相关论文: Solving the Forward Position Problem of an In-Para…

We study parametric equations, which describe the position of an in-parallel planar manipulator. We discuss isometries in the Gauss plane, then we write the loop-closure equations in terms of the rotations as the parameters.

This paper investigates the cuspidal configurations of 3-RPR parallel manipulators that may appear on their singular surfaces in the joint space. Cusp points play an important role in the kinematic behavior of parallel manipulators since…

This paper investigates singular configurations of planar 3-RPR parallel manipulators, which result from applying the averaging technique to solution pairs of their direct kinematic problem. Without computing the zeros of the corresponding…

A class of analytic planar 3-RPR manipulators is analyzed in this paper. These manipulators have congruent base and moving platforms and the moving platform is rotated of 180 deg about an axis in the plane. The forward kinematics is reduced…

Recursive modelling for the kinematics of a 3-PRP planar parallel robot is presented in this paper. Three planar chains connecting to the moving platform of the manipulator are located in a vertical plane. Knowing the motion of the…

The aim of this paper is the kinematic study of a 3-RPR planar parallel manipulator where the three fixed revolute joints are actuated. The direct and inverse kinematic problem as well as the singular configuration is characterized. On…

Recursive matrix relations for the complete dynamics of a 3-PRP planar parallel robot are established in this paper. Three identical planar legs connecting to the moving platform are located in the same vertical plane. Knowing the motion of…

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 propose an effective method for solving the inverse kinematic problem of a specific model of 6-degree-of-freedom (6-DOF) robot manipulator using computer algebra. It is known that when the rotation axes of three consecutive rotational…

This paper investigates two situations in which the forward kinematics of planar 3-RPR parallel manipulators degenerates. These situations have not been addressed before. The first degeneracy arises when the three input joint variables r1,…

Computations over the rational numbers often encounter the problem of intermediate coefficient growth. A solution to this is provided by modular methods, which apply the algorithm under consideration modulo a number of primes and then lift…

This paper presents an advanced method for addressing the inverse kinematics and optimal path planning challenges in robot manipulators. The inverse kinematics problem involves determining the joint angles for a given position and…

We apply the theory of Groebner bases to the study of signed, symmetric polyomino tilings of planar domains. Complementing the results of Conway and Lagarias we show that the triangular regions T_N=T_{3k-1} and T_N=T_{3k} in a hexagonal…

This work aims to accelerate the convergence of proximal gradient methods used to solve regularized linear inverse problems. This is achieved by designing a polynomial-based preconditioner that targets the eigenvalue spectrum of the normal…

This paper introduces a methodology to analyze geometrically the singularities of manipulators, of which legs apply both actuation forces and constraint moments to their moving platform. Lower-mobility parallel manipulators and parallel…

Planar polynomial automorphisms are polynomial maps of the plane whose inverse is also a polynomial map. A map is reversible if it is conjugate to its inverse. Here we obtain a normal form for automorphisms that are reversible by an…

We develop the theory of Gr\"obner bases for ideals in a polynomial ring with countably infinite variables over a field. As an application we reconstruct some of the one-one correspondences among various sets of partitions by using division…

This paper presents an algorithm for detecting and computing the cusp points in the joint space of 3-RPR planar parallel manipulators. In manipulator kinematics, cusp points are special points, which appear on the singular curves of the…

We study in this paper a class of 3-RPR manipulators for which the direct kinematic problem (DKP) is split into a cubic problem followed by a quadratic one. These manipulators are geometrically characterized by the fact that the moving…

A Maple package for computing Groebner bases of linear difference ideals is described. The underlying algorithm is based on Janet and Janet-like monomial divisions associated with finite difference operators. The package can be used, for…