There exist some mechanisms with variable topologies that have interesting applications, for examples, legged walking machines, mechanical push-button stopper locks, and various toys. A variable kinematic joint is a kinematic joint that is capable of topological variation in a mechanism with variable topology. This work aims at the topological representations and characteristic analysis of variable kinematic joints. During the operation process of a mechanism, the topology states of a variable kinematic joint can be expressed symbolically as the joint sequences, graphically the digraphs, and mathematically the matrices. With the applications of graph theory, it proves that the topological characteristics of variable kinematic joints appeared with the abilities of reversibility, continuity, variability of degrees of freedom, joint homomorphism, contractibility, and expansibility. Two examples are provided for illustrating how the proposed concepts can be used to analyze and synthesize the variable joints. The results of this work provide a logical foundation for the systematic structural synthesis regarding the kinematic joints and mechanisms with variable topologies.

The mechanisms with variable topologies (MVTs) are usually changing their topological structures in accordance with the varying mobility and quasi-singular configurations. The mobility analysis and configuration singularity of MVTs are studied via screw theory in this paper. The configurations of MVTs are formulated by a set of variable combinations of screw coordinates. For the mobility analysis, two examples provided show that the proposed approach is adoptable for dealing with common MVTs. For the configuration singularity, the concepts of stationary configuration and uncertainty configuration are utilized to demonstrate the topology varying strategy of MVTs. The result in this work provides the theoretical basis and inspiration for the configuration synthesis and analysis of mechanisms with variable topologies.

A mechanism that encounters a certain changes in its topological structure during operation is called a mechanism with variable topologies (MVT). This paper is developed for the structural and motion state representations and identifications of MVTs. For representing the topological structures of MVTs, a set of methods including graph and matrix representations is proposed. For representing the motion state characteristics of MVTs, the idea of finite-state machines is employed via the state tables and state graphs. And, two new concepts, the topological homomorphism and motion homomorphism, are proposed for the identifications of structural and motion state characteristics of MVTs. The results of this work provide a logical foundation for the topological analysis and synthesis of mechanisms with variable topologies.

This paper presents a design approach for the configuration synthesis of series-parallel hybrid transmissions with eight-bar mechanisms. The final design consists of 54 mechanisms with eight members and twelve joints including a simple planetary gear train (PGT) and a double planet PGT. Then, by using the techniques of power and clutch arrangements, new series-parallel hybrid transmissions are synthesized. The power arrangement process generates 97 clutchless hybrid systems. The clutch arrangement process generates 100 corresponding series-parallel transmissions. To demonstrate the feasibility of the synthesized configurations, a new hybrid transmission is selected as an example to analyze the working principle with operation modes and power flow paths.

The purpose of this paper is to synthesize systematically the feasible configurations of series–parallel hybrid transmissions for automotive systems utilized in passenger vehicles subject to the deduced design constraints. The design process includes the following steps: first, search for all feasible mechanisms that can be used for synthesizing hybrid transmissions; second, identify all potential locations for the inputs and the output to the mechanisms; third, identify all potential locations for clutches and the brakes of the systems subject to the required operation modes. Through the proposed design process, 30 planetary gear trains for hybrid electric vehicle transmissions with seven members and 10 joints are generated. The power arrangement process generates 42 clutchless hybrid systems. Then, the clutch arrangement process generates 48 corresponding series–parallel transmissions. To demonstrate the feasibility of the synthesized configurations, a novel configuration system is taken as a numerical example to illustrate the principles of operation and performance.

An approach is presented, based on combinatorial theory, for the complete enumeration of nonisomorphic mechanisms precisely from kinematic chains. And, based on the permutation groups, the concept of the generating function, and Polya’s Theory, mathematical expressions are derived for counting the number of the identified mechanisms subject to the design constraints of the adjacent/incident relationship among links, joints, or links and joints. Examples are provided to illustrate the proposed approach. The results of this work can instead of the observation method to inspect the isomorphism for mechanisms; furthermore, all nonisomorphic mechanisms can be obtained exactly and systematically.