Isometry in mechanism design

Abstract

Isometric designs are those that carry the same linear dimensions. Unique specification of the motion requirements of a mechanism between skew axes, with the help of a suitable set of conventions, removes all alternative designs isometric to the original mechanism, with one exception: an isometric design satisfying exactly the same motion requirements is available but with the algebraic sign of the axis distance changed. The transformation is one of reflection and is called an opposite isometry. Extending the use of unique specification of motion requirements to the special case of two-position design with identical specification of motion derivatives at the two positions (as in the case of a crank-rocker design), one is left with an alternative isometric design, without change of sign of axis distance. The device consists of a change of direction of motion of the mechanism, coupled with an interchange of mechanism positions that correspond to the two distinct positions on the curve of motion relationship. There is, in this case, what is called a direct isometry. The two transformations are shown to be useful: (i) in reducing the extent of design cataloguing, and (ii) in reducing the area of search for suitable mechanism designs. 1983.