Pole arrangements that introduce prismatic joints into the design space of four- and five-position rigid-body synthesis

• Published in: Mechanism and machine theory Vol. 45; no. 9; pp. 1314 - 1325
• Main Authors: Myszka, David H., Murray, Andrew P.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01-09-2010; Elsevier
• Subjects: Actuation; Applied sciences; Center-point curves; Compatibility linkage; Devices; Drives; Exact sciences and technology; Infinity; Linkage mechanisms, cams; Mechanical engineering. Machine design; Planar synthesis; Poles; Positioning; Rigid-body guidance; Synthesis; Tasks; Planar synthesis; Rigid-body guidance; Center-point curves; Compatibility linkage; Guidance; Mechanism synthesis; Prismatic joint; Linkage mechanism; Compatibility; Revolute joint; Arrangement
• ISSN: 0094-114X; 1873-3999
• DOI: 10.1016/j.mechmachtheory.2010.04.001

Although a general five-position, rigid-body guidance problem admits a discrete number of revolute–revolute (RR) dyads, this paper identifies arrangements of five task positions that result in a center-point curve. For these special arrangements, a one-dimensional set of revolute-prismatic (RP) dyads exist to achieve the task positions. Other five-position arrangements are identified where a one-dimensional set of prismatic-revolute (PR) dyads exist to achieve the task positions. For a general case of five task positions, neither PR nor RP dyads are possible. In a general case of four-position rigid-body guidance problems, a unique PR dyad and RP dyad exist. Four-position arrangements are identified where the associated center-point curve includes the line at infinity and admits a PR dyad with a line of slide in any direction. Likewise, arrangements of the four positions are identified where the circle-point curve includes the line at infinity, permitting a one-dimensional set of RP dyads. These special four and five positions lead to dyads that can be coupled to solve a rigid-body guidance synthesis problem with a PRRP or RPPR device which is generally not possible. These solutions are particularly useful in design situations where actuation through a prismatic joint is desired.