Workspace variation of a hexapod machine tool

Conti, Joseph P.; Clinton, Charles M.; Zhang, Guangming; Wavering, Albert J.

doi:10.6028/nist.ir.6135

Cited by 21 publications

(8 citation statements)

References 9 publications

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“…The consistency of the results given above was corroborated by the use of a discretization method, similar to the one that was first introduced in Conti et al (1996), that was developed in MATLAB code. We computed, in a spherical coordinate system for a given orientation Q, the corresponding constantorientation workspace (minimum and maximum spheres corresponding to the singularity locus of type I), which is located inside the critical singularity surface described by eq.…”

Section: Graphical Representation Of the Singularity Surfacesmentioning

confidence: 66%

Singularity Analysis of a Three-Leg Six-Degree-of-Freedom Parallel Platform Mechanism Based on Grassmann Line Geometry

Monsarrat

Gosselin

2001

The International Journal of Robotics Research

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This paper addresses the determination of the singularity loci of a six-degree-of-freedom spatial parallel platform mechanism of a new type that can be statically balanced. The mechanism consists of a base and a mobile platform that are connected by three legs using five-bar linkages. A general formulation of the Jacobian matrix is first derived that allows one to determine the Plücker vectors associated with the six input angles of the architecture. The linear dependencies between the corresponding lines are studied using Grassmann line geometry, and the singular configurations are presented using simple geometric rules. It is shown that most of the singular configurations of the three-leg six-degree-of-freedom parallel manipulator can be reduced to the generation of a general linear complex. Expressions describing all the corresponding singularities are then obtained in closed form. Thus, it is shown that for a given orientation of the mobile platform, the singularity locus corresponding to the general complex is a quadratic surface (i.e., either a hyperbolic, a parabolic, or an elliptic cylinder) oriented along the z-axis. Finally, three-dimensional representations that show the intersection between the singularity loci and the constant-orientation workspace of the mechanism are given.

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Section: Graphical Representation Of the Singularity Surfacesmentioning

confidence: 66%

Singularity Analysis of a Three-Leg Six-Degree-of-Freedom Parallel Platform Mechanism Based on Grassmann Line Geometry

Monsarrat

Gosselin

2001

The International Journal of Robotics Research

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“…The complicated structures of six degrees of freedom PKMs made it difficult to achieve significant results. Various methods to estimate and measure the workspace were also suggested [3][4][5][6], and workspace optimization with objective to achieve a wellshaped and large workspace is also attempted [7].…”

Section: Introductionmentioning

confidence: 99%

Optimal Design for Improved Hybrid Kinematic Machine Tools Structures

Harib¹,

Ullah

Moustafa³

2013

Procedia CIRP

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The structures of machine tools used nowadays require improvement for achieving the sustainability of manufacturing in terms of functionality, cost, and energy consumption. This study deals with the optimal design problem formulation for improving the kinematic design of machine tools having hybrid kinematic structures (i.e., structures having both serial and parallel kinematic mechanisms). The solutions for overcoming such challenges as 1) size of workspace, 2) shape of workspace, 3) enhancement of dexterity, and 4) compactness of the machine are presented. The mobility of over-constrained parallel and hybrid kinematic structures is also discussed. Throughout the article, examples are cited for the sake of better understanding.

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“…For the hexapod-based DZCS (without bearing), the rotation angle α could be worked out as a function of the length variation of the six actuators between the two faces and the hexapod's constructive constants (e.g., leg separation), cf. Conti et al (1998).…”

mentioning

confidence: 99%

Expected accuracy of tilt measurements on a novel hexapod-based digital zenith camera system: a Monte-Carlo simulation study

Hirt

Papp

Pál

et al. 2014

Meas. Sci. Technol.

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Digital Zenith Camera Systems (DZCS) are dedicated astronomical-geodetic measurement systems for the observation of the direction of the plumb line. A DZCS key component is a pair of tilt meters for the determination of the instrumental tilt with respect to the plumb line.Highest accuracy (i.e., 0.1 arc-seconds or better) is achieved in practice through observation with precision tilt meters in opposite faces (180° instrumental rotation), and application of rigorous tilt reduction models. A novel concept proposes the development of a hexapod (Stewart platform)-based DZCS. However, hexapod-based total rotations are limited to about 30° to 60° in azimuth (equivalent to ±15° to ±30° yaw rotation), which raises the question of the impact of the rotation angle between the two faces on the accuracy of the tilt measurement. The goal of the present study is the investigation of the expected accuracy of tilt measurements to be carried out on future hexapod-based DZCS, with special focus placed on the role of the limited rotation angle. A Monte-Carlo simulation study is carried out in order to derive accuracy estimates for the tilt determination as a function of several input parameters, and the results are validated against analytical error propagation. As main result of the study, limitation of the instrumental rotation to 60° (30°) deteriorates the tilt accuracy by a factor of about 2 (4) compared to a 180° rotation between the faces. Nonetheless, a tilt accuracy at the 0.1 arc-second level is expected when the rotation is at least 45°, and 0.05 arcsecond (about 0.25 microradian) accurate tilt meters are deployed. As such, a hexapod-based DZCS can be expected to allow sufficiently accurate determination of the instrumental tilt.This provides supporting evidence for the feasibility of such a novel instrumentation. The outcomes of our study are not only relevant to the field of DZCS, but also to all other types of instruments where the instrumental tilt must be corrected. Examples include electronic theodolites or total stations, gravity meters, and other hexapod-based telescopes.

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Workspace variation of a hexapod machine tool

Cited by 21 publications

References 9 publications

Singularity Analysis of a Three-Leg Six-Degree-of-Freedom Parallel Platform Mechanism Based on Grassmann Line Geometry

Singularity Analysis of a Three-Leg Six-Degree-of-Freedom Parallel Platform Mechanism Based on Grassmann Line Geometry

Optimal Design for Improved Hybrid Kinematic Machine Tools Structures

Expected accuracy of tilt measurements on a novel hexapod-based digital zenith camera system: a Monte-Carlo simulation study

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