Class II plane mechanisms according to Artobolevsky classification are considered. This classification allows for a modular approach to the position, velocity, and acceleration analyses. The idea of a modular approach is to divide the mechanism into class I mechanisms and structural groups. Any II class mechanism includes only I class mechanisms and structural groups of the II class according to Artobolevsky classification, which are also called Assur dyads. A complete kinematic analysis of class I mechanisms is trivial, it can be performed using the methods of rotational or translational kinematics. As for the positional analysis of Assur dyads, the difficulty is to solve the vector contour equations. In this paper, an analytical approach is proposed to solve the last ones, using a vector solution of Chace equation. As a result, expressions for all radius vectors describing the movement of the characteristic points of the dyads were obtained in a unified vector form. The advantage of this approach is the absence of the rotation angles of the links of structural groups, which significantly facilitates analysis and algorithmization. On the basis of the obtained expressions, the velocity and acceleration analyses were carried out in two ways. The first method consists in using of the automatic differentiation technique of radius vectors, the second one is based on the vector solution of general kinematic equations corresponding to the structure of Assur dyads. The proposed approach can be an algorithmic basis of software specializing in the automated design of class II plane mechanisms according to Artobolevsky classification.