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Technical Briefs

The Synthesis of Dyads With One Prismatic Joint

[+] Author and Article Information
Chao Chen

Department of Mechanical Engineering, Monash University, 3800 Australiachao.chen@eng.monash.edu.ca

Shaoping Bai

Department of Mechanical Engineering, Aalborg University, DK-9220 Denmarkshb@ime.aau.dk

Jorge Angeles

Department of Mechanical Engineering, Centre for Intelligent Machines, McGill University, H3A 2K6 Canadaangeles@cim.mcgill.ca

Burmester: “Are there any points in a rigid body whose corresponding positions lie on a circle of the fixed plane for the four arbitrarily prescribed positions?” (1).

This idea was first put forth by Bottema and Roth (2).

One single vector uj would suffice. We take the mean value here in order to filter out roundoff-error.

http://www.cim.mcgill.ca/~rms1/Angeles_html/cden/

J. Mech. Des 130(3), 034501 (Feb 04, 2008) (6 pages) doi:10.1115/1.2829979 History: Received April 10, 2006; Revised October 29, 2007; Published February 04, 2008

The classic Burmester problem aims at finding the geometric parameters of a planar four-bar linkage for a prescribed set of finitely separated poses. The synthesis related to the Burmester problem deals with revolute-revolute (RR), prismatic-revolute (PR), and revolute-prismatic (RP) dyads. A PR dyad is a special case of the RR dyad, namely, a dyad of this kind with its fixed joint center at infinity; a similar interpretation applies to the RP dyad. The special nature of dyads with one P joint warrants a special treatment, outside of the general methods of four-bar linkage synthesis, which target mainly RR dyads. In proposing robust computational means to synthesize PR and RP dyads, we adopt an invariant formulation, which, additionally, sheds light on the underlying geometry.

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Copyright © 2008 by American Society of Mechanical Engineers
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References

Figures

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Figure 7

The linkage synthesized for the five prescribed poses

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Figure 8

(a) The linkage generated by solution 2 and (b) the linkage generated by solution 3

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Figure 9

Contours of center- and circlepoints of the RR dyad

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Figure 1

A four-bar linkage with revolute-revolute dyads

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Figure 2

Two finitely separated poses of a rigid body carried by the coupler link of a four-bar linkage

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Figure 3

Relation between the ith and jth poses and the circlepoints

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Figure 4

Four cubic centerpoint curves with their asymptotes parallel to each other

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Figure 5

Contour plots to determine the circlerpoint of a PR dyad: (a) the big picture; (b) a zoom-in around the common intersection of all circles

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Figure 6

Contour plots to find the centerpoint of a RR dyad

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