Linear Linkage

Copyright 2011 by Paul Niquette All rights reserved.

 

hree lengths fully characterize the Linear Linkage puzzle:
Support Separation AB,
Long Link BC, and
Short Link AD = CF
For a theoretical case wherein the entire linkage were to be collapsed, BC = BE, such that AB + AD = BC.  The angles ABC = DAE = 0 for that case. 

As the Linear Linkage expands, the following trigonometric relationships will always apply:

BE = BC cos ABC + AD cos DAE

...and since AD = CF...

BE = BC cos ABC + CF cos DAE

...which keeps the point F at the same elevation as A for all positions of the linkage and solves the Linear Linkage puzzle...

Does it work?
 Yes.

ome solvers may be astonished to learn that the link-lengths do not matter -- that any number of Linear Linkages can be designed with no sliding elements.  Of course, there will be application-specific dimensions to consider for, say, optimizing the span ratio. 

One thought is that the Linear Linkage might play a role in deploying solar panels in space, as suggested by this photograph.  You are invited to send your ideas here

International Space Station's solar array panels are featured in this image 
photographed by the Expedition 17 crew in August 2008. Credit: NASA


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