Related papers: An Overconstrained Vertical Darboux Mechanism
Darboux transformations are non-group type symmetries of linear differential operators. One can define Darboux transformations algebraically by the intertwining relation $ML=L_1M$ or the intertwining relation $ML=L_1N$ in the cases when the…
This work presents the coordinated motion control and obstacle-crossing problem for the four wheel-leg independent motor-driven robotic systems via a model predictive control (MPC) approach based on an event-triggering mechanism. The…
We give a new mechanism for constructing Backlund transformations by using symmetry reduction of differential systems. We then characterize a family of Backlund transformations between Darboux integrable systems where the Backlund…
This paper presents an overview of a design methodology for the optimal synthesis of hybrid mechanisms. Hybrid mechanisms have been defined as multi-degree of freedom systems where the input motions are supplied by different motor types. In…
We study a complex intertwining relation of second order for Schroedinger operators and construct third order symmetry operators for them. A modification of this approach leads to a higher order shape invariance. We analyze with particular…
We express Darboux transformations of discrete polarised curves as parallel sections of discrete connections in the quaternionic formalism. This immediately leads to the linearisation of the monodromy of the transformation. We also consider…
We characterise the kinematic image of the constraint variety of a 2R dyad as a regular ruled quadric in a 3-space that contains a "null quadrilateral". Three prescribed poses determine, in general, two such quadrics. This allows us to…
A selective chronological survey of Darboux transformations as related to supersymmetric quantum mechanics, intertwining operators and inverse scattering techniques is presented. Short comments are appended to each quotation and basic…
A new Darboux transformation is presented for the Hirota-Satsuma coupled KdV system. It is shown that this Darboux transformation can be constructed by means of two methods: Painlev\'{e} analysis and reduction of a binary Darboux…
The work in this article is inspired by a classical problem: the statistical physical properties of a closed polymer loop that is wound around a rod. Historically the preserved topology of this system has been addressed through…
The Darboux transformation operator technique in differential and integral forms is applied to the generalized Schrodinger equation with a position-dependent effective mass and with linearly energy-dependent potentials. Intertwining…
Based on the idea of variable stiffness mechanisms, a variety of such mechanisms is shown in this work. Specifically, 2-DOF parallel kinematic machines equipped with redundant actuators and non-linear springs in the actuated joints are…
The subject of this paper is the optimal design of a parallel mechanism intended for three-axis machining applications. Parallel mechanisms are interesting alternative designs in this context but most of them are designed for three- or…
Here we present the theoretical clarification of possibility of eight Majorana-like modes (quasi-particles which are self-conjugate) close to the experimentally inaccessible Dirac points of a two-dimensional monolayer Dirac system. The…
An asymmetric two-link robot supported atop a flat platform by wheels that roll and pivot freely, but do not slip laterally, will develop forward momentum if the joint between the links is actuated internally. In particular, oscillations in…
Designing an m-bar linkage with a maximal number of assembly modes is important in robot kinematics, and has further applications in structural biology and computational geometry. A related question concerns the number of assembly modes of…
Darboux developed an ingenious algebraic mechanism to construct infinite chains of ''integrable'' second-order differential equations as well as their solutions. After a surprisingly long time, Darboux's results were rediscovered and…
Typical leg exoskeletons employ open-loop kinematic chains with motors placed directly on movable joints; while this design offers flexibility, it leads to increased costs and heightened control complexity due to the high number of degrees…
Two-dimensional quadratic algebras are generalizations of Lie algebras that include the symmetry algebras of 2nd order superintegrable systems in 2 dimensions as special cases. The superintegrable systems are exactly solvable physical…
Exceptional orthogonal polynomials constitute the main part of the bound-state wavefunctions of some solvable quantum potentials, which are rational extensions of well-known shape-invariant ones. The former potentials are most easily built…