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Research Papers

Reconfiguration Analysis of a Two Degrees-of-Freedom 3-4R Parallel Manipulator With Planar Base and Platform1

[+] Author and Article Information
Xianwen Kong

School of Engineering and Physical Sciences,
Heriot-Watt University,
Edinburgh EH14 4AS, UK
e-mail: X.Kong@hw.ac.uk

Jingjun Yu

Robotics Institute,
School of Mechanical Engineering
and Automation,
Beihang University,
Beijing 100191, China
e-mail: jjyu@buaa.edu.cn

Duanling Li

Automation School,
Beijing University of Posts
and Telecommunications,
Beijing 100876, China
e-mail: liduanling@163.com

2Corresponding author.

Manuscript received April 4, 2015; final manuscript received July 1, 2015; published online August 18, 2015. Assoc. Editor: Federico Thomas.

J. Mechanisms Robotics 8(1), 011019 (Aug 18, 2015) (7 pages) Paper No: JMR-15-1081; doi: 10.1115/1.4031027 History: Received April 04, 2015

This paper deals with a 2-DOF (degrees-of-freedom) 3-4R parallel manipulator (PM) with planar base and platform—a novel PM with multiple operation modes (or disassembly free reconfigurable PM) that can use the minimum number of actuated joints. At first, a set of constraint equations of the 3-4R PM are derived with the orientation of the moving platform represented using a Euler parameter quaternion (also Euler–Rodrigues quaternion) and then solved using the algebraic geometry method. It is found that this 3-4R PM has six 2-DOF operation modes, including the two expected spherical translation mode and sphere-on-sphere rolling mode when the PM was synthesized. The motion characteristics of the moving platform are obtained using the kinematic interpretation of Euler parameter quaternions with certain number of constant zero components, which was presented in a recent paper by the first author of this paper, instead of the eigenspace-based approach in the literature. The transition configurations, which are constraint singular configurations, among different operation modes are also presented. This work provides a solid foundation to the development and control of the 2-DOF 3-4R PM with both 2-DOF spherical translation mode and 2-DOF sphere-on-sphere rolling mode.

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Figures

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Fig. 1

2-DOF sphere-on-sphere rolling [3]

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Fig. 2

A 2-DOF 3-4R PM with planar base and platform

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Fig. 3

3-4R PM undergoing 2-DOF spherical translation: (a) operation mode 1 and (b) operation mode 2

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Fig. 4

3-4R PM undergoing 2-DOF planar motion mode: (a) operation mode 3 and (b) operation mode 4

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Fig. 5

3-4R PM undergoing 2-DOF sphere-on-sphere rolling: (a) operation mode 5 and (b) operation mode 6

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Fig. 6

The reconfiguration of a 2-DOF 3-4R PM between operation modes 1 and 6: (a) operation mode 1: spherical translation mode, (b) transitional configuration, and (c) operation mode 6: sphere-on-sphere rolling mode

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