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Research Papers

A Family of Rotational Parallel Manipulators With Equal-Diameter Spherical Pure Rotation

[+] Author and Article Information
Kang Wu

Robotics Institute,
Beihang University,
Beijing 100191, China
e-mail: wukangjk@gmail.com

Jingjun Yu

Robotics Institute,
Beihang University,
Beijing 100191, China
e-mail: jjyu@buaa.edu.cn

Guanghua Zong

Robotics Institute,
Beihang University,
Beijing 100191, China
e-mail: ghzong@buaa.edu.cn

Xianwen Kong

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

1Corresponidng author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received July 6, 2013; final manuscript received September 20, 2013; published online December 27, 2013. Assoc. Editor: Yuefa Fang.

J. Mechanisms Robotics 6(1), 011008 (Dec 27, 2013) (10 pages) Paper No: JMR-13-1127; doi: 10.1115/1.4025860 History: Received July 06, 2013; Revised September 20, 2013

In this work, a family of two degrees of freedom (2-DOF) rotational parallel manipulators (RPMs) with an equal-diameter spherical pure rotation (ESPR) is presented and discussed systematically. The theoretical models of both kinematics and constraints inherited in the manipulators are analyzed through a graphical approach. Based on the established constraint model, these 2-DOF ESPR RPMs are classified into three types according to their compositions of constraint spaces and several novel parallel manipulators are illustrated correspondingly. Finally, two common necessary geometric conditions satisfied for these manipulators are discussed in details with examples. The two conditions will be helpful for engineers with designing ESPR RPMs. Moreover, as one characteristic existing in the ESPR RPMs, two cases of self-rotations accompanying revolutions around fixed axes are revealed. As a result, the corresponding loci of points in the moving platform are proved to be compositions of two subrotations, which are spatial curves and surfaces rather than spherical curves and surfaces.

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Figures

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Fig. 1

A kinematic model of two equal-diameter hemispheroids generating a 2-DOF ESPR

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Fig. 2

Reciprocal diagram of constraint lines and freedom lines in 2-DOF rotational mechanisms with an equal-diameter spherical pure rotational motion: (a) constraints and freedoms of the manipulator model; (b) geometrical relationship between constraints lines and freedom lines; (c) equivalent constraints

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Fig. 3

Two novel 2-DOF ESPR RPMs with centro-symmetric structures: (a) 1-SS&3-CRC; (b) 1-SS&3-URU

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Fig. 4

A novel 2-DOF ESPR RPM with hybrid limbs (1-RRRR&2-RSR)

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Fig. 5

A 3-RRRR ESPR RPM with different link length: (a) an isosceles triangle formed by the first limb; (b) isometric view of the novel manipulator with three different isosceles triangles

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Fig. 6

Two 1-US&3-RSR ESPR RPMs with different link lengths (nonoverconstrained). Geometric conditions for Type C.

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Fig. 7

Two 1-RRRR&2-RSR ESPR RPMs with different link length (nonoverconstrained)

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Fig. 8

1-DOF ESPR around a fixed axis X: (a) isometric view; (b) projective view in plane YO1Z

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Fig. 9

1-DOF ESPR around axis Z with an incline angle θ: (a) isometric view; (b) projective view in plane YO1Z

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Fig. 10

Loci of point A: (a) locus of motion in case I; (b) locus of motion in case II; (c) complete workspace

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