Research Papers: Mechanisms and Robotics

On the Input Joint Rotation Space and Mobility of Linkages

[+] Author and Article Information
Kwun-Lon Ting

Center for Manufacturing Research, Tennessee Technological University, Cookeville, TN 38505kting@tntech.edu

J. Mech. Des 130(9), 092303 (Aug 11, 2008) (12 pages) doi:10.1115/1.2943299 History: Received August 28, 2007; Revised March 07, 2008; Published August 11, 2008

This paper presents the concept and application of input joint rotation space of linkages and offers updates on the N-bar rotatability laws. A thorough discussion on the joint rotation space of single-loop planar five-bar linkages is first presented. The concept is then extended to spherical linkages and the generalization to N-bar linkages is discussed. It offers a visualization tool for the input joint rotatability and fills up a void in the N-bar rotatability laws regarding the coordination among multiple inputs. It explains the formation of branches and how to establish a one-to-one correspondence between the inputs and the linkage configurations. The applications to multiloop linkages and spatial linkages are highlighted with Stephenson six-bar linkages, geared linkages, and spatial RCRCR mechanisms. These examples exhibit simplicity and benefits of the proposed concept to the mobility analysis of diversified mechanisms. The concept of virtual loop in spatial linkages is proposed and demonstrated with simple RCRCR and Stephenson six-bar mechanisms.

Copyright © 2008 by American Society of Mechanical Engineers
Topics: Linkages , Bifurcation
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Figure 1

Two branches of a three-bar chain and a four-bar chain

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Figure 2

Types of I∕O relationship of four-bar linkages: (a) CC-I, (b) CR-I, (c) RR-I, and (d) RR-II

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Figure 3

A five-bar chain

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Figure 4

JRS types of Class I five-bar linkages

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Figure 5

JRS types of Class II five-bar linkages

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Figure 6

Two two-side JRS sheets

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Figure 7

A linkage with non-neighboring input joints

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Figure 8

JRS of linkages (a,b,c,d,e) with non-neighboring input Joints (a) (3, 10, 4, 10, 12), (b) (3, 3, 5, 4, 2), (c) (4, 2, 3, 5, 7), and (d) (2, 3, 5, 9, 4)

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Figure 9

Linkage with a (a) CCC type JRS at Joints A, B, and C, and a (b) RRR-II type singular linkage

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Figure 10

A conversion of a supplemental linkage to the fundamental representation

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Figure 11

A Stephenson six-bar linkage and its JRS

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Figure 12

(a) A five-bar linkage; ((b) and (c)) gear constraints in JRS

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Figure 13

RCRCR: (a) dimension notations, (b) spherical indicatrix, and (c) analogy (S33=0) to a six-bar linkage

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Figure 14

Mobility of (a) a one-branch linkage and (b) a two-branch linkage



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