Manfred Husty

An algorithm for solving the direct kinematics of general Stewart-Gough platforms

In this paper an algorithm for solving the direct kinematics of general Stewart-Gough platforms is introduced. A minimal set of constraint equations obtained by a kinematic mapping to produce ultimately the univariate polynomial of 40th degree is used. The algorithm is illustrated with an example for which the univariate polynomial is computed.

Advances in Robot Kinematics: Analysis and Control

From the Publisher: The book provides a state-of-the-art and recent advances in the area of kinematics of robots and mechanisms. The book consists of about fifty outstanding contributions dedicated to various aspects of kinematic modelling and control, emphasising in particular the kinematics performances of robots and mechanisms, workspace and trajectory analysis, numerical and symbolic computational methods and algorithms, analysis, simulation and optimisation. The book is of interest to researchers, graduate students, and engineers specialising in the kinematics of robots and mechanisms. The book should also be of interest to those engaged in work relating to kinematic chains, mechatronics, mechanism design, biomechanics and intelligent systems.

Algebraic methods in mechanism analysis and synthesis

Algebraic methods in connection with classical multidimensional geometry have proven to be very efficient in the computation of direct and inverse kinematics of mechanisms as well as the explanation of strange, pathological behavior. In this paper, we give an overview of the results achieved within the last few years using the algebraic geometric method, geometric preprocessing, and numerical analysis. We provide the mathematical and geometrical background, like Studys parametrization of the Euclidean motion group, the ideals belonging to mechanism constraints, and methods to solve polynomial equations. The methods are explained with different examples from mechanism analysis and synthesis.

Self-motions of Griffis-Duffy type parallel manipulators

A special type of parallel platform manipulator, proposed by Griffis and Duffy (1993), is investigated. It is shown that a large class among the proposed platform types is architecture singular and admits self motions from every point of its workspace. Using a kinematic image space we compute image curves which correspond to the self motions and discuss several special cases.

Algebraic Geometry and Kinematics

In this overview paper we show how problems in computational kinematics can be translated into the language of algebraic geometry and subsequently solved using techniques developed in this field. The idea to transform kinematic features into the language of algebraic geometry is old and goes back to Study. Recent advances in algebraic geometry and symbolic computation gave the motivation to resume these ideas and make them successful in the solution of kinematic problems. It is not the aim of the paper to provide detailed solutions, but basic accounts to the used tools and examples where these techniques were applied within the last years. We start with Study’s kinematic mapping and show how kinematic entities can be transformed into algebraic varieties. The transformations in the image space that preserve the kinematic features are introduced. The main topic are the definition of constraint varieties and their application to the solution of direct and inverse kinematics of serial and parallel robots. We provide a definition of the degree of freedom of a mechanical system that takes into account the geometry of the device and discuss singularities and global pathological behavior of selected mechanisms. In a short paragraph we show how the developed methods are applied to the synthesis of mechanical devices.

A Special Type of Singular Stewart-Gough Platform

A Stewart-Gough platform, whose base attachment points occupy a particular cubic surface, may exhibit continuous motion while all six prismatic actuators are locked. Line geometric analysis reveals that, during such motion, the six leg axes remain in a specific linear complex, congruence or hyperboloidal ruled surface. Furthermore the pose or direct kinematics of any platform, five of whose leg base attachment points lie in such a cubic surface, is readily obtained and admits no more than four real solutions.

Workspace Analysis of Stewart-Gough-Type Parallel Manipulators

Abstract In this paper, for the first time, a complete analysis of the reachable workspace of a spatial Stewart—Gough platform with planar base and platform (SGPP) is presented. The devised workspace algorithms are applied to a commercial 6–6 design. Major importance is given to the visualization of the results of this workspace analysis to provide fast information to the designer on the overall kinematic behaviour of the designed mechanism. Furthermore, it is shown that the reachable workspace also gives the necessary information on how to construct a building enclosing all motion instances of an actual hexapod design.

Identification of the Workspace Boundary Of a General 3-R Manipulator

In this paper an algebraic formulation is presented for the boundary workspace of 3-R manipulators in Cartesian Space. It is shown that the cross-section boundary curve can be described by a 16th order polynomial as function of radial and axial reaches. The cross-section boundary curve and workspace boundary surface are fully cyclic. Geometric singularities of the curve are identified and characterized. Numerical examples are presented to show the usefulness of the proposed investigation and to classify the design characteristics.

Non-singular assembly mode change in 3-RPR-parallel manipulators

Non singular assembly mode change of parallel manipulators has been discussed for a while within the robotics community. This term means that a parallel robot can pass from one solution of the direct kinematics into another without crossing a singularity. In this paper we will show that opposed to the accepted opinion all general planar 3-RPR parallel manipulators have this ability. Using geometric properties of the singularity surface of this manipulator we will give a rigorous mathematical proof for this proposition. This proof will use the fact that the singularity surface is a fourth order surface having only very special singularities. A secondary result of this proof will be the first proof for the widespread used property that the singularity surface divides the workspace of the manipulator into two aspects that are path connected. We derive a simple technique how to construct singularity free trajectories that join all assembly modes of one connected component.

On Self-Motions of a Class of Parallel Manipulators

In this paper we shall introduce an algorithm to determine self-motions of a special class of platform mechanisms. This class of mechanisms has a geometry that generalizes the geometry of existing flight simulator platforms. The algorithm uses the Study representation of the Lie group of space congruences and the quadratic constaint equation which decribes the condition that a point of the moving system is bound to move on a sphere.