A Sarrus-like overconstrained eight-bar linkage and its associated Fulleroid-like platonic deployable mechanisms

This paper, for the first time, presents an overconstrained spatial eight-bar linkage and its application to the synthesis of a group of Fulleroid-like deployable platonic mechanisms. Structure of the proposed eight-bar linkage is introduced, and constrain and mobility of the linkage are revealed based on screw theory. Then by integrating the proposed eight-bar linkage into platonic polyhedron bases, synthesis of a group of Fulleroid-like deployable platonic mechanism is carried out; which is demonstrated by the synthesis and construction of a Fulleroid-like deployable tetrahedral mechanism. Further, mobility of the Fulleroid-like deployable platonic mechanisms is formulated via constraint matrices by following Kirchhoff’s circulation law for mechanical networks, and kinematics of the mechanisms is presented with numerical simulations illustrating the intrinsic kinematic properties of the group of Fulleroid-like deployable platonic mechanisms. In addition, a prototype of the Fulleroid-like deployable spherical-shape hexahedral mechanism is fabricated and tested; verifying the mobility and kinematic characteristics of the proposed deployable polyhedral mechanisms. Finally, application of the proposed deployable platonic mechanisms is demonstrated in the development of a transformable quadrotor. This paper hence presents a novel overconstrained spatial eight-bar linkage and a new geometrically intuitive method for synthesising Fulleroid-like regular deployable polyhedral mechanisms that have great potential applications in deployable, reconfigurable and multifunctional robots

Rigidity of frameworks on expanding spheres

A rigidity theory is developed for bar-joint frameworks in $\mathbb{R}^{d+1}$ whose vertices are constrained to lie on concentric $d$-spheres with independently variable radii. In particular, combinatorial characterisations are established for the rigidity of generic frameworks for $d=1$ with an arbitrary number of independently variable radii, and for $d=2$ with at most two variable radii. This includes a characterisation of the rigidity or flexibility of uniformly expanding spherical frameworks in $\mathbb{R}^{3}$. Due to the equivalence of the generic rigidity between Euclidean space and spherical space, these results interpolate between rigidity in 1D and 2D and to some extent between rigidity in 2D and 3D. Symmetry-adapted counts for the detection of symmetry-induced continuous flexibility in frameworks on spheres with variable radii are also provided.Comment: 22 pages, 2 figures, updated reference

Synthesis and analysis of Fulleroid-like deployable Archimedean mechanisms based on an overconstrained eight-bar linkage

This paper presents a novel intuitive synthesis approach for constructing Fulleroid-like Archimedean DPMs based on a Sarrus-like overconstrained spatial eight-bar linkage. Firstly, structure and the associated foundations of the eight-bar linkage are presented and characterized. Then, by integrating the eight-bar linkage into the Archimedean polyhedron bases, synthesis of a group of Fulleroid-like Archimedean DPMs is implemented; demonstrated by the design and construction of a Fulleroid-like deployable cuboctahedral mechanism and a Fulleroid-like deployable truncated tetrahedral mechanism. Subsequently, the mobility of these Fulleroid-like DPMs is verified through formulating the constraint matrices with Kirchhoff's circulation law and the associate constraint graphs. Further, kinematics of proposed polyhedral mechanisms is derived with numerical simulations, leading to the motion characterization of the eight-bar linkage and the group of Fulleroid-like deployable Archimedean mechanisms

Kinetic Voronoi Diagrams and Delaunay Triangulations under Polygonal Distance Functions

Let $P$ be a set of $n$ points and $Q$ a convex $k$-gon in ${\mathbb R}^2$. We analyze in detail the topological (or discrete) changes in the structure of the Voronoi diagram and the Delaunay triangulation of $P$, under the convex distance function defined by $Q$, as the points of $P$ move along prespecified continuous trajectories. Assuming that each point of $P$ moves along an algebraic trajectory of bounded degree, we establish an upper bound of $O(k^4n\lambda_r(n))$ on the number of topological changes experienced by the diagrams throughout the motion; here $\lambda_r(n)$ is the maximum length of an $(n,r)$-Davenport-Schinzel sequence, and $r$ is a constant depending on the algebraic degree of the motion of the points. Finally, we describe an algorithm for efficiently maintaining the above structures, using the kinetic data structure (KDS) framework

Loo.py: transformation-based code generation for GPUs and CPUs

Today's highly heterogeneous computing landscape places a burden on programmers wanting to achieve high performance on a reasonably broad cross-section of machines. To do so, computations need to be expressed in many different but mathematically equivalent ways, with, in the worst case, one variant per target machine. Loo.py, a programming system embedded in Python, meets this challenge by defining a data model for array-style computations and a library of transformations that operate on this model. Offering transformations such as loop tiling, vectorization, storage management, unrolling, instruction-level parallelism, change of data layout, and many more, it provides a convenient way to capture, parametrize, and re-unify the growth among code variants. Optional, deep integration with numpy and PyOpenCL provides a convenient computing environment where the transition from prototype to high-performance implementation can occur in a gradual, machine-assisted form

On the Flexibility of Deployable Dome Structures and their Application in Architecture

In this paper we discuss flexibility and applicability of deployable dome structures in contemporary architecture. A deployable dome is a spatial structure derived from appropriately connected planar polygonal panels. Nowadays, deployable domes are little researched comparing to other deployable structures, such as pseudo-cylinders, for example. When designing these configurations, either changeable supports' spans or strain of some structural elements might occur, depending on the underlying geometrical analysis. Such occurrences, usually being undesirable, can be avoided by the adequate geometrical solution which can also satisfy various sizes of the structures. Therefore, they could answer the purpose both in architectural and urban design. Thus, choosing suitable dimension of the structure, numerous applications can be obtained, starting from street furniture to large scale convertible structures for covering open spaces

Enabling New Functionally Embedded Mechanical Systems Via Cutting, Folding, and 3D Printing

Traditional design tools and fabrication methods implicitly prevent mechanical engineers from encapsulating full functionalities such as mobility, transformation, sensing and actuation in the early design concept prototyping stage. Therefore, designers are forced to design, fabricate and assemble individual parts similar to conventional manufacturing, and iteratively create additional functionalities. This results in relatively high design iteration times and complex assembly strategies