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Research Papers

# Parametric Design of a Spherical Eight-Bar Linkage Based on a Spherical Parallel Manipulator

[+] Author and Article Information
Gim Song Soh

Robotics and Automation Laboratory, University of California, Irvine, 3140 Engineering Gateway Building, Irvine, CA 92697gsoh@uci.edu

J. Michael McCarthy

Robotics and Automation Laboratory, University of California, Irvine, 3140 Engineering Gateway Building, Irvine, CA 92697jmmccart@uci.edu

J. Mechanisms Robotics 1(1), 011004 (Jul 30, 2008) (8 pages) doi:10.1115/1.2959093 History: Received May 01, 2008; Revised June 20, 2008; Published July 30, 2008

## Abstract

This paper presents a procedure that determines the dimensions of two constraining links to be added to a three degree-of-freedom spherical parallel manipulator so that it becomes a one degree-of-freedom spherical (8, 10) eight-bar linkage that guides its end-effector through five task poses. The dimensions of the spherical parallel manipulator are unconstrained, which provides the freedom to specify arbitrary base attachment points as well as the opportunity to shape the overall movement of the linkage. Inverse kinematics analysis of the spherical parallel manipulator provides a set of relative poses between all of the links, which are used to formulate the synthesis equations for spherical $RR$ chains connecting any two of these links. The analysis of the resulting spherical eight-bar linkage verifies the movement of the system.

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Copyright © 2008 by American Society of Mechanical Engineers
Topics: Linkages , Chain , Design
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## Figures

Figure 1

The (6, 6) spherical parallel manipulator formed by an end-effector supported by two spherical 3R chains

Figure 2

The 2RRR spherical parallel manipulator formed from two spherical 3R chains is a single loop spherical six-bar chain. The graph of this chain forms a hexagon with a vertex for each link in the manipulator.

Figure 3

There are six ways to add the first RR chain

Figure 4

The linkage graphs show the synthesis sequence for the 17 constrained (6, 6) spherical closed chains in which the two spherical RR chains are attached independently

Figure 5

The linkage graphs show the synthesis sequence for the 15 constrained (6, 6) spherical closed chains in which the second spherical RR chain connects to the first spherical RR chain

Figure 6

The joint angle and link length parameters for the (8, 10) spherical eight-bar linkage

Figure 7

A schematic of the chosen spherical (8, 10) design candidate

Figure 8

The basic kinematic chains of a spherical (8, 10) eight-bar linkage mechanism: the single-loop spherical triangle, the two-loop pentad structure, and types 3a, 3b, and 3c of the three-loop structures. (Figure used with permission from Ref. 15).

Figure 9

The image sequence for the spherical (8, 10) eight-bar linkage reaching a set of five task poses

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