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Research Papers

A Task-Driven Unified Synthesis of Planar Four-Bar and Six-Bar Linkages With R- and P-Joints for Five-Position Realization

[+] Author and Article Information
Ping Zhao

School of Mechanical and Automotive Engineering,
Hefei University of Technology,
Hefei, Anhui 230009, China
e-mail: ping.zhao@hfut.edu.cn

Xiangyun Li

School of Mechanical Engineering,
Southwest Jiaotong University,
Chengdu, Sichuan 610031, China

A. Purwar, Q. J. Ge

Department of Mechanical Engineering,
Stony Brook University,
Stony Brook 11794-2300, NY

1Corresponding author.

Manuscript received December 10, 2015; final manuscript received April 14, 2016; published online June 10, 2016. Assoc. Editor: Hai-Jun Su.

J. Mechanisms Robotics 8(6), 061003 (Jun 10, 2016) (8 pages) Paper No: JMR-15-1337; doi: 10.1115/1.4033434 History: Received December 10, 2015; Revised April 14, 2016

This paper deals with the problem of integrated joint type and dimensional synthesis of planar four-bar and six-bar linkages, which could contain both revolute (R) and prismatic (P) joints, for guiding through five specified task positions of the end-effector. In a recent work, we developed a simple algorithm for analyzing a set of given task positions to determine all feasible planar dyads with revolute and/or prismatic joints that can be used to guide through the given positions. This paper extends this algorithm to the integrated joint type and dimensional synthesis of Watt I and II and Stephenson I, II, and III six-bar linkages that contain both R- and P-joints. In the process, we developed a new classification for planar six-bar linkages according to whether the end-effector can be constrained by two dyads (type I), one dyad (type II), or no dyad (type III). In the end, we demonstrate this task-driven synthesis approach with three examples including a novel six-bar linkage for lifting an individual with age disability from seating position to standing position.

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Figures

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Fig. 1

Three types of linkages constrained by two dyads

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Fig. 2

Four types of Stephenson six-bar linkages. The end-effector (link 3) is constrained by one dyad.

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Fig. 3

Two types of Watt I six-bar linkages for each choice of a triad. The end-effector (link 4) is not constrained by any dyad.

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Fig. 4

A planar displacement of a moving frame M with respect to the fixed frame F

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Fig. 5

Coupling of two constraint manifolds (RR open-chain) in image space, where each intersection curve represents one circuit/assembly mode of the resulting RRRR four-bar linkage, and the task positions are converted to a set of image points

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Fig. 6

Example 1: Four circle constraints defining four RR dyads

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Fig. 7

Example 2: Two six-bar linkages obtained by constraining a five-bar chain with an additional link connecting to the ground: a Stephenson IIIa six-bar linkage with no P-joint (a) and one P-joint (b),

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Fig. 8

Example 3: The synthesized six-bar linkage for the generation of STS motion at the third task position

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Fig. 9

Example 3: The sit-and-stand six-bar linkage at task positions 1 and 2 (top) and 4 and 5 (bottom)

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Fig. 10

Example 3: The sketch for the prototype that employs the six-bar linkages designed in Fig. 8, with position 4 (Fig. 9) being realized

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