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In our previous papers [13, 14] we presented a variable compression mechanism. In this paper we study the kinematic analysis of this mechanism. Two cases are considered: there is no motion for the control lever, and the second one is characterized by the existence of a known motion for one edge of the control lever. The kinematic analysis is performed firstly in a classical way by determining the positions of some characteristic geometric parameters and by derivation of these parameters with respect to time. The second way is by use of the multibody approach to determine the matrix of constraints for the mechanism. In the last situation we can not determine all the linear and angular velocities for the mechanism. Usually, a number of new equations (this number is equal to the degree of mobility of the mechanism) must be added in order to determine all kinematic parameters. A numerical example concludes this study.