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Research Papers

Closed-Form Solution for Constant-Orientation Workspace and Workspace-Based Design of Radially Symmetric Hexapod Robots

[+] Author and Article Information
Mahdi Agheli

Assistant Teaching Professor
Mem. ASME
Department of Mechanical Engineering,
Worcester Polytechnic Institute,
Worcester, MA 01609
e-mail: mmaghelih@wpi.edu

Stephen S. Nestinger

Assistant Professor
Mem. ASME
Department of Mechanical Engineering,
Affiliate, Robotics Engineering Program,
Affiliate, Computer Science Department,
Worcester Polytechnic Institute,
Worcester, MA 01609
e-mail: ssnestinger@wpi.edu

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received October 26, 2013; final manuscript received February 4, 2014; published online April 3, 2014. Assoc. Editor: Yuefa Fang.

J. Mechanisms Robotics 6(3), 031007 (Apr 03, 2014) (13 pages) Paper No: JMR-13-1218; doi: 10.1115/1.4026827 History: Received October 26, 2013; Revised February 04, 2014

The workspace of hexapod robots is a key performance parameter which has attracted the attention of numerous researchers during the past decades. The selection of the hexapod parameters for a desired workspace generally employs the use of numerical methods. This paper presents a general methodology for solving the closed-form constant orientation workspace of radially symmetric hexapod robots. The closed-form solution facilitates hexapod robot design and minimizes numerical efforts with on-line determination of stability and workspace utilization. The methodology can be used for robots with nonsymmetric and nonidentical kinematic chains. In this paper, the methodology is used to derive the closed-form equations of the boundary of the constant-orientation workspace of axially symmetric hexapod robots. Several applications are provided to demonstrate the capability of the presented closed-form solution in design and optimization. An approach for workspace-based design optimization is presented using the provided analytical solution by applying an iterative optimization algorithm to the find optimized structural parameters and an optimized workspace.

Copyright © 2014 by ASME
Topics: Robots , Design
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Figures

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Fig. 1

The Hexapod Robot model. (a) The model of a Hexapod Robot with virtual prismatic legs. (b) The model of a Hexapod Robot as three 2-RPR mechanisms.

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Fig. 2

The procedural flowchart for analytically determining the 3D COW of a hexapod robot

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Fig. 3

The model of a 2-RPR planar parallel mechanism. (a) A model of a 2-RPR planar parallel mechanism. (b) An example COW of a 2-RPR mechanism.

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Fig. 4

The COW is constrained by multiple circles

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Fig. 5

The 2-RPR mechanism with symmetric COW

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Fig. 6

The COW of a 2-RPR mechanism. (a) View of the 2D COW of a 2-RPR mechanism. (b) View of the 3D COW of a revolved 2-RPR mechanism. (c) Isometric view of the 3D COW of a revolved 2-RPR mechanism.

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Fig. 7

The top view of a radially symmetric hexapod robot

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Fig. 8

The top view of a radially symmetric hexapod robot with the three 2-RPR workspaces

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Fig. 9

The summation of the 3D 2-RPR mechanisms before and after the Boolean operation. (a) The union of the 3D COW of the 2-RPR mechanisms. (b) The intersection of the 3D COW of the 2-RPR mechanisms. (c) A top view comparing the intersection workspace with the union workspace. (d) A side view comparing the intersection workspace with the union workspace.

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Fig. 10

The symmetric workspace of a hexapod robot. (a) Top view of the union workspace with the intersection workspace overlayed. (b) Top view of the 3D COW workspace showing the upper surfaces and curves. (c) Perspective view of the 3D COW showing the points pt and p0.

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Fig. 11

An optimized hexapod COW encapsulating the desired cylindrical workspace

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Fig. 12

The lateral COW of the hexapod robot covering the desired workspace

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Fig. 13

The procedural flowchart for determining the optimal structures of hexapod robot for a desired workspace

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Fig. 14

Visualization of the desired cylindrical workspace within the 3D COW of the optimized hexapod robot

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Fig. 15

A maximized 3D COW of a hexapod robot within a desired cylindrical workspace

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Fig. 16

Maximizing the workspace of hexapod robot

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