Related papers: Position Equations of a 3RPR Planar Manipulator
Using deformations inspired by relativistic considerations and phase space symmetry, we deform the position and momentum operators in one dimension. The resulting algebra is shown to yield the q-oscillator algebra in one limiting case and…
This paper proposes a new design method to determine the feasible set of parameters of translational or position/orientation decoupled parallel robots for a prescribed singularity-free workspace of regular shape. The suggested method uses…
In analogy with the well-known 2-linkage tractor-trailer problem, we define a 2-linkage problem in the plane with novel non-holonomic ``no-slip'' conditions. Using constructs from sub-Riemannian geometry, we look for geodesics corresponding…
We consider a hierarchy of many particle systems on the line with polynomial potentials separable in parabolic coordinates. Using the Lax representation, written in terms of $2\times 2$ matrices for the whole hierarchy, we construct the…
Boundary value problem for a fractional power of an elliptic operator is considered. An integral representation by means of a standard solution problem for parabolic equations is used to solve such problems. Quadrature generalized…
This paper investigates the stabilization of a coupled system comprising a parabolic PDE and an elliptic PDE with nonlinear terms. A rigorous backstepping design provides an explicit boundary control law and exponentially convergent…
The representations of position and momentum operators of a planar phase space having both position and momentum noncommutativity are obtained. Using these representations the dynamics of a particle in a gravitational quantum well is…
Workspace and joint space analysis are essential steps in describing the task and designing the control loop of the robot, respectively. This paper presents the descriptive analysis of a family of delta-like parallel robots by using…
We use a semi-numerical method to find the position and period of periodic orbits in a bisymmetrical potential, made up of a two dimensional harmonic oscillator, with an additional term of a Plummer potential, in a number of resonant cases.…
This article synthezises the most important results on the kinematics of cuspidal manipulators i.e. nonredundant manipulators that can change posture without meeting a singularity. The characteristic surfaces, the uniqueness domains and the…
In this work, we present a manipulation planning algorithm for a robot to keep an object stable under changing external forces. We particularly focus on the case where a human may be applying forceful operations, e.g. cutting or drilling,…
The configuration space of the mechanism of a planar robot is studied. We consider a robot which has $n$ arms such that each arm is of length 1+1 and has a rotational joint in the middle, and that the endpoint of the $k$-th arm is fixed to…
Continuum parallel robots (CPR) combine rigid actuation mechanisms with multiple elastic rods in a closed-loop topology, making forward statics challenging when rigid--continuum junctions are enforced by explicit kinematic constraints. Such…
The Gauss map of non-degenerate surfaces in the three-dimensional Minkowski space are viewed as dynamical fields of the two-dimensional O(2,1) Nonlinear Sigma Model. In this setting, the moduli space of solutions with rotational symmetry is…
We study the Wigner function of phase-locked nondegenerate optical parametric oscillator and find the signatures of both phase-locking and self-pulsing phenomena in phase space. We also analyze the problem of continuous-variable…
We study spherically symmetric spacetimes for matter distributions with isotropic pressures. We generate new exact solutions to the Einstein field equations which also contains isotropic pressures. We develop an algorithm that produces a…
This thesis studies instabilities and singularities in a geometrical approach to the planar 3-body problem as well as instabilities, chaos and ergodicity in the 3-rotor problem. Trajectories of the planar 3-body problem are expressed as…
This article surveys modularity, level raising and level lowering questions for two-dimensional representations modulo prime powers of the absolute Galois group of the rational numbers. It contributes some new results and describes…
In this paper we discuss the relationship between the moving planes of a rational parametric surface and the singular points on it. Firstly, the intersection multiplicity of several planar curves is introduced. Then we derive an equivalent…
In the paper, some geometric properties of the plane interception curve defined by a nonlinear ordinary differential equation are discussed. Its parametric representation is used to find the limits of some triangle elements associated with…