Conceptual configuration design of line-foldable deployable space truss structures employing graph theory

From the perspective of the truss as a whole, this research investigates the conceptual configuration design for deployable space truss structures that are line-foldable with the help of graph theory. First, the bijection between a truss and its graph model is established. Therefore, operations can be performed based on graph models. Second, by introducing Maxwell’s rule, maximum clique, and chordless cycle, the principle of conceptual configuration synthesis is analyzed. A corresponding procedure is formed and it is verified by a truss with seven nodes. Third, assisted by some theorems of graph theory, the simplified double-color topological graph of deployable space truss structures is acquired and it also displays the procedure with a case. Finally, based on the above analysis, it obtains the optimal conceptual configurations. This novel research lays the foundation for kinematic synthesis and geometric dimension designs.

Conceptual Configuration Synthesis of Line-Foldable Deployable Space Truss Structures Utilizing Graph Theory and Entropy

From the perspective of the truss as a whole, this research presents an approach to synthesizing conceptual configurations for deployable space truss structures that are line-foldable with the help of graph theory and entropy. First, according to graph theory, the bijection between a truss and its graph model is established by defining a bijective mapping between set elements. Therefore, operations can be performed based on graph models. Second, the principle of configuration evolution is interpreted by employing Maxwell’s rule, it also discusses the necessary and sufficient condition of configuration evolution. Configurations of evolution belong to three phases: space configuration, transformation configuration, and linear configuration. And it finds that the reasonable transformation configuration plays a key role. Further, maximum clique detection depending on backtracking is used to screen out unreasonable transformation configurations. Third, it introduces entropy, and the phenomenon of entropy change in configuration evolution is revealed and induction weights of rigid links are defined. It calculates the weight value of a transformation configuration by adding up induction weights of rigid links removed, also, weight values are used to classify transformation configurations. Finally, based on the previous analysis, a procedure to synthesize transformation configurations is formed and it is verified by a truss model with 7 nodes. This research lays the foundation for geometric dimension design and engineering applications.

Synthesis method for planetary gear trains without using rotation graphs

The displacement graphs (d-graphs) are the final form of planetary gear trains (PGTs) synthesis. The existing configuration synthesis methods for the d-graphs of PGTs need rotation graphs (r-graphs) as the intermediate step and produce a large amount of isomorphic KCs. This paper proposes a method to obtain d-graphs directly from the geared graph. Meanwhile, a uniform isomorphism identification method suitable for parent graphs, geared graphs, and d-graphs is presented. Finally, a fully automatic method based on parent graphs is tested on synthesizing 1-DOF PGTs with up to nine links. Our synthesis results and those in the literature are comparatively analyzed, and the reasons for contradictory synthesis results are analyzed.

Instant Center Identification of Single-Loop Multi-DOF Planar Linkage Using Virtual Link

Instant center is an important kinematic characteristic which can be used for velocity and singularity analysis, configuration synthesis and dynamics modeling of multi-degree of freedom (multi-DOF) planar linkage. The Aronhold–Kennedy theorem is famous for locating instant centers of four-bar planar linkage, but for single-loop multi-DOF linkages, it fails. Increasing with the number of the links of single-loop multi-DOF planar linkages, the lack of link relationship makes the identification of instant center become a recognized difficulty. This paper proposes a virtual link method to identify instant centers of single-loop multi-DOF planar linkage. First, three types of instant centers are redefined and the instant center identification process graph is introduced. Then, based on coupled loop chain characteristic and definition of instant center, two criteria are presented to convert single-loop multi-DOF planar linkage into a two-loop virtual linkage by adding the virtual links. Subsequently, the unchanged instant centers are identified in the virtual linkage and used to acquire all the instant centers of original single-loop multi-DOF planar linkage. As a result, the instant centers of single-loop five-bar, six-bar planar linkage with several prismatic joints are systematically researched for the first time. Finally, the validity of the proposed method is demonstrated using loop equations. It is a graphical and straightforward method and the application is wide up to single-loop multi-DOF N-bar (N ≥ 5) planar linkage.