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Research Papers

# Type Synthesis of Two-Degrees-of-Freedom 3-4R Parallel Mechanisms With Both Spherical Translation Mode and Sphere-on-Sphere Rolling Mode

[+] 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

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received June 21, 2014; final manuscript received October 24, 2014; published online April 6, 2015. Assoc. Editor: J. M. Selig.

J. Mechanisms Robotics 7(4), 041018 (Nov 01, 2015) (8 pages) Paper No: JMR-14-1143; doi: 10.1115/1.4029118 History: Received June 21, 2014; Revised October 24, 2014; Online April 06, 2015

## Abstract

Parallel manipulators (PMs) with multiple operation modes are novel reconfigurable PMs, which use less number of actuators and can be reconfigured without disassembly. This paper deals with the type synthesis of 2-DOF (degrees-of-freedom) PMs with both spherical translation mode and sphere-on-sphere rolling mode. A spherical translation is the 2-DOF spatial translation under which the trajectory of any point on the moving link is a sphere. A sphere-on-sphere rolling refers to the rolling of a sphere without slipping and spinning on another sphere of the same diameter. At first, a 2-DOF 3-4R overconstrained PM is proposed based on an existing 5-DOF US equivalent PM. From this 2-DOF PM, we further obtain a 3-4R PM for sphere-on-sphere rolling and a 3-4R PM for spherical translation. By finding the common conditions for the 2-DOF 3-4R PM for spherical translation and 2-DOF 3-4R PM for sphere-on-sphere rolling, the types of 2-DOF 3-4R PMs with both spherical translation mode and sphere-on-sphere rolling mode are then obtained. The 2-DOF 3-4R PMs with both spherical translation mode and sphere-on-sphere rolling mode fall into two classes. In one class of PMs with both spherical translation mode and sphere-on-sphere rolling mode, the moving platform has four instantaneous DOF in a transition configuration. In another class of PMs with both spherical translation mode and sphere-on-sphere rolling mode, the moving platform has at most three instantaneous DOF in a transition configuration. This work enriches the types of PMs with multiple operation modes and overconstrained mechanisms.

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## Figures

Fig. 1

2-DOF sphere-on-sphere rolling

Fig. 2

Leg-wrench systems of two legs: (a) leg with a 2-ζ0-system, and (b) leg with a 1-ζ∞-1-ζ0-system

Fig. 3

Type synthesis of a 2-DOF 3-4R PM: (a) 3-5R US = PM, and (b) 2-DOF 3-4R PM

Fig. 4

2-DOF 3-4R PM for sphere-on-sphere rolling

Fig. 5

2-DOF 3-4R PM for spherical translation

Fig. 6

Legs for PMs with both spherical translation mode and sphere-on-sphere rolling mode (in a transition configuration): (a) case 1, (b) case 2, (c) case 3, (d) case 4, and (e) case 5

Fig. 7

Two PMs with both spherical translation mode and sphere-on-sphere rolling mode at a transition configuration: (a) case 1 and (b) case 2

Fig. 8

Reconfiguration of case 1 of PM with both spherical translation mode and sphere-on-sphere rolling mode: (a) sphere-on-sphere rolling operation mode, (b) transitional configuration, and (c) spherical translation mode

Fig. 9

Reconfiguration of case 2 of PM with both spherical translation mode and sphere-on-sphere rolling mode: (a) sphere-on-sphere rolling operation mode, (b) transitional configuration, and (c) spherical translation mode

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