Related papers: An algebraic study of linkages with helical joints
We provide a complete classification of paradoxical closed-loop $n$-linkages, where $n\geq6$, of mobility $n-4$ or higher, containing revolute, prismatic or helical joints. We also explicitly write down strong necessary conditions for…
We address the question of identifying non-smooth points in affine real algebraic varieties. A simple algebraic criterion will be formulated and proven. As an application we can answer several questions about the configuration spaces of…
A linkage mechanism consists of rigid bodies assembled by joints which can be used to translate and transfer motion from one form in one place to another. In this paper, we are particularly interested in a family of spacial linkage…
The algebras for all possible Lorentzian and Euclidean kinematics with $\frak{so}(3)$ isotropy except static ones are re-classified. The geometries for algebras are presented by contraction approach. The relations among the geometries are…
The configuration space of a mechanical linkage, consisting of rigid bodies moving in space constrained by joints, is defined by algebraic conditions. If these equations do not define a complete intersection, then the dimension of the…
A close relationship between the classical Hamilton-Jacobi theory and the kinematic reduction of control systems by decoupling vector fields is shown in this paper. The geometric interpretation of this relationship relies on new…
It has become obvious that certain singular phenomena cannot be explained by a mere investigation of the configuration space, defined as the solution set of the loop closure equations. For example, it was observed that a particular 6R…
This paper details an accessible geometric derivation of the forward and inverse kinematics of a parallel robotic linkage known as the Canfield joint, which can be used for pointing applications. The original purpose of the Canfield joint…
The complete classification of hexapods - also known as Stewart Gough platforms - of mobility one is still open. To tackle this problem, we can associate to each hexapod of mobility one an algebraic curve, called the configuration curve. In…
We extend the equations of motion that describe non-relativistic elastic collision of two particles in one dimension to an arbitrary associative algebra. Relativistic elastic collision equations turn out to be a particular case of these…
Many researchers tried to understand/explain the geometric reasons for paradoxical mobility of a mechanical linkage, i.e. the situation when a linkage allows more motions than expected from counting parameters and constraints. Bond theory…
Courant algebroids provide a useful mathematical tool (not only) in string theory. It is thus important to define and examine their morphisms. To some extent, this was done before using an analogue of canonical relations known from…
In this paper we propose an algebraic formalization of connectors in the quantitative setting, in order to address their non-functional features in architectures of component-based systems. We firstly present a weighted Algebra of…
We present an analytical solution for the inverse kinematics (IK) of a robotic arm with one prismatic joint and four revolute joints. This 5-DoF design is a result of minimizing weight while preserving functionality of the device in a…
This paper presents a motion analysis framework for an athlete wearing sport-specific flexible prosthesis based on the soft-rigid hybrid-link system. Such a motion analysis is a challenging problem because we need to consider the…
Screw theory provides geometrical insight into the mechanics of rigid bodies. Screw axis is defined as the line coinciding with the joint axis. Line transformations in the form of a screw operator are used to determine the joint axes of a…
Relational lattice is a formal mathematical model for Relational algebra. It reduces the set of six classic relational algebra operators to two: natural join and inner union. We continue to investigate Relational lattice properties with…
It is shown that any dynamic equation on a configuration bundle $Q\to R$ of non-relativistic time-dependent mechanics is associated with connections on the affine jet bundle $J^1Q\to Q$ and on the tangent bundle $TQ\to Q$. As a consequence,…
In this paper, we present a novel kinematic model of the human phalanges based on the elliptical motion of their joints. The presence of the soft elastic tissues and the general anatomical structure of the hand joints highly affect the…
In the present paper we investigate the noncommutative geometry of a class of algebras, called the Hom-associative algebras, whose associativity is twisted by a homomorphism. We define the Hochschild, cyclic, and periodic cyclic homology…