Mechanisms with multiple topological structures during the operation process are called mechanisms with variable topologies (MVTs), and their corresponding kinematic chains are called variable chains. The kinematic joints whose types and/or motion orientations are changeable during the operation process of an MVT are called variable joints. This work presents a systematic design methodology for MVTs. First, locutions of mechanisms with multiple configurations are introduced. Then, the topological characteristics of variable joints subject to input motions are investigated. A mapping function...