Fulleroid-Like Linkages

In this paper we present a new type of over-constrained spatial linkages obtained by inserting planar double-ring mechanisms (modules) into the faces of a polyhedron so that they form closed networks over the polyhedron after being interconnected by appropriate gussets. Such linkages will be called “double-ring polyhedral linkages”. Though highly over constrained, these linkages are deformable with one degree of freedom. Recently it was shown that polyhedral linkages can be synthesized with single ring mechanisms as modules. Therefore the question arises: what is the advantage of using double-ring mechanisms as modules instead of single-ring mechanisms? The first answer is: double-ring polyhedral linkages show much greater global stability. This is proved by all manufactured models, and the reason is evident: the single-ring mechanism has twice as many degrees of freedom as there are sides in the polyhedral face into which it is inserted, while the double-ring mechanism is movable with only one degree of freedom. A second answer is: from a double-ring polyhedral linkages a variety of cup-like linkages can be found by simply dividing them into parts.

This paper aims to construct a novel family of deployable mechanisms from a class of two-layer and two-loop spatial linkages, each of which consists of an eight revolute pair (8R) single-loop linkage connected by a 5R serial chain. First, structural characteristics of the class of linkages as deployable units are analyzed and illustrated. Then, the two-layer and two-loop spatial linkages with 5R chains satisfying the structural characteristics are systematically synthesized. Mobile assembly modes between deployable units are established based on degree-of-freedom (DOF) analysis. Finally, a family of single DOF deployable mechanisms is constructed based on the synthesized deployable units and the established assembly modes. The derived deployable mechanisms have the characteristic of the umbrella-like structure, and they have various mesh shapes, which can meet different kinds of application requirements.

Covalent linkages between constituent blocks of macromolecules and ligands have been subject to inconsistent treatment during the model-building, refinement and deposition process. This may stem from a number of sources, including difficulties with initially detecting the covalent linkage, identifying the correct chemistry, obtaining an appropriate restraint dictionary and ensuring its correct application. The analysis presented herein assesses the extent of problems involving covalent linkages in the Protein Data Bank (PDB). Not only will this facilitate the remediation of existing models, but also, more importantly, it will inform and thus improve the quality of future linkages. By considering linkages of known type in the CCP4 Monomer Library (CCP4-ML), failure to model a covalent linkage is identified to result in inaccurate (systematically longer) interatomic distances. Scanning the PDB for proximal atom pairs that do not have a corresponding type in the CCP4-ML reveals a large number of commonly occurring types of unannotated potential linkages; in general, these may or may not be covalently linked. Manual consideration of the most commonly occurring cases identifies a number of genuine classes of covalent linkages. The recent expansion of the CCP4-ML is discussed, which has involved the addition of over 16 000 and the replacement of over 11 000 component dictionaries using AceDRG. As part of this effort, the CCP4-ML has also been extended using AceDRG link dictionaries for the aforementioned linkage types identified in this analysis. This will facilitate the identification of such linkage types in future modelling efforts, whilst concurrently easing the process involved in their application. The need for a universal standard for maintaining link records corresponding to covalent linkages, and references to the associated dictionaries used during modelling and refinement, following deposition to the PDB is emphasized. The importance of correctly modelling covalent linkages is demonstrated using a case study, which involves the covalent linkage of an inhibitor to the main protease in various viral species, including SARS-CoV-2. This example demonstrates the importance of properly modelling covalent linkages using a comprehensive restraint dictionary, as opposed to just using a single interatomic distance restraint or failing to model the covalent linkage at all.

The fecund torus, its bitangent-circles and derived linkages

This paper presents the kinematic modeling of the human forearm rotation constructed with a spatial four-bar linkage. Especially, a circumduction of the distal ulna is modeled for a minimal displacement of the position of the hand during the forearm rotation from the supination to the pronation. To establish its model, four joint types of the four-bar linkage are, firstly, assigned with the reasonable grounds, and then the spatial linkage having the URUU (Universal-Revolute-Universal-Universal) joint type is proposed. Kinematic analysis is conducted to show the behavior of the distal radio-ulna as well as to evaluate the angular displacements of all the joints. From the simulation result, it is, finally, revealed that the URUU spatial linkage can be substituted for the URUR (Universal-Revolute-Universal-Revolute) spatial linkage by a kinematic constraint.

A four-bar linkage having a quadratic input-output equation can admit a constant value of the output variable for any value of the input variable. Such a linkage is termed constant-branch four-bar linkage in this paper. The general conditions governing the existence of this special class of linkages are derived through an in-depth analysis of the input-output equation. Geometric, mobility, and force-transmission properties are discussed with regard to most common types of planar, spherical, and spatial four-bar linkages. As an application example, a clutch mechanism, based on a constant-branch spatial RSSR four-bar linkage, is proposed.

This paper presents the kinematic analysis and optimization technique required for the optimal attachment of a spherical joint (i.e., a ball in a socket) to the ground pivoted link of an RSSR spatial four-bar linkage. The optimization technique is a searching algorithm, which can be applied to the problem of optimal spherical joint attachment in other types of spatial linkages as well. This attachment optimization is necessary if the socket of the joint is to have its maximum ball retention capability. The optimization technique is illustrated by an example.

Structural and electronic properties of binary and ternary platinum oxides

The paper presents a general concept regarding the joint rotation space (JRS) of single loop planar and spherical N-bar linkages as well as its significance and applicability in multiple loop and spatial linkages. A JRS refers to the input domain of a linkage. The paper first discusses and classifies the JRS types of single loop five-bar linkages based on the types of the JRS boundary. The concept of sheets and pages of JRS is then introduced as an aid to understand the mobility of linkages. A sheet refers to the JRS of a linkage branch (or circuit). A JRS sheet may have one or more pages and each page refers to an uncertainty singularity free JRS. The concept is then generalized to any single loop planar and spherical N-bar linkages (N ≥ 3). The paper offers geometric insights to the input domain of a linkage and establishes a one-to-one correspondence between the input domain and the linkage configurations. The applications to the mobility identification of complex linkages are discussed and demonstrated with geared five-bar linkages, Stephenson six-bar linkages, as well as spatial RCRCR mechanisms. The paper presents a useful model explaining the fundamental principle regarding the formation of branches and sub-branches in Stephenson six-bar linkages as well as some other multiloop and spatial linkages. The Mobility similarity between multiloop linkages and spatial linkages is also highlighted.

Deployable polyhedron mechanisms constructed by connecting spatial single-loop linkages of different types and/or in different sizes using S joints

A large cariety of mixed-valence silicate and oxide minerals occur in rocks from the Earth, Moon and Meteorites, They frequently contain Fe2+ -Fe3+, Ti3+ -Ti4+ and Fe2+ -Ti4+ assemblages and often display anomalous color or opacity, high thermal and electrical conductives, and unusual spectral variations with temperature or pressure. Such properties are not attributable to transitions in single cations and indicate the presence of intervalence transitions. The intervalence transitions are observed either as charge transfer (CT) bands in the visible-near infrared region and frequently cause blue colors in FeFe2+ -Fe3+ and Fe2+ -Ti4+ bearing minerals (e.g. viviante, sapphire, dordierite, kyanite, bearing minerals (e.g. vivianite, sapphire, cordierite, kyanite glaucophane, aquamarine), or as electron decolalozation (ED) often causing opacity and semiconductor behavior (e.g. magnetite, ilvaite, deerite, riebeckite). Many of the physical and spectral properties of mixed-valence silicate and oxide minerals may be correlated with crystal structure features and site Occupancies of the metals. Structural variables which affect properties of mixed-valence oxide and silicate minerals or distorted octahedra, tetrahedra, dodecahedra), type of polyhedral linkage (e.g. face-shared, edge-shared, corner-shared) metal-oxygen (M-O) distances, metal-metal (M-M) distances, and M-O-M bond angles; and orientation and extend of linked polyhedra (e.g. isolated pairs, chains, bands, sheets; blocking by Mg2+ and AI3+ in solid solution series). These features may be used to interpret the temperature and pressure dependencies of CT bands in minerals with isolated Fe2+-Fe3+ and Fe2+-Ti4+ clustes (e.g. vivianite, sapphire, glaucophane, kyanite, cordierite, omphacite, pyroxenes, etc.), and the occurance of Fe in intermediate electronic environments in minerals with infinite chains of edge-shared Fe2+-Fe3+ polyhedra (e.g. magnetite, ilvaite, deerite, schorlomite garnets, riebeckite, and potentially aenigmatite, howieite, babingtonite).

Performance evaluation of path-generating planar, spherical and spatial four-bar linkages

In this paper the input, sales, and subcontracting linkages for a sample of high-technology establishments in Northeast Ohio are described. Viewed from theoretical perspectives on subcontracting, the types of linkages which these establishments maintain and the spatial extent of their subcontracting arrangements are investigated. Inputs to the production process and sales of intermediate and final goods are also examined to identify the regional and interregional patterns of activities. These establishments maintain the bulk of their linkages with the durable goods industries of the industrial heartland. Subcontracting transactions are confined largely to Northeast Ohio and the other major metropolitan industrial regions of the Midwest. Sales of products are more geographically dispersed, both interregionally and internationally. These findings demonstrate that interfirm transactions are both numerous and geographically specific. They support theoretical statements about the structure and extent of transactions in metropolitan-based industrial complexes.

Quadruple dwell from a four-bar spatial linkage

Design and Analysis of Mast Based on Spatial Polyhedral Linkages Mechanism along Radial Axes