: i)according to die derived formula, the moment balance conditions can be written down directly instead of extracting them from kinematic equations of the linkage; ii)the basic idea of this method is the same as of the mass-moment substitution method. Perhaps, the mass-moment and momentum-moment substitution method is a systematical and practical theory for complete force and moment balance of planar and spatial linkages.