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We elucidate the large-N dynamics of one-dimensional sigma models with spherical and hyperbolic target spaces and find a duality between the Lagrange multiplier and the angular momentum. In the hyperbolic model we propose a new class of…
It is shown that a compound elastic structure, which displays a dynamic instability, may be designed as the union (or 'fusion') of two structures which are stable when separately analyzed. The compound elastic structure has two degrees of…
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…
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,…
We investigate localization properties in a two-coupled uniform chains with quasiperiodic modulation on interchain coupling strength. We demonstrate that this ladder is equivalent to a Aubry-Andre (AA) chain when two legs are symmetric.…
The paper focuses on the stiffness modeling of a new type of compliant manipulator and its non-linear behavior while interacting with the environment. The manipulator under study is a serial mechanical structure composed of dualtriangle…
Recent interest in mobile manipulation has resulted in a wide range of new robot designs. A large family of these designs focuses on modular platforms that combine existing mobile bases with static manipulator arms. They combine these…
This paper describes a new parallel kinematic architecture for machining applications: the orthoglide. This machine features three fixed parallel linear joints which are mounted orthogonally and a mobile platform which moves in the…
We develop parallel transport on path spaces from a differential geometric approach, whose integral version connects with the category theoretic approach. In the framework of 2-connections, our approach leads to further development of…
To design efficient parallel algorithms, some recent papers showed that many sequential iterative algorithms can be directly parallelized but there are still challenges in achieving work-efficiency and high-parallelism. Work-efficiency can…
We use topological techniques to do a workspace analysis of the Canfield Joint, a mechanical linkage constructed with two plates connected by three legs. The Canfield Joint has three degrees of freedom and can be controlled using three…
We introduce moduli spaces of quasi-admissible hyperelliptic covers with at worst A and D singularities. The stability conditions for these moduli spaces depend on two parameters describing allowable singularities. By varying these…
We introduce a one-dimensional quasiperiodic mosaic model with analytically solvable mobility edges that exhibit different phase transitions depending on the system parameters. Specifically, by combining mosaic quasiperiodic…
Kendall shape spaces are a widely used framework for the statistical analysis of shape data arising from many domains, often requiring the parallel transport as a tool to normalise time series data or transport gradient in optimisation…
Serially connected robots are promising candidates for performing tasks in confined spaces such as search-and-rescue in large-scale disasters. Such robots are typically limbless, and we hypothesize that the addition of limbs could improve…
This paper investigates the conditions in the design parameter space for the existence and distribution of the cusp locus for planar parallel manipulators. Cusp points make possible non-singular assembly-mode changing motion, which…
Recent advancements in generalized symmetries have drawn significant attention to gapped phases of matter exhibiting novel symmetries, such as noninvertible symmetries. By leveraging the duality transformations, the classification and…
Constructions and exploration of plane algebraic curves has received a new push with the development of automated methods, whose algorithms are continuously improved and implemented in various software packages. We use them to explore the…
Many systems of interest to control engineering can be modeled by linear complementarity problems. We introduce a new notion of equivalence between linear complementarity problems that sets the basis to translate the powerful tools of…
In robotics, structural design and behavior optimization have long been considered separate processes, resulting in the development of systems with limited capabilities. Recently, co-design methods have gained popularity, where bi-level…