August 4, 2008 DETC2008-49040 (Wanner et al.) 1

Moving Pivot Specification for Three Precision Position Planar Linkage Synthesis

John T. Wanner

Northwestern University

Benjamin J. Fisher

XeteX Inc.

Thomas R. Chase

University of Minnesota

Andrew E. Sherman

Goodrich Corp.

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Motivation

graphical solution: analytical solution:Textbook Textbook

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Overview• Relation to existing solutions• Develop synthesis equations for dyads• Extension to triads & example:

Stephenson I vehicle suspension linkage

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Closely Related Solutions

• Graphical equivalent (textbooks): Hall (1961), Erdman et al. (2001), Norton (2004)– Complex # solution:

programmable, speed, accuracy

• Algebraic equivalent: Bawab and Thiruvenkatachari (1995)– Complex # solution: consistency with other complex #

solutions; direct solution for link rotations; expanded beyond 4-bars

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Loosely Related Solutions

• Ground pivot specification: Loerch et al. (1975), Suh & Radcliffe (1978)

• Hybrid complex # solution (specify angle of coupler at position 1 & angles of vectors locating ground pivots): Soni (1974)

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Basic Loop Equation

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Knowns vs. Unknowns

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Closing the Loop

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Locating the Ground Pivot

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Lower Link Angles

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Summary: 3PP Motion Gen, Moving Pivot Specification

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Application: Solar Vehicle Suspension Design

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Synthesis Strategy

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1. Set Wheel Travel

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2. Set Damper Motion

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JMTAD Vol 109 No 4 (1987)

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3. Synthesize Triad (Part 1)

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3. Synthesize Triad (Part 2)

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Suspension Final Solution

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Summary

• Solution of moving pivot specification for dyads at 3 prec pos using complex #’s

• Easily programmed• Speed & accuracy advantages over well known

graphical solutions• Easily extended to triads (for 6-bars & beyond)

using relative precision positions• Example: Solar vehicle Stephenson I 6-bar

suspension