Copyright ©2011by Paul Niquette. All rights reserved.
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.
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of historical documents and engravings has been published by Project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.
Referring to the drawing below, we shall use Daniel's integer dimensions as follows:
Distance between supports (green) ~~~ 16