The study of the forces and the pairs of shaking that appear in mechanisms, are of main interest in the study of the dynamics of the internal combustion engines. An internal combustion engine is modeled from a particular arrangement of a set of mechanisms of the connecting-rod-crank type. During the performance of the internal combustion engine, the repetitive movement of the slide or piston induces accelerations and forces that are transmitted and distributed between the connecting rod and the crank or crankshaft. When the crankshaft is subjected to the components of the forces induced by the piston, the shaking torques are generated in turn. The purpose of the analysis of the pairs of shaking is to determine the dynamic values of the counterweights that must be added to each mechanism, with the aim of reducing the set of shaking actions. In the traditional bibliography in which the dynamic equations are presented, the complete analytical developments are not always presented; there are references that present partial results, in this work the algebraic developments are presented that allow to validate the correspondence between the expressions of different bibliographic sources in the teaching of these subjects.