相关论文: Pentapods with Mobility 2
In a foregoing publication the authors studied pentapods with mobility 2, where neither all platform anchor points nor all base anchor points are located on a line. It turned out that the given classification is incomplete. This addendum is…
We give a full classification of all pentapods with linear platform possessing a self-motion beside the trivial rotation about the platform. Recent research necessitates a contemporary and accurate re-examination of old results on this…
We show that all self-motions of pentapods with linear platform of Type 1 and Type 2 can be generated by line-symmetric motions. Thus this paper closes a gap between the more than 100 year old works of Duporcq and Borel and the extensive…
This paper deals with the old and classical problem of determining necessary conditions for the overconstrained mobility of some mechanical device. In particular, we show that the mobility of pentapods/hexapods implies either a collinearity…
A linear pentapod is a parallel manipulator with five collinear anchor points on the motion platform (end-effector), which are connected via extendible legs to the base. This manipulator has five controllable degrees-of-freedom and the…
The understanding of mobile hexapods, i.e., parallel manipulators with six legs, is one of the driving questions in theoretical kinematics. We aim at contributing to this understanding by employing techniques from algebraic geometry. The…
Explicit solutions of the two-dimensional floating body problem (bodies that can float in all positions) for relative density different from 1/2 and of the tire track problem (tire tracks of a bicycle, which do not allow to determine, which…
Pods are mechanical devices constituted of two rigid bodies, the base and the platform, connected by a number of other rigid bodies, called legs, that are anchored via spherical joints. It is possible to prove that the maximal number of…
We consider the bifurcation diagram of radial solutions for the Gelfand problem with a positive radially symmetric weight in the unit ball. We deal with the exponential nonlinearity and a power-type nonlinearity. When the weight is…
The complete classification of hexapods - also known as Stewart Gough platforms - of mobility one is still open. To tackle this problem, we can associate to each hexapod of mobility one an algebraic curve, called the configuration curve. In…
We systematically construct and study Type II Orientifolds based on Gepner models which have N=1 supersymmetry in 3+1 dimensions. We classify the parity symmetries and construct the crosscap states. We write down the conditions that a…
Just as links may be algebraically described as certain morphisms in the category of tangles, compact surfaces smoothly embedded in R^4 may be described as certain 2-morphisms in the 2-category of `2-tangles in 4 dimensions'. In this…
In the present article we prove and discuss several properties of pseudo-Riemannian Bertrand manifolds, and give an overview of the state of the theory together with problems for future work. In particular, we prove that there are no…
We study the problem of stationary bi-axially symmetric solutions of the $5$-dimensional minimal supergravity equations. Essentially all possible solutions with nondegenerate horizons are produced, having the allowed horizon cross-sectional…
We investigate the emergence of finite-amplitude non-zonal flows on the sphere $\mathbb{S}^2$ arising from stationary solutions to the 2D Euler equations. By restricting the Laplace-Beltrami eigenspace to the invariant subspace of the…
Just as knots and links can be algebraically described as certain morphisms in the category of tangles in 3 dimensions, compact surfaces smoothly embedded in R^4 can be described as certain 2-morphisms in the 2-category of `2-tangles in 4…
The aim of the present paper is to study conditions under which all the non-wandering points are periodic points, for a discrete dynamical system of two variables defined on a compact manifold. We include a survey of known results in all…
This paper presents the kinematic analysis of the 3-PPPS parallel robot with an equi-lateral mobile platform and an equilateral-shaped base. Like the other 3-PPPS robots studied in the literature, it is proved that the parallel…
Autonomous locomotion is a ubiquitous phenomenon in biology and in physics of active systems at microscopic scale. This includes prokaryotic, eukaryotic cells (crawling and swimming) and artificial swimmers. An outstanding feature is the…
We construct five types of polyhedra by generalizing the description of Bricard octahedra and applying the generalizations to polyhedral suspensions. The resulting polyhedra are flexible, are of genus 0, exhibit self-intersections, have…