1T2R Parallel Mechanisms Without Parasitic Motion

• Published in: IEEE transactions on robotics Vol. 26; no. 3; pp. 401 - 410
• Main Authors: Li, Qinchuan, Hervé, Jacques Marie
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01-06-2010; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Bifurcation; Bonding; Computer science; control theory; systems; Construction; Control theory. Systems; Correlation analysis; Cost function; Degrees of freedom; Drives; Exact sciences and technology; Fabrication; Geometry; Group theory; Kinematics; Limbs; Linkage mechanisms, cams; Machining; Magnetic heads; Mathematical analysis; Mechanical engineering. Machine design; Motion detection; Parallel robots; parasitic motion; Robot kinematics; Robotics; Rotational; Synthesis; Translations; type synthesis; parasitic motion; parallel robots; Engine idle; Mechanism synthesis; Type synthesis; Limb; Linkage mechanism; Group theory; Parallel mechanism
• ISSN: 1552-3098; 1941-0468
• DOI: 10.1109/TRO.2010.2047528

Parasitic motion is a major drawback of the general 1T2R parallel mechanism (PM), where T denotes a translation degree of freedom (DOF) and R a rotational DOF. This paper investigates the type synthesis of the 1T2R PM without parasitic motion. First, a brief review on the planar-spherical bond and its mechanical generators is presented. Then, the difference between the general and special a T b R motion is discussed. Relations between the parasitic motion and the general and special a T b R motion are revealed. An infinitesimal 1T2R PM with rotation bifurcation is presented as a special case. Further, the definition of the 1T2R PM without parasitic motion is presented, and the limb bond { {\bf G} ( {\bf u} )}{ {\bf S} ( N )} is identified. Geometrical conditions to construct an 1T2R PM without parasitic motion are presented, and nonoverconstrained 1T2R PMs without parasitic motion are synthesized. Idle pairs in the nonoverconstrained 1T2R PMs without parasitic motion are detected. Finally, overconstrained 1T2R PMs without parasitic motion are obtained by removing the idle pairs in the nonoverconstrained 1T2R PMs.