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A spherical wrist of the serial type is said to be isotropic if it can attain a posture whereby the singular values of its Jacobian matrix are all identical and nonzero. What isotropy brings about is robustness to manufacturing, assembly,…

The design of a spherical wrist with parallel architecture is the object of this article. This study is part of a larger project, which aims to design and to build an eel robot for inspection of immersed piping. The kinematic analysis of…

This study presents a systematic enumeration of spherical ($SO(3)$) type parallel robots' variants using an analytical velocity-level approach. These robots are known for their ability to perform arbitrary rotations around a fixed point,…

This work addresses the inverse kinematics of serial robots using conformal geometric algebra. Classical approaches include either the use of homogeneous matrices, which entails high computational cost and execution time or the development…

The aim of this paper is the isotropic design of a hybrid morphology dedicated to 3-axis machining applications. It is necessary to ensure the feasibility of continuous, singularity-free trajectories, as well as a good manipulability in…

In this paper we study rational real algebraic knots in $\R P^3$. We show that two real algebraic knots of degree $\leq5$ are rigidly isotopic if and only if their degrees and encomplexed writhes are equal. We also show that any irreducible…

The singularities of serial robotic manipulators are those configurations in which the robot loses the ability to move in at least one direction. Hence, their identification is fundamental to enhance the performance of current control and…

This paper deals with the in-depth kinematic analysis of a special spherical parallel wrist, called the Agile Eye. The Agile Eye is a three-legged spherical parallel robot with revolute joints in which all pairs of adjacent joint axes are…

Spinning flexible objects, exemplified by traditional Chinese handkerchief performances, demands periodic steady-state motions under nonlinear dynamics with frictional contacts and boundary constraints. To address these challenges, we first…

For every $n \geq 4$, we demonstrate the existence of non-isotopic smooth $(n-2)$-knots in $S^n$ with diffeomorphic traces by generalising the RBG link construction to all dimensions. Conversely, we prove that for every $n \geq 4$, the…

Adding linear combinations $R^2,R_{\mu\nu}R^{\mu\nu}$ and $R_{\mu\nu\eta\delta}R^{\mu\nu\eta\delta}$ with Einstein-Hilbert action we obtain interior metric of an an-isotropic spherically symmetric collapsing (ASSC) stellar cloud. We assume…

A skew brace is a triplet $(A,\cdot,\circ)$, where $(A,\cdot)$ and $(A,\circ)$ are groups such that the brace relation $x\circ (y\cdot z) = (x\circ y)\cdot x^{-1}\cdot (x\circ z)$ holds for all $x,y,z\in A$. In this paper, we study the…

Orthogonal designs and weighing matrices have many applications in areas such as coding theory, cryptography, wireless networking and communication. In this paper, we first show that if positive integer $k$ cannot be written as the sum of…

Let K be a knot in the 3-sphere. A slope p/q is said to be characterising for K if whenever p/q surgery on K is homeomorphic, via an orientation-preserving homeomorphism, to p/q surgery on another knot K' in the 3-sphere, then K and K' are…

This paper introduces ByteWrist, a novel highly-flexible and anthropomorphic parallel wrist for robotic manipulation. ByteWrist addresses the critical limitations of existing serial and parallel wrists in narrow-space operations through a…

We provide a geometric approach to two combinatorically symmmetric overconstrained spatial linkages. Both contain eight bodies and twelve revolute joints and collapse in aligned poses. The first one is spherical and the union of six…

This article presents a new hand architecture with three under-actuated fingers. Each finger performs spatial movements to achieve more complex and varied grasping than the existing planar-movement fingers. The purpose of this hand is to…

We study the Einstein equations of the static spherically symmetric anisotropic fluid system in curvature coordinates to find algorithms that generate all solutions and all solutions that are regular at the center. All possible combinations…

Spherical $t$-designs on $\mathbb{S}^{d}\subset\mathbb{R}^{d+1}$ provide $N$ nodes for an equal weight numerical integration rule which is exact for all spherical polynomials of degree at most $t$. This paper considers the generation of…

Let N(n, t) be the minimal number of points in a spherical t-design on the unit sphere S^n in R^{n+1}. For each n >= 3, we prove a new asymptotic upper bound N(n, t) <= C(n)t^{a_n}, where C(n) is a constant depending only on n, a_3 <= 4,…