Related papers: Analyse Comparative des Manipulateurs 3R \`a Axes …
The goal of this paper is to explain, using a typical example, the distribution of the different assembly modes in the workspace and their effective role in the execution of trajectories. The singular and non-singular changes of assembly…
We explore the structure of the space of quasisymmetric configurations identifying them by their magnetic axes, described as 3D closed curves. We demonstrate that this topological perspective divides the space of all configurations into…
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…
The orthoglide is a 3-DOF parallel mechanism designed at IRCCyN for machining applications. It features three fixed parallel linear joints which are mounted orthogonally and a mobile platform which moves in the Cartesian x-y-z space with…
With advancing technologies, robotic manipulators and visual environment sensors are becoming cheaper and more widespread. However, robot control can be still a limiting factor for better adaptation of these technologies. Robotic…
We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part (arXiv:2501.15657), we discused…
We consider families of reductive complexes related by level-raising operators and originating from an associative algebra. In the main theorem it is shown that the multiple cohomology of that complexes is given by the factor space of…
In this paper a new asymmetric 3-translational (3T) parallel manipulator, i.e., RPa(3R) 2R+RPa, with zero coupling degree and decoupled motion is firstly proposed according to topology design theory of parallel mechanism (PM) based on…
The configuration manifolds of parallel manipulators exhibit more nonlinearity than serial manipulators. Qualitatively, they can be seen to possess extra folds. By projecting such manifolds onto spaces of engineering relevance, such as an…
Modular reconfigurable manipulators enable quick adaptation and versatility to address different application environments and tailor to the specific requirements of the tasks. Task performance significantly depends on the manipulator's…
Rotation representations are foundational in fields such as computer graphics, robotics, and machine learning, where precise and efficient modeling of 3D orientations is critical. This paper comprehensively investigates diverse…
A quadric in $\R P^3$ cuts a curve of degree 6 on a cubic surface in $\R P^3$. The papers classifies the nonsingular curves cut in this way on non-singular cubic surfaces up to homeomorphism. Two issues new in the study related to the first…
This paper presents a classification of generic 6-revolute jointed (6R) manipulators using homotopy class of their critical point manifold. A part of classification is listed in this paper because of the complexity of homotopy class of…
This paper describes a general algorithm for finding the commensurator of a non-arithmetic cusped hyperbolic manifold, and for deciding when two such manifolds are commensurable. The method is based on some elementary observations regarding…
We consider twelve different ways of modelling the 3-body problem in dimension $\geq 2$. These can be viewed as models of classical and quantum background independence. We show that a different type of monopole is realized in each's…
Redundant parallel robots are normally employed in scenarios requiring good precision, high load capability, and large workspace compared to traditional parallel mechanisms. However, the elementary robotic configuration and geometric…
It has been observed that the very important motion planning problem of robotics mathematically speaking boils down to the problem of finding a section to the path-space fibration, raising the notion of topological complexity, as introduced…
Robotic manipulator applications often require efficient online motion planning. When completing multiple tasks, sequence order and choice of goal configuration can have a drastic impact on planning performance. This is well known as the…
We study topological transitivity/hypercyclicity and topological (weak) mixing for weighted composition operators on locally convex spaces of scalar-valued functions which are defined by local properties. As main application of our general…
Quantum fields are investigated in the (2+1)-open-universes with non-trivial topologies by the method of images. The universes are locally de Sitter spacetime and anti-de Sitter spacetime. In the present article we study spacetimes whose…