Related papers: Linkage Mechanisms Governed by Integrable Deformat…
A closed linkage mechanism in three-dimensional space is an object comprising rigid bodies connected with hinges in a circular form like a rosary. Such linkages include Bricard6R and Bennett4R. To design such a closed linkage, it is…
A mechanical linkage is a mechanism made of rigid rods linked together by flexible joints, in which some vertices are fixed and others may move. The partial configuration space of a linkage is the set of all the possible positions of a…
The configuration space of a mechanical linkage, consisting of rigid bodies moving in space constrained by joints, is defined by algebraic conditions. If these equations do not define a complete intersection, then the dimension of the…
Linkages are mechanical devices constructed from rigid bars and freely rotating joints studied both for their utility in engineering and as mathematical idealizations in a number of physical systems. Recently, there has been a resurgence of…
The plate trick or belt trick is a striking physical demonstration of properties of the double cover of the three-dimensional rotation group by the sphere of unit quaternions or spinors. The two ends of a flexible object are continuously…
A mechanical linkage is a mechanism made of rigid rods linked together by flexible joints, in which some vertices are fixed and others may move. The partial configuration space of a linkage is the set of all the possible positions of a…
From the complex motions of robots to the oxygen binding of hemoglobin, the function of many mechanical systems depends on large, coordinated movements of their components. Such movements arise from a network of physical interactions in the…
In this paper, we consider a special kind of overconstrained 6R closed linkages which we call angle-symmetric 6R linkages. These are linkages with the property that the rotation angles are equal for each of the three pairs of opposite…
From a pseudo-triangulation with $n$ tetrahedra $T$ of an arbitrary closed orientable connected 3-manifold (for short, {\em a 3D-space}) $M^3$, we present a gem $J '$, inducing $\IS^3$, with the following characteristics: (a) its number of…
Networks of rigid bars connected by joints, termed linkages, provide a minimal framework to design robotic arms and mechanical metamaterials built out of folding components. Here, we investigate a chain-like linkage that, according to…
A linkage is a finite graph with lengths assigned to each edge. A planar realization is a map to the plane which preserves edge lengths. It can be thought of as a mechanical device formed from stiff rods and rotating joints. We look at the…
A kinematic chain in three-dimensional Euclidean space consists of $n$ links that are connected by spherical joints. Such a chain is said to be within a closed configuration when its link lengths form a closed polygonal chain in three…
An oriented link projection is the image of a generic immersion of oriented circles into the 2-sphere. The circle arrangement of a link projection is a disjoint union of unoriented circles on the 2-sphere obtained by orientation-incoherent…
A planar kinematic chain consists of $n$ links connected by joints. In this work we investigate the space of configurations, described in terms of joint angles, that guarantee that the kinematic chain is closed. We give explicit formulas…
We provide a complete classification of paradoxical closed-loop $n$-linkages, where $n\geq6$, of mobility $n-4$ or higher, containing revolute, prismatic or helical joints. We also explicitly write down strong necessary conditions for…
Understanding the drift motion and dynamical locking of crystalline clusters on patterned substrates is important for the diffusion and manipulation of nano- and micro-scale objects on surfaces. In a previous work, we studied the…
The miniaturization of machines towards the micron and nanoscales requires the development of joint-like elements that enable and constrain motion. We present a facile method to create colloidal joints, that is, anisotropic colloidal…
Kinematics of mechanisms is intricately coupled to their geometry and their utility often arises out of the ability to perform reproducible motion with fewer actuating degrees of freedom. In this article, we explore the assembly of…
A geometric triangulation of a Riemannian manifold is a triangulation where the interior of each simplex is totally geodesic. Bistellar moves are local changes to the triangulation which are higher dimensional versions of the flip operation…
We discuss integrable discretizations of 3-dimensional cyclic systems, that is, orthogonal coordinate systems with one family of circular coordinate lines. In particular, the underlying circle congruences are investigated in detail, and…