This paper presents a systematical comparative study of various modular methods based on the different module types: basic kinematic chains (BKCs), single opened chains (SOCs), loops (or a tree and co-tree), links-joints, etc. for analysis and synthesis of structure, kinematics and dynamics of planar linkages. The basic idea is that any linkage can be divided into (or built up by) some modular components in sequence, and based on the component constraints and network entirty constraints of the linkage, the unified modular approaches have been used for analysis and synthesis. In systematical comparative study, the main issues of a modular method have been discussed, such as: the topological characteristics revealed via different module types; the dimension of a set of kinematic equations; the automated generation and solution of kinematic equations; the dimension and automated generation of dynamical equations, and computation complexity for generating and solving dynamical equation; the automated generation of structural analysis and type synthesis; the generation of kinematic synthesis equations etc.. This paper gives a summary of the use of modular techniques for analyzing and synthesizing planar linkages in the recently thirty years. This comparative study includes two parts: Part I-modular structural analysis and modular kinematic analysis; Part II-modular dynamic analysis, modular structural synthesis and modular kinematic synthesis. This paper is the second part.