IDENTIFYING SETS OF FOUR AND FIVE POSITIONS THAT GENERATE DISTINCTIVE CENTER-POINT CURVES

The fixed pivots of a planar 4R linkage that can achieve four design positions are constrained to a center-point curve. The curve is a circular cubic function and plots can take one of five different forms. The center-point curve can be generated with a compatibility linkage obtained from an opposite pole quadrilateral of the four design positions. This paper presents a method to identify design positions that generate distinctive shapes of the center-point curves. The form of the center-point curve is dependent on whether the shape of the opposite pole quadrilateral is an open or closed form of a rhombus, kite, parallelogram, or when the sum of two sides equals the other two. Interesting cases of three and five position synthesis are also explored. Four and five position cases are generated that have center points at infinity allowing a PR dyad with line of slide in any direction to achieve the design positions. Further, a center-point curve for five specific design positions is revealed.Copyright © 2009 by ASME