Abstract: Based on the algebra of rotation, this paper derives the relations between the derivatives of successive rot at ions, bringing to a number of important properties of infinitesimal rotation. The algebra of infinitesimal rotation is the mathematical background of the micro-rotation method,a method for the kinematic analysis of mechanisms. As a concrete example of application cf tbs algebra, the paper also discusses ths kinematic analysis of a general spatial 7R, 7-link mechanism.