 ere
are a couple of ordinary household accessories, a desk lamp and a vanity
mirror. They are both designed to be wall-mounted and each features
a Linear Linkage that affords cantilevered
support plus convenient positioning at variable distances away from the
wall. Some solvers may observe another common attribute in
addition to the dozen hinges on scissors-like arms...
To maintain a vertical lamp or mirror while accommodating
extension along a horizontal straight line, each configuration must be
equipped with a sliding element at the base.
 
| Below on the left is another application of a similar
mechanism, this time designed for a child's protective gate, typically
mounted at the top of a flight of stairs. Again we see the equal
links and sliding elements -- in this case taking the form
of a telecoping handrail along the top. |
Below on the right is a sketch that applies a curious
array of links having more than one size. The mechanism accomplishes the
design objective of linear positioning with
sliding elements! That exclamation point recognizes a singular
historical significance.. |
 
 inear
mechanisms, which date back at least to Leonardo
da Vinci (1452-1519), have dominated the design of uncountable inventions,
reaching full flourish in the early 19th Century with the work of a most
gifted designer of mechanisms, James
Watt (1736-1819). For interested solvers, a magnificent collection
of historical documents and engravings has been published by Project
Gutenberg. Particular relevance to the Linear
Linkage puzzle will be found in Kinematics
of Mechanisms from the Time of Watt.
| The sketch above appeared in the January 1968 edition
of Product Engineering, where it was described as "straight-line
carrier device" patented by J. A. Daniel, Jr. of Newton, NJ. A certain
puzzler clipped the article, thinking that its analysis would make an interesting
challenge some day. More than 42 years went by... |
Referring to the drawing below, we shall use Daniel's
integer dimensions as follows:
Distance between supports
(green)
~~~ 16
Long link (red) ~~~~~~~~~~~~~~~~~
23
Short link (blue) ~~~~~~~~~~~~~~~~
9
GO TO SOLUTION PAGE
|