Mobility of Single-Loop N-Bar Linkage With Active/Passive Prismatic Joints

[+] Author and Article Information
W. Z. Guo1

School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai, P.R.C. 200240wzguo@sjtu.edu.cn

R. Du

Department of Automation and Computer Aided Engineering, The Chinese University of Hong Kong, Shatin, N. T. Hong Kong, P.R.C.


Corresponding author.

J. Mech. Des 128(6), 1261-1271 (Dec 30, 2005) (11 pages) doi:10.1115/1.2337315 History: Received July 10, 2005; Revised December 30, 2005

Single-loop N-bar linkages that contain one prismatic joint are common in engineering. This type of mechanism often requires complicated control and, hence, understanding its mobility is very important. This paper presents a systematic study on the mobility of this type of mechanism by introducing the concept of virtual link. It is found that this type of mechanism can be divided into three categories: Class I, Class II, and Class III. For each category, the slide reachable range is cut into different regions: Grashof region, non-Grashof region, and change-point region. In each region, the rotation range of the revolute joint or rotatability of the linkage can be determined based on Ting’s criteria. The characteristics charts are given to describe the rotatability condition. Furthermore, if the prismatic joint is an active joint, the revolvability of the input revolute joint is dependent in non-Grashof region but independent in other regions. If the prismatic joint is a passive joint, the revolvability of the input revolute joint is dependent on the offset distance of the prismatic joint. Two examples are given to demonstrate the presented method. The new method is able to cover all the cases of N-bar planar linkages with one or a set of adjoined prismatic joints. It can also be used to study N-bar open-loop planar robotic mechanisms.

Copyright © 2006 by American Society of Mechanical Engineers
Topics: Linkages
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Figure 1

Illustration of single-loop N-bar linkages with one P joint. The presented theory works on both cases, though, the discussion is focused on the simplified case.

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Figure 2

The slide reachable range and the structure boundaries

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Figure 3

The polygon (triangle) formed by the linkage

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Figure 4

The void when rmax>rmid+rmin+Σ. The three cases correspond to the cases in Fig. 3.

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Figure 5

Grashof divisions of the slide reachable range

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Figure 6

Slide reachable range with Grashof divisions

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Figure 7

Characteristics charts for Class I and its subclasses

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Figure 8

Characteristics charts for Class II and its subclasses

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Figure 9

Characteristics charts for Class III-1

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Figure 10

Characteristics charts for Class III-2

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Figure 11

Characteristics charts for Class III-5

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Figure 12

Special configurations in the characteristics chart for Class I-1

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Figure 13

Four-bar linkage with one P joint. The dashed line is the slide track.

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Figure 14

Special characteristics charts of five-bar linkages

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Figure 15

N-bar linkage with adjoined P joints

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Figure 16

Scheme of an RRRPR-type adjustable mechanism

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Figure 17

The 4R-type planar open-chain manipulator

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Figure 18

Evolution from R joint to P joint

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Figure 19

Evolution from R joint to P joint in four-bar case

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Figure 20

Evolution from R joint to P joint in five-bar case




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