Related papers: Hexapods with a small linear span
Human motion taxonomies serve as high-level hierarchical abstractions that classify how humans move and interact with their environment. They have proven useful to analyse grasps, manipulation skills, and whole-body support poses. Despite…
Presented in this paper is the kinematic analysis of a symmetrical three-degree-of-freedom planar parallel manipulator. In opposite to serial manipulators, parallel manipulators can admit not only multiple inverse kinematic solutions, but…
We extend the usual notion of parallel transport along a path to triangulated surfaces. A homotopy of paths is lifted into a fibered category with connection and this defines a functor between the fibers above the boundary paths. These…
A geometric figure is a reptile if it can be dissected into at least two similar copies congruent to each other. We prove that if a trapezoid is a reptile and not a parallelogram, then the length of each base is a linear combination of the…
This work considers the problem of using multiple aerial carriers to hold a cable-suspended load while remaining in periodic motion at all times. Using a novel differential geometric perspective, it is shown that the problem may be recast…
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 group-theoretic method for constructing symmetric isometric embeddings is used to describe all possible four-dimensional surfaces in flat $(1,9)$-dimensional space, whose induced metric is static and spherically symmetric. For such…
The evolute of a curve is the envelope of its normals. In this note we consider a projectively natural discrete analog of this construction: we define projective perpendicular bisectors of the sides of a polygon in the projective plane, and…
Projective geometry provides the preferred framework for most implementations of Euclidean space in graphics applications. Translations and rotations are both linear transformations in projective geometry, which helps when it comes to…
This is a draft of a monograph to appear in the Springer series "Encyclopaedia of Mathematical Sciences", subseries "Invariant Theory and Algebraic Transformation Groups". The subject is homogeneous spaces of algebraic groups and their…
This paper continues a geometric study of Harvey's Complex of Curves, whose ultimate goal is to apply the theory of hyperbolic spaces and groups to algorithmic questions for the Mapping Class Group and geometric properties of Kleinian…
Region based knowledge graph embeddings represent relations as geometric regions. This has the advantage that the rules which are captured by the model are made explicit, making it straightforward to incorporate prior knowledge and to…
The aim of this paper is to present a new six degree-of-freedom (dof) haptic device using two parallel mechanisms. The first one, called orthoglide, provides the translation motions and the second one produces the rotational motions. These…
The paper proposes a novel approach for the geometrical model calibration of quasi-isotropic parallel kinematic mechanisms of the Orthoglide family. It is based on the observations of the manipulator leg parallelism during motions between…
This chapter is dedicated to the so-called cuspidal robots, i.e. those robots that can move from one inverse geometric solution to another without meeting a singular confuguration. This feature was discovered quite recently and has then…
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…
Unlike conventional mechanisms, compliant mechanisms produce the desired deformations by exploiting elastic strain and do not need, therefore, moving parts. The number of degrees of freedom of a conventional mechanism, also called mobility,…
Abstractly, tropical hyperelliptic curves are metric graphs that admit a two-to-one harmonic morphism to a tree. They also appear as embedded tropical curves in the plane arising from triangulations of polygons with all interior lattice…
This paper considers the motion planning problem for multiple tethered planar mobile robots. Each robot is attached to a fixed base by a flexible cable. Since the robots share a common workspace, the interactions amongst the robots, cables,…
In this work, we give parallel transport frame of a curve and we introduce the relations between the frame and Frenet frame of the curve in 4-dimensional Euclidean space. The relation which is well known in Euclidean 3-space is generalized…