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Research Papers

Mobility and Singularity Analysis of a Class of Two Degrees of Freedom Rotational Parallel Mechanisms Using a Visual Graphic Approach

[+] Author and Article Information
Jingjun Yu

Xin Dong, Xu Pei

Robotics Institute,  Beihang University, Beijing 100191, China

Xianwen Kong

School of Engineering and Physical Sciences,  Heriot-Watt University Edinburgh, EH14 4AS, UKX.Kong@hw.ac.uk

J. Mechanisms Robotics 4(4), 041006 (Sep 17, 2012) (10 pages) doi:10.1115/1.4007410 History: Received May 23, 2011; Revised April 18, 2012; Published September 17, 2012; Online September 17, 2012

In this paper, a visual graphic approach is presented for the mobility and singularity analysis of mechanisms with no helical pair. The presented method is established upon the reciprocal screw system theory. Using the visual graphic approach, the mobility and singularity analysis mainly requires applying a few simple rules and involves into no formula derivation. As a case study, the mobility and singularity analysis is implemented for a class of two degrees of freedom (DOF) rotational parallel mechanisms (RPMs), including the Omni-Wrist III with four limbs and its two derived architectures with three limbs called the T-type and Δ-type RPMs. The Δ-type one is found to has kinematic properties close to the Omni-Wrist III.

Copyright © 2012 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Three screw systems in a parallel mechanism [10]

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Figure 2

A rotational freedom line

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Figure 3

A translational freedom couple

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Figure 4

Kinematic chains and their freedom pattern

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Figure 5

A constraint force line

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Figure 6

A constraint torque

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Figure 7

Constraint patterns corresponding to the kinematic chains in Fig. 4

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Figure 8

FCCPs corresponding to kinematic chains in Fig. 3

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Figure 9

Flowchart of mobility analysis process

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Figure 10

Two lines intersecting at a point are independent

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Figure 11

Three lines coinciding with a point are independent

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Figure 12

A couple (torque) and a perpendicular line are equivalent to two parallel lines

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Figure 13

Only three of four lines on the two planes are independent

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Figure 14

Schematic diagram of the Omni-Wrist III

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Figure 15

Schematic diagram of two derived 2-DOF RPMs

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Figure 16

The freedom lines of limb 1 in the Omni-Wrist III

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Figure 17

The FCCP of one limb in the Omni-Wrist III

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Figure 18

The FCCP of Omni-Wrist III at its initial position

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Figure 19

The FCCP of Omni-Wrist III at a special position

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Figure 20

The FCCP of the Omni-Wrist III at a random position

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Figure 21

FCCP of the mechanism at its two special positions

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Figure 22

FCCP of T-type variant at its general configuration

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Figure 23

FCCP of T-type RPM at it special positions

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Figure 24

FCCP of Δ-type RPM at its general position

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Figure 25

CAD model of the Δ-type RPM

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Figure 26

2-4R kinematic chain and its corresponding FCCP

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