Related papers: Singular surfaces and cusps in symmetric planar 3-…
We study invariant surfaces generated by one-parameter subgroups of simply and pseudo isotropic rigid motions. Basically, the simply and pseudo isotropic geometries are the study of a three-dimensional space equipped with a rank 2 metric of…
Parallel kinematic manipulators (PKM) are characterized by closed kinematic loops, due to the parallel arrangement of limbs but also due to the existence of kinematic loops within the limbs. Moreover, many PKM are built with limbs…
3D printing of surfaces has become an established method for prototyping and visualisation. However, surfaces often contain certain degenerations, such as self-intersecting faces or non-manifold parts, which pose problems in obtaining a 3D…
Constraining motion to a flat surface is a fundamental requirement for equipment across science and engineering. Modern precision robotic motion systems, such as gantries, rely on the flatness of components, including guide rails and…
We study the Monotone Sliding Reconfiguration (MSR) problem, in which $\textit{labeled}$ pairwise interior-disjoint objects in a planar workspace need to be brought $\textit{one by one}$ from their initial positions to given target…
This paper demonstrates that any general 3-DOF three-legged planar parallel robot with extensible legs can change assembly modes without passing through parallel singularities (configurations where the mobile platform loses its stiffness).…
A cuspidal robot can move from one inverse kinematics (IK) solution to another without crossing a singularity. Multiple industrial robots are cuspidal. They tend to have a beautiful mechanical design, but they pose path planning challenges.…
Soft robots were introduced in large part to enable safe, adaptive interaction with the environment, and this interaction relies fundamentally on contact. However, modeling and planning contact-rich interactions for soft robots remain…
In this paper we obtain a formula for the number of rational degree d curves in $\mathbb{P}^3$ having a cusp, whose image lies in a $\mathbb{P}^2$ and that passes through $r$ lines and $s$ points (where $r + 2s = 3d + 1$). This problem can…
We study a generalization of constant Gauss curvature -1 surfaces in Euclidean 3-space, based on Lorentzian harmonic maps, that we call pseudospherical frontals. We analyze the singularities of these surfaces, dividing them into those of…
Motion planning techniques for quadrotors have advanced significantly over the past decade. Most successful planners have two stages: a front-end that determines a path that incorporates geometric (or kinematic or input) constraints and…
The Eckardt hypersurface in $\mathbb{P}^{19}$ parameterizes smooth cubic surfaces with an Eckardt point, which is a point common to three of the $27$ lines on a smooth cubic surface. We describe the cubic surfaces lying on the singular…
Parallel robots (PRs) have singular configurations where the robot gains at least one degree of freedom and loses control. Theoretically, such singularity occurs when the Forward Jacobian-matrix determinant becomes zero (Type II). However,…
This paper proposes a new design method to determine the feasible set of parameters of translational or position/orientation decoupled parallel robots for a prescribed singularity-free workspace of regular shape. The suggested method uses…
This paper presents a manipulation planning algorithm for robots to reorient objects. It automatically finds a sequence of robot motion that manipulates and prepares an object for specific tasks. Examples of the preparatory manipulation…
We investigate singularities of all parallel surfaces to a given regular surface. In generic context, the types of singularities of parallel surfaces are cuspidal edge, swallowtail, cuspidal lips, cuspidal beaks, cuspidal butterfly and…
Near kinematic singularities of a serial manipulator, the inverse kinematics (IK) problem becomes ill-conditioned, which poses computational problems for the numerical solution. Computational methods to tackle this issue are based on…
The aim of this paper is to characterize the notion of aspect in the workspace and in the joint space for parallel manipulators. In opposite to the serial manipulators, the parallel manipulators can admit not only multiple inverse kinematic…
In manipulation tasks, a robot interacts with movable object(s). The configuration space in manipulation planning is thus the Cartesian product of the configuration space of the robot with those of the movable objects. It is the complex…
We study K3 surfaces with 9 cusps, i.e. 9 disjoint $A_2$ configurations of smooth rational curves, over algebraically closed fields of characteristic $p\neq 3$. Much like in the complex situation studied by Barth, we prove that each such…