Transcript Moving Pivot Specification for Three Precision Position

Moving Pivot Specification for Three Precision Position
Planar Linkage Synthesis
John T. Wanner
Northwestern University
Andrew E. Sherman
Goodrich Corp.
Benjamin J. Fisher
XeteX Inc.
Thomas R. Chase
University of Minnesota
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Motivation
Textbook
graphical solution:
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Textbook
analytical solution:
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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
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